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<DATE>2008-05-02</DATE>
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<NAME>John Pas</NAME>
<RESP>MURP</RESP>
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<STC T="W">M2741</STC>
<STC T="T">E652_16</STC>
<BIBNO T="umi">99863048</BIBNO>
<VID>115230</VID>
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<TEXT LANG="eng lat">
<FRONT>
<DIV1 TYPE="frontispiece">
<PB REF="1" MS="y">
<P><FIGURE>
<HEAD>HORO|LOGIOGRAPHIA OPTICA Dialing Universall and perticuler. <HI>Speculatiue and Practicall together with y^e di&s;cription of the</HI> Courte <HI>of</HI> Arts <HI>by a new Method</HI></HEAD>
<P>By Sylvanus Morgan</P>
<SIGNED>JJ. &s;culp</SIGNED>
</FIGURE></P>
</DIV1>
<DIV1 TYPE="title page">
<PB REF="2">
<PB REF="2" MS="y">
<P>Horologiographia Optica.</P>
<P>DIALLING Vniver&s;all and Particular: Speculative and Practicall.</P>
<P>In a threefold PRAECOGNITA, <HI>viz.</HI> Geometricall, Philo&s;ophicall, and A&s;tronomicall: and a threefold practi&s;e, <HI>viz.</HI> Arithmeticall, Geometricall, and In&s;trumentall. With diver&s;e Propo&s;itions of the u&s;e and benefit of &s;hadows, &s;erving to prick down the Signes, Declination, and Azimuths, on Sun-Dials, and diver&s;e other benefits.</P>
<P>Illu&s;trated by diver&s;e Opticall Conceits, taken out of <HI>Augilonius, Kercherius, Clavius,</HI> and others.</P>
<P><HI>LASTLY,</HI> TOPOTHESIA, OR, A feigned de&s;cription of the <HI>CO&V;RT OF ART.</HI></P>
<P>Full of benefit for the making of Dials, U&s;e of the Globes, Difference of Meridians, and mo&s;t Propo&s;itions of ASTRONOMIE.</P>
<P>Together with many u&s;efull In&s;truments and Dials in Bra&s;&s;e, made by <HI>Walter Hayes,</HI> at the Cro&s;&s;e Daggers in<HI>More Fields</HI> </P>
<P>Written by <HI>Silvanus Morgan.</HI></P>
<P>LONDON, Printed by <HI>R</HI> &amp; <HI>W. Leybourn,</HI> for <HI>Andrew Kemb,</HI> and <HI>Robert Boydell&punc;<GAP DESC="illegible" EXTENT="1 letter"></HI> and are to be &s;old at St <HI>Margarets</HI> Hill in <HI>Southwark,</HI> and at the Bulwark neer the Tower. 1657.</P>
</DIV1>
<DIV1 TYPE="dedication">
<PB REF="3">
<PB REF="3">
<HEAD><LIST>
<ITEM>TO WILLIAM BATEMAN, E&s;q^r^s.</ITEM>
<ITEM>TO ANTHONY BATEMAN, E&s;q^r^s.</ITEM>
<ITEM>TO THOMAS BATEMAN, E&s;q^r^s.</ITEM>
</LIST> Sons to the late Honourable THOMAS BATEMAN, <ABBR>E&s;q</ABBR> Chamberlain of <HI>LONDON,</HI> Decea&s;ed.</HEAD>
<OPENER><SALUTE>GENTLEMEN,</SALUTE></OPENER>
<P>_YOur late Father being a Patron of this Honourable City, doth not a little invite me to you, though young, yet to patroni&s;e no le&s;s then the a&s;piring of <HI>Coelum,</HI> which, as the Poets feign, was the anciente&s;t of the gods, and where you may &s;ee <HI>Sol</HI> only of the
<PB REF="4">
<HI>Titans,</HI> favouring <HI>Jupiters&punc;</HI> &s;igne, and by their power and operation hath e&s;tabli&s;hed Arts or Learning, the fable rather according to that e&s;tabli&s;hment which God hath given them, <HI>they are,</HI> I &s;ay, <HI>&s;ought out of tho&s;e that take their plea&s;ure therein:</HI> Pardon my boldne&s;s, I be&s;eech you, if like <HI>Promethe|us</HI> I have made a man of clay; and now come to light my bundle of twigs at the Chariot of the Sun, de&s;iring that you would infu&s;e vigor in that which cannot at all move of it &s;elf, &amp; if your benevolence &s;hall but &s;hine upon it, the angles of <HI>incidence &amp; reflection</HI> &s;hall be all one: your love invites me to be &s;o bold as to think you worthy of my labour, wherein, if faults &s;hall ari&s;e in the <HI>Cu&s;pis</HI> of the A&s;cen|dent, they &s;hall al&s;o have their fall upon my
<PB REF="4">
&s;elfe. And if any &s;hall be offended at this Worke, my device &s;hall be a Dyall with this Mottoe, <HI>A&s;picio ut a&s;piciar,</HI> only to all favourers of Art I am direct erect plaine, as I am, Gentlemen, to you, and de|&s;ire to be</P>
<CLOSER><SIGNED>Yours in the be&s;t of my &s;ervices, S. M.</SIGNED></CLOSER>
</DIV1>
<DIV1 TYPE="author to the reader">
<PB REF="5">
<HEAD>TO THE <HI>READER.</HI></HEAD>
<P>_REader, I here pre&s;ent thee with &s;ome Coele|&s;tiall operations drawn from the Macroco&s;|mall World, if I &s;hould tel you of plurality, it may &s;eem ab&s;urd, but I'le di&s;tingui&s;h the word.</P>
<P><HI>Mundus</HI> the World is &s;omtimes taken Archtypically, and &s;o is God, only in who&s;e divine minde is an example of all things.</P>
<P><HI>Mundus</HI> the World is &s;omtimes taken Angelicall, and this is the Hierarchicall government of Angels in Ceru|phins, Cherubins, and Thrones.</P>
<P><HI>Mundus</HI> the World is &s;omtimes taken elementary, and this is the Philo&s;ophers common place: the Salamander in Fire, the Birds in Air, the Fi&s;h in Water, and Men and Bea&s;ts on Earth.</P>
<P>Somtimes Macroco&s;mally, con&s;idering the whol Uni|ver&s;e, as well Aetheriall as Subterene, yea, and every Orb, and this is imaginarily &s;et down in the <HI>Praecognita A&s;tro|nomicall.</HI></P>
<P>Somtimes Microco&s;mally, as in the little World man,
<PB REF="5">
and this is de&s;cribed in the la&s;t Chapter of the <HI>Praecognita Philo&s;ophicall.</HI></P>
<P>Somtimes Typically, and that either Geographicall or Gnomonicall, or mentally in the minde of the workman.</P>
<P>Geographically in Maps or Globes, or Sphears in <HI>pla|no.</HI> Gnomonicall in this pre&s;ent Art of Dialling, of which it may be &s;aid that</P>
<LG>
<L>Umbra horas <HI>Phoebi</HI> de&s;ignat climate no&s;tro</L>
<L>Nodus, quod &s;ignum Sol tenet arte docet.</L>
</LG>
<P>And by which they mu&s;t nece&s;&s;arily trace out our times by the orbiculation of the Rady of the circle of the body of the Sunne.</P>
<P>Again, the World is mentally con&s;idered in the minde of an Arti&s;t, as in Painting, Graving, Carving, &amp;c. But having thus defined the word, you may think from hence that I am with <HI>Democrates Platoni&s;&s;ans,</HI> acquainting thee with infinity of Worlds, and in his words, <HI>Stanza</HI> 20.</P>
<LG>
<L>&mdash;&mdash;and</L>
<L>To &s;peake out though I dete&s;t the Sect</L>
<L>Of <HI>Epicurus</HI> for their manner vile.</L>
<L>Yet what is true I may not well neglect</L>
<L>Of truths incorruptible, ne can the &s;tile</L>
<L>Of vicious pen her &s;acred worth defile.</L>
<L>If we no more of truth &s;hould deign to &s;peak</L>
<L>Then what unworthy mouthes did never &s;oyle,</L>
<L>No truths at all mong&s;t men would finde a place</L>
<L>But make them &s;p&eacute;edy wings, &amp; back to heaven apace.</L>
</LG>
<P>How&s;oever thou ha&s;t here a field large enough to walke in, which if thou affect the light, thou may&s;t trace
<PB REF="6">
out the truth, and I pre&s;ume I have done that for thee who art a learner, the mo&s;t plain wayes that were ever publi&s;hed, and have &s;tudyed not to make it the Art of &s;hadows, &s;o much as the &s;hadow of that art who&s;e Gno|mons may be &s;aid to touch the Poles, and who&s;e planes may be &s;everall Plani&s;pheres, a Scale to the Geometrici|an, a Pole to the Navigator, a Chart to the Geographer, a Zodiaque to the A&s;tronomer, a Table of Hou&s;es to the A&s;trologian, the Meridian and Needle to the Surveyor, a Dyall to us all, to put us in minde of that pretious time which &s;aith to us <HI>Fugio, Fuge,</HI> and which time &s;hall be &s;wallowed up of Eternity, when there &s;hall be but one day without Tropicall di&s;tinctions, where thou &s;halt not need helps from any other, nor from me who am thine,</P>
<CLOSER><SIGNED>S. M.</SIGNED></CLOSER>
</DIV1>
<DIV1 LANG="lat" TYPE="poem">
<HEAD>In Solarium.</HEAD>
<LG>
<L>HIc tibi cum numero &s;pectantur Nodus &amp; umbra,</L>
<L>Quae tria quid doceant, commemor are libet</L>
<L>Umbra notat dextr&egrave; quota cur&s;itet hora dici,</L>
<L>Hinc&abque; monet vitam &s;ic properare tuam</L>
<L>A&s;t in quo &s;igno magni lux publica mundi</L>
<L>Ver&s;etur mira nodulus arte docet</L>
<L>Si vis &s;cire, dies quot quilibet occupet horas,</L>
<L>Id numerus media &s;ede locatus habet.</L>
</LG>
</DIV1>
<DIV1 TYPE="encomium">
<PB REF="6">
<HEAD>On my Friend M^r. <HI>Silvanus Morgan,</HI> his Book of <HI>Dialling.</HI></HEAD>
<LG>
<L>THe u&s;e of <HI>Dials</HI> all men under&s;tand;</L>
<L>To make them few: &amp; I am one of tho&s;e.</L>
<L>I am not of the <HI>Mathematick</HI> Band:</L>
<L>Nor know I more of <HI>Ver&s;,</HI> then <HI>Ver&s;</HI> from <HI>Pro&s;e.</HI></L>
<L>But though nor <HI>Dialli&s;t</HI> I am, nor <HI>Poet:</HI></L>
<L>I honour tho&s;e in either doe excell;</L>
<L>Our <HI>Author's</HI> skill'd in both alike, I know it,</L>
<L><HI>Shadows,</HI> and <HI>Sub&s;tance,</HI> here run parallel.</L>
<L>Con&s;ider then the pains the <HI>Author</HI> took,</L>
<L>And thank him, as thou benefit'&s;t by's <HI>Book.</HI></L>
</LG>
<CLOSER><SIGNED>Edward Barwick.</SIGNED></CLOSER>
</DIV1>
<DIV1 TYPE="encomium">
<PB REF="7">
<HEAD>On the Author and his Book.</HEAD>
<LG>
<L>DAres <HI>Zoil</HI> or <HI>Momus</HI> for to carp at thee,</L>
<L>And let &s;uch Ideots as &s;ome Authors be</L>
<L>Boldly to pro&s;ecute or take in hand</L>
<L>Such noble &s;ubjects they not under&s;tand,</L>
<L>Only for o&s;tentation, pride, or fame,</L>
<L>Or el&s;e becau&s;e they'd get them&s;elves a name,</L>
<L>Like that lewd fellow, who with hatefull ire,</L>
<L>Flinch'd not, but &s;et <HI>Diana's</HI> Court on fire:</L>
<L>His name will la&s;t and be in memory</L>
<L>From age to age&punc; although for infamie.</L>
<L>What more abiding Tombe can man invent</L>
<L>Then Books, which (if they'r good) are permanent</L>
<L>And monuments of fame, the which &s;hall la&s;t</L>
<L>Till the late evening of the World be pa&s;t:</L>
<L>But if erroneous, &s;ooth'd with vertues face,</L>
<L>Their Authors cridit's nothing but di&s;grace.</L>
<L>If I &s;hould prai&s;e thy Book it might be thought,</L>
<L>Friends will commend, although the work be nought,</L>
<L>But I'le forbeare, le&s;t that my Ver&s;es doe</L>
<L>Belie that prai&s;e that's only due to you.</L>
<L>Good Wiue requires no Bu&s;h, and Books will &s;peak</L>
<L>Their Authors credit, whether &s;trong or weak.</L>
</LG>
<CLOSER><SIGNED>W. Leybourn.</SIGNED></CLOSER>
</DIV1>
<DIV1 TYPE="errata">
<PB REF="7">
<HEAD>ERRATA.</HEAD>
<P><HI>REader,</HI> I having writ this &s;ome years &s;ince, while I was a childe in Art, and by this appear to be little more, for want of a review hath the&s;e faults, which I de&s;ire thee to mend with thy pen, and if there be any errour in <HI>Art,</HI> as in Chap. 17, which is only true at the time of the <HI>Equinoctiall,</HI> take that for an over&s;ight, and where thou finde&s;t <HI>equilibra</HI> read <HI>equilibrio,</HI> and in the dedication (in &s;ome Copies) read <HI>Robert Bateman</HI> for <HI>Thomas,</HI> and &s;ide for &s;igne, and know that <HI>Optima prima cadunt, pe&s;&s;imas aeve manent.</HI></P>
<P><TABLE>
<ROW>
<CELL><HI>pag.</HI></CELL>
<CELL><HI>line</HI></CELL>
<CELL><HI>Correct.</HI></CELL>
</ROW>
<ROW>
<CELL><GAP DESC="illegible" EXTENT="1 letter"></CELL>
<CELL>10</CELL>
<CELL>equall lines</CELL>
</ROW>
<ROW>
<CELL>18</CELL>
<CELL>16</CELL>
<CELL><HI>Galaxia</HI></CELL>
</ROW>
<ROW>
<CELL>21</CELL>
<CELL>1</CELL>
<CELL><HI>Galaxia</HI></CELL>
</ROW>
<ROW>
<CELL>21</CELL>
<CELL>8</CELL>
<CELL><HI>Mars&punc;</HI></CELL>
</ROW>
<ROW>
<CELL>24</CELL>
<CELL>12</CELL>
<CELL>Scheame</CELL>
</ROW>
<ROW>
<CELL>35</CELL>
<CELL>1</CELL>
<CELL>Hath</CELL>
</ROW>
<ROW>
<CELL>38</CELL>
<CELL>8</CELL>
<CELL>of the Tropicks &amp; polar Circles</CELL>
</ROW>
<ROW>
<CELL>40</CELL>
<CELL>22</CELL>
<CELL>AB is</CELL>
</ROW>
<ROW>
<CELL>44</CELL>
<CELL>31</CELL>
<CELL>Artificiall</CELL>
</ROW>
<ROW>
<CELL>46</CELL>
<CELL><HI>ult</HI></CELL>
<CELL><HI>heri</HI></CELL>
</ROW>
<ROW>
<CELL>49</CELL>
<CELL>4</CELL>
<CELL>forenoon</CELL>
</ROW>
<ROW>
<CELL>63</CELL>
<CELL>29</CELL>
<CELL>AB</CELL>
</ROW>
<ROW>
<CELL>65</CELL>
<CELL>11</CELL>
<CELL>6</CELL>
</ROW>
<ROW>
<CELL>80</CELL>
<CELL>16</CELL>
<CELL>BD</CELL>
</ROW>
<ROW>
<CELL>92</CELL>
<CELL>17</CELL>
<CELL>Arch CD</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL><HI>ult</HI></CELL>
<CELL>in &s;ome copies omit cen|ter</CELL>
</ROW>
<ROW>
<CELL>126</CELL>
<CELL>4</CELL>
<CELL>happen</CELL>
</ROW>
<ROW>
<CELL>126</CELL>
<CELL>6</CELL>
<CELL>tovvard B&punc;</CELL>
</ROW>
<ROW>
<CELL>127</CELL>
<CELL>26</CELL>
<CELL>before</CELL>
</ROW>
<ROW>
<CELL>126</CELL>
<CELL><HI>prop.</HI> 10&punc; for &s;ine read tang. elev.</CELL>
<CELL>&nbsp;</CELL>
</ROW>
</TABLE>
<LIST>
<ITEM><HI>Figure of the Dodicahedron fal&s;e cut</HI> pag. 4</ITEM>
<ITEM>LF <HI>omitted at end of Axis</HI>  25</ITEM>
<ITEM><HI>For</HI> A <HI>read</HI> D 26</ITEM>
<ITEM><HI>In the Ea&s;t and We&s;t Diall</HI> A <HI>omitted on the top of the middle line,</HI> C <HI>on the left hand,</HI> B <HI>on the right</HI> 55</ITEM>
<ITEM><HI>Small arch at</HI> B <HI>omitted in the fir&s;t polar plane</HI> 58</ITEM>
<ITEM><HI>For</HI> E <HI>read</HI> P <HI>on the &s;ide of the &s;hadowed line toward the left hand</HI> I <HI>omitted next to</HI> M, <HI>and</HI> L <HI>in the center omitted</HI> 81</ITEM>
<ITEM>K <HI>omitted in figure</HI> 85</ITEM>
<ITEM><HI>On the line</HI> FC <HI>for 01 read 6, for 2 read 12, line</HI> MO <HI>for 15 read</HI> 11 96</ITEM>
<ITEM><HI>A &s;mall arch omitted at</HI> E &amp; F, G &amp; H <HI>omitted at the ende of the line where 9 is</HI> 116</ITEM>
<ITEM>I &amp; L <HI>omitted on the little Epicicle.</HI> 122</ITEM>
</LIST></P>
</DIV1>
</FRONT>
<BODY>
<DIV1 TYPE="argument">
<PB REF="8">
<HEAD>THE ARGVMENT OF THE Praecognita Geometricall, and of the Work in generall.</HEAD>
<LG>
<L>_WHat &s;hall I doe? I &s;tand in doubt</L>
<L>To &s;hew thee to the light;</L>
<L>For <HI>Momus</HI> &s;till will have a flout,</L>
<L>And like a Satyre bite:</L>
<L>His Serpentarian tongue will &s;ting,</L>
<L>His tongue can be no &s;lander,</L>
<L>He's one to wards all that hath a fling</L>
<L>His fingers ends hath &s;can'd her.</L>
<L>But &s;eeing then his tongue can't hurt,</L>
<L>Fear not my little Book,</L>
<L>His &s;landers all la&s;t but a &s;purt,</L>
<L>And give him leave to look</L>
<L>And &s;can thee thorough, and if then</L>
<L>This <HI>Momus</HI> needs mu&s;t bite</L>
<L>At &s;hadows which dependant is</L>
<L>Only upon the light.</L>
<L>Withdraw thy light and be ob&s;cure.</L>
<L>And if he yet can &s;ee</L>
<L>Faults in the be&s;t that ever writ,</L>
<L>He mu&s;t finde fault with me.</L>
<L>How ere proceed in private and deline</L>
<L>The time of th' day as oft as &s;un &s;hall &s;hine:</L>
<L>And fir&s;t define a Praecognitiall part</L>
<L>Of magnitude, as u&s;efull to this art.</L>
</LG>
</DIV1>
<DIV1 TYPE="part">
<PB N="1" REF="8">
<HEAD>THE PRAECOGNITA GEOMETRICAL.</HEAD>
<P>_THe Arts, &s;aith <HI>Arnobius,</HI> are not together with our mindes, &s;ent out of the heavenly places, but all are found out on earth, and are in proce&s;&s;e of time, &s;oft and fair, forged by a continuall meditation; our poor and needy life perceiving &s;ome ca&s;ual things to happen pro|&s;perou&s;ly, while it doth imi|tate&punc; attempt and try, while it doth &s;lip, reform and change, hath out of the&s;e &s;ame a&s;&s;iduous apprehen&s;ions made up &s;mall Sciences of Art, the which afterwards, by &s;tudy, are brought to &s;ome perfection.</P>
<P>By which we &s;ee, that Arts are found out by daily
<PB N="2" REF="9">
practice, yet the practice of Art is not manife&s;t but by &s;pe|culative illu&s;tration, becau&s;e by &s;peculation: <HI>Scimus ut &s;cia|mus,</HI> we know that we may the better know: And for this cau&s;e I fir&s;t cho&s;e a &s;peculative part, that you might the better know the practice; and therefore have fir&s;t cho&s;e this &s;peculative part of practicall Geometry, which is a Science declaring the nature, quantity, and quality of Mag|nitude, which proceeds from the lea&s;t imaginable thing.</P>
<P>To begin then, <HI>A</HI> Point <HI>is an indivi&s;ible,</HI> yet is the fir&s;t of all dimen&s;ion; it is the Philo&s;ophers <HI>Atome,</HI> &s;uch a Nothing, as that it is the very <HI>Energie</HI> of all things, In God it carryeth its extreams from eternity to eternity: in the World it is the &s;ame which <HI>Mo&s;es</HI> calls the beginning, and is his <HI>Gene&s;is:</HI> 'tis the <HI>Clotho</HI> that gives <HI>Clio</HI> the mat|ter to work upon, and &s;pins it forth from <HI>terminus &agrave; quo,</HI> to <HI>terminus ad quem:</HI> in the Alphabet 'tis the <HI>Alpha,</HI> and is in the Cu&s;pe of the A&s;cendant in every Science, and the hou&s;e of Life in every operation. Again, a <HI>Point</HI> is either <HI>centricall</HI> or <HI>excentricall,</HI> both which are con&s;idered <HI>Geome|trically</HI> or <HI>Optically,</HI> that is, a <HI>point,</HI> or a &s;eeming <HI>point:</HI> a <HI>point</HI> Geometrically con&s;idered is indivi&s;ible, and being centrall is of magnitude without con&s;ideration of form, or of rotundity, with reference to Figure as a <HI>Circle,</HI> or a <HI>Globe,</HI> &amp;c. or of pondero&s;ity, with reference to weight, and &s;uch a point is in tho&s;e Balances which hang in <HI>equili|bra,</HI> yet have one beam longer than the other. If it be a &s;eeming <HI>point,</HI> it is increa&s;ed or dimini&s;hed Optically, that is, according to the di&s;tance of the object and &s;ubject. 'Tis the birth of any thing, and indeed is to be con&s;idered as our principall &s;ignificator, which being increa&s;ed doth produce quantity which is the required to Magnitude; for Magnitude is no other then a continuation of Quantity,
<PB N="3" REF="9">
which is either from a Line to a plain Superficies, or from a plain Superficies to a Solid Body: every of which are con&s;idered according to the quantity or form.</P>
<P>The quantity of a <HI>Line</HI> is length, without breadth or thickne&s;&s;e, the forme either right or curved.</P>
<P>The quantity of a <HI>Superficies</HI> con&s;i&s;teth in length and breadth, without thickne&s;&s;e, the form is divers, either regular or irregular; Regular are <HI>Triangles, Squares, Cir|cles, Pentagons, Hexagons, &amp;c.</HI></P>
<P><HI>An equilaterall Triangle</HI> con&s;i&s;teth of three right lines &amp; as many angles, his in&s;cribed &s;ide in a Circle contains 120 degrees.</P>
<P>A <HI>Square</HI> of four equall right lines, and as many right angles, and his in&s;cribed &s;ide is 90 degrees.</P>
<P>A <HI>Pentagon</HI> con&s;i&s;teth of five equall lines and angles, and his in&s;cribed &s;ide is 72 degrees of a Circle.</P>
<P>A <HI>Hexagon</HI> is of &s;ix equall lines and angles, and his &s;ide within a Circle is 60 degrees, which is equall to the <HI>Radius</HI> or Semidiameter.</P>
<P>An <HI>Angle</HI> is the meeting of two lines not in a &s;treight concurring, but which being extended will cro&s;&s;e each o|ther; but if they will never cro&s;&s;e, then they are parallel.</P>
<P>The quantity of an angle is the mea&s;ure of the part of a Circle divided into 360 degrees between the open ends, and the angle it &s;elf is the <HI>Center</HI> of the <HI>Circle.</HI></P>
<P>The quantity of a <HI>Solid</HI> con&s;i&s;ts of length, breadth, and thickne&s;s, the form is various, regular or irregular: The five regular or <HI>Platonick</HI> Bodies are, the <HI>Tetrahedron, Hexahedron, Octohedron, Dodecahedron, Ico&s;ahedron.</HI></P>
<P><HI>Tetrahedron</HI> is a Solid Body con&s;i&s;ting of four equall equilaterall Triangles.</P>
<P><FIGURE>
</FIGURE></P>
<P><PB N="4" REF="10">
<FIGURE>
</FIGURE></P>
<P>A <HI>Hexahedron</HI> is a Solid Bo|dy con&s;i&s;ting of &s;ix equal Squares, and is right angled every way.</P>
<P><FIGURE>
</FIGURE></P>
<P>An <HI>Octahedron</HI> is a Solid Body con&s;i&s;ting of eight equal Equilaterall Triangles.</P>
<P><FIGURE>
</FIGURE></P>
<P>A <HI>Dodecahedron</HI> is a Solid Body con&s;i&s;t|ing of 12 equall Pen|tagons.</P>
<P><FIGURE>
</FIGURE></P>
<P>An <HI>Ico&s;ahedron</HI> is a Solid Body con&s;i&s;ting of 20 equal Equilaterall Triangles: All which are here de&s;cribed in <HI>plano,</HI> by which they are made in pa&s;teboard: Or if you would cut them in Solid it is performed by Mr. <HI>Wells</HI> in his <HI>Art of Shadows,</HI> where al&s;o he hath fitted planes for the &s;ame Bodies.</P>
<P>A Parallel line is a line equidi&s;tant in all places from another line, which two lines can never meet.</P>
<P><PB N="5" REF="10">A Perpendicular is a line rightly elevated to another at right angles, and is thus erected.</P>
<P>Suppo&s;e AB be a line, and in the point A you would erect a perpendicular: &s;et one foot of your Compa&s;&s;es in A, extend the other upwards, anywhere, as at C, then keeping the foot fixed in C, remove that foot as was in A towards B, till it fall again in the line AB, then if you lay a Ruler by the feet of your Compa&s;&s;es, keep the foot fixed in C, and turn the other foot toward D by the &s;ide of the Ruler, and where that falls make a marke, from whence draw the line DA, which is perpendicular to AB. And &s;o much &s;hall &s;uffice for the <HI>Praecognita Geometricall,</HI> the Philo&s;ophicall followeth.</P>
<P><FIGURE>
</FIGURE></P>
<TRAILER>The end of the <HI>Praecognita Geometricall.</HI></TRAILER>
</DIV1>
<DIV1 TYPE="argument">
<PB REF="11">
<HEAD>THE ARGVMENT OF THE Praecognita Philo&s;ophicall.</HEAD>
<LG>
<L>_NOt to maintain with nice <HI>Philo&s;ophie,</HI></L>
<L>What unto rea&s;on &s;eems to be ob&s;cure,</L>
<L>Or &s;hew you things hid in ob&s;curity,</L>
<L>Who&s;e grounds are nothing &s;ure.</L>
</LG>
<LG>
<L>'Tis not the drift of this my BOOK,</L>
<L>The world in two to part,</L>
<L>Nor &s;hew you things whereon to looke</L>
<L>But what hath ground by <HI>Art.</HI></L>
</LG>
<LG>
<L>If Art confirm what here you read,</L>
<L>Sure you'l confirmed be,</L>
<L>If rea&s;on wonte demon&s;trate it,</L>
<L>Learn &s;omwhere el&s;e for me.</L>
</LG>
<LG>
<L>There's &s;hew'd to you what &s;hadow is,</L>
<L>And the Earths proper place,</L>
<L>How it the middle doth po&s;&s;e&s;&s;e,</L>
<L>And how heavens run their race.</L>
</LG>
<LG>
<L>Re&s;olving many a <HI>Propo&s;ition,</HI></L>
<L>Which are of u&s;e, and needfull to be known.</L>
</LG>
</DIV1>
<DIV1 TYPE="part">
<PB N="7" REF="11">
<HEAD>THE PRAECOGNITA PHILOSOPHICAL.</HEAD>
<DIV2 N="1" TYPE="chapter">
<HEAD>CHAP I.</HEAD>
<ARGUMENT>
<P>Of Light and Shadows.</P>
</ARGUMENT>
<P>_HE that &s;eeketh Shadow in its predicaments, &s;eeketh a reality in an imitation, he is rightly an&s;wered, <HI>umbram per &s;e in nullo praedicamento e&s;&s;e,</HI> the rea&s;on is thus rendred as hath been, it is not a reality, but a confu&s;ed imi|tation of a Body, ari&s;ing from the objecting of light,</P>
<P>So then there can be no other definition then this, Shadow is but the imitation of &s;ub|&s;tance, not incident to parts cau&s;ed by the interpo&s;ition of a &s;ub&s;tance, for, <HI>Umbra non pote&s;t agere &s;ine lumine.</HI> And</P>
<P><PB N="8" REF="12">And it is twofold, cau&s;ed by a twofold motion of light, that is, either from a direct beam of light, which is prima|ry, or from a &s;econdary, which is reflective: hence it is, that Sun Dials are made where the direct beams can never fall, as on the &s;eeling of a Chamber or the like.</P>
<P>But in vain man &s;eeketh after a &s;hadow, what then, &s;hall we proceed no farther? &s;urely not &s;o, for <HI>qui &s;emper e&s;t in &s;uo officio, is &s;emper orat,</HI> for there are no good and lawful actions but doe conde&s;cend to the glory of God, and e&s;pe|cially good and lawfull Arts.</P>
<P>And that &s;hadow may appear to be but dependant on light, it is thus proved, <HI>Quod e&s;t &amp; exi&s;tit in &s;e, id non ex|i&s;tit in alio:</HI> that which is, and &s;ub&s;i&s;teth in it &s;elfe, that &s;ub&s;i&s;teth not in another: but &s;hadow &s;ub&s;i&s;teth not in it &s;elfe, for take away the cau&s;e, that is light, and you take a|way the effect, that is &s;hadow.</P>
<P>Hence we al&s;o ob&s;erve the Sun to be the fountain of light, who&s;e daily and occurrent motions doth cau&s;e an ad|mirable lu&s;tre to the glory of God; &s;eeing that by him we mea&s;ure out our Times, Sea&s;ons, and Years.</P>
<P>Is it not his annuall revolution, or his proper motion that limits our Year?</P>
<P>Is it not his Tropicall di&s;tinctions that limits our Sea|&s;ons?</P>
<P>Is it not his Diurnall motion that limits out our Dayes and Houres?</P>
<P>And man truly, that arch type of perfection, hath limi|ted the&s;e motions even in the &s;mall type of a Dyall plane, as &s;hall be made manife&s;t in things of the &s;econd notion, that is, Demon&s;tration, by which all things &s;hall be made plain.</P>
</DIV2>
<DIV2 N="2" TYPE="chapter">
<PB N="9" REF="12">
<HEAD>CHAP II.</HEAD>
<ARGUMENT>
<P>Of the World, proving that the Earth po&s;&s;e&s;&s;eth its own proper place.</P>
</ARGUMENT>
<P>_WE have now with the Philo&s;opher, found out that common place, or place of being, that is, the World, will you know his rea&s;on? 'tis rendred, <HI>Quia omnia reliqua mundi corpora in &s;e includit.</HI></P>
<P>I'le tell you of no plurality, not of planetary inha|bitants, &s;uch as the Lunaries&punc; le&s;t you grabble in darkne&s;s, in expecting a &s;hadow from the light without interpo&s;ition, for can the light really without a &s;ub&s;tance be its own Gno|mon? &s;urely no, neither can we imagine our earth to be a changing Cynthia, or a Moon to give light to the Luna|ry inhabitants: For if our Earth be a light (as &s;ome would have it) how comes it to pa&s;&s;e that it is a Gnomon al&s;o to ca&s;t a &s;hadow on the body of the Moon far le&s;&s;e then it &s;elfe, and &s;o by con&s;equence a greater light cannot &s;eem to be darkned on a le&s;&s;er or duller light, and if not darkned, no &s;hadow can appear?</P>
<P>But from this common place the World with all its parts, &s;hall we de&s;cend to a &s;econd grade of di&s;tinction, and come now to another, which is a <HI>proprius locus,</HI> and divide it into proper places, con&s;idering it as it is divided into <HI>Coelum, Solum, Salum,</HI> Heaven, Earth, Sea, we need not &s;o far a di&s;tinction, but to prove that the earth is in its own proper place, I thus rea&s;on: <HI>Proprius locus e&s;t qui proxime nullo alio interveniente continet locatum:</HI> but it is certain that nothing can come &s;o between the earth as to
<PB N="10" REF="13">
di&s;po&s;&s;e&s;&s;e it of its place, therefore it po&s;&s;e&s;&s;eth its proper place, furthermore, <HI>ad quod aliquid movetur, id e&s;t ejus locus,</HI> to what any thing moves that is its place: but the earth moves not to any other place, as being &s;table in its own proper place.</P>
<P>And this proper place is the <HI>terminus ad quem,</HI> to which (as the place of their re&s;t) all heavie things tend, <HI>in quo mo|tus terminantur,</HI> in which their motion is ended.</P>
<P>Hence we rea&s;on, that a Mil-&s;tone, or any ponderous thing cannot pa&s;&s;e the center of the earth, becau&s;e the cen|ter of the earth is the farthe&s;t from the Heavens, for we all know that no man can di&s;po&s;e any heavie thing in the aire to re&s;t, neither can any one force a &s;tone to pa&s;&s;e through the earth if there were a way per&s;picu|ous, for ha|ving pa&s;&s;ed the center of the earth, 'tis as it were to throw a&s;tone upward which will a|gain return to its center. For example, &s;up|po&s;e the great Circle ABC D to be the co~. cave &s;uperficies of the Firma|ment, which all men know to compa&s;&s;e the earth on all
<FIGURE>
</FIGURE>
<PB N="11" REF="13">
&s;ides, and let the earth be the &s;maller Circle within that, the center whereof is E. Now if a line and plummet at A be let fall towards the earth it will tend in a right line towards E: al&s;o, if another plummet be let fall from B or any other place as C or D, that will fall al&s;o in a right line towards E, &s;o that they would all meet in the center E, which point they cannot pa&s;&s;e, for then they return as it were upward, and &s;o mu&s;t fall in the Skie or nowhere, contrary to all ponderous motions, whence is proved the earth to be the center of the World, and what manner of center &s;hall be &s;hewn in the next en&s;uing Chapter.</P>
</DIV2>
<DIV2 N="3" TYPE="chapter">
<HEAD>CHAP III.</HEAD>
<ARGUMENT>
<P>Shewing how the Earth is to be under&s;tood to be the Center.</P>
</ARGUMENT>
<P>_A Center is either to be under&s;tood Geometrically or Optically, either as it is a point, or &s;eeming a point.</P>
<P>If it be a point, it is conceived to be either a center of magnitude, or a center of pondero&s;ity, or a cen|ter of rotundity: if it be a &s;eeming point, that is increa&s;ed or dimini&s;hed according to the ocular a&s;pect, as being &s;om|time neerer, and &s;omtime farther from the thing in the vi|&s;uall line, the thing is made more or le&s;&s;e apparent.</P>
<P>A center of magnitude is an equal di&s;tribution from that point, an equality of di&s;tribution of the parts, giving to each end alike, and to each a like vicinity to that point or center.</P>
<P>A center of pondero&s;ity is &s;uch a point in which an un|equall thing hangs in <HI>equi libra,</HI> in an equall di&s;tribution
<PB N="12" REF="14">
of the weight, though one end be longer or bigger than the other of the quantity of the pondero&s;ity.</P>
<P>A center of rotundity is &s;uch a center as is the center of a Globe or Circle, being equally di&s;tant from all places.</P>
<P>Now the earth is to be under&s;tood to be &s;uch a center as the center of a Globe or Sphear, being equally di&s;tant from the concave &s;uperficies of the Firmament, neither is it to be under&s;tood to be a center as a point indivi&s;ible, but either comparatively or optically: comparatively in re&s;pect of the &s;uperior Orbs; Optically by rea&s;on of the far di|&s;tance of the one from the earth; as that the fixed Stars being far di&s;tant &s;eeme, by the weakne&s;&s;e of the &s;en&s;e, to be conceived as a center indivi&s;ible, when by the force and vi|gour of rea&s;on and demon&s;tration, they are found to ex|ceed this Globe of earth much in magnitude; &s;o that what our &s;en&s;e cannot apprehend, mu&s;t be comprehended by rea&s;on: As in the Circles of the Coele&s;tiall Orbs, becau&s;e they cannot be perceived by &s;en&s;e, yet mu&s;t nece&s;&s;arily be imagined to be &s;o. Whence it is ob&s;ervable, that all Sun Dials, though they &s;tand on the &s;urface of the earth, doe as truly &s;hew the houre as if they &s;tood in the center.</P>
</DIV2>
<DIV2 N="4" TYPE="chapter">
<HEAD>CHAP IV.</HEAD>
<ARGUMENT>
<P>Declaring what rea&s;on might move the Philo&s;ophers and others to think the Earth to be the center, and that the World moves on an axis, <HI>circa quem convertitur.</HI></P>
</ARGUMENT>
<P>_OCular ob&s;ervations are affirmative demon&s;trations, &s;o that what is made plain by &s;en&s;e is apparent to rea&s;on: hence it &s;o happeneth, that we imagine the Earth to move as it were on an axis, becau&s;e, both by ocular
<PB N="13" REF="14">
and In&s;trumentall ob&s;ervation, in re&s;pect that by the eye it is ob&s;erved that one place of the Skie is <HI>&s;emper apparens,</HI> neither making Co&s;micall, Haeliacall or Achronicall ri&s;ing or &s;etting, but &s;till remaining as a point, as it were, im|moveable, about which the whole heavens are turned. The&s;e yet are nece&s;&s;ary to be imagined for the better de|mon&s;tration of the ground of art; for all men know the heavens to be &s;upported only by the providence of God. Thus much for the rea&s;on &s;hewing why the World may be imagined to be turned on an Axis, the demon&s;tration proving that the earth is the center, is thus, not in main|taining unlikely arguments, but verity of ob&s;ervation; for all Gnomons ca&s;ting &s;hadow on the face of the earth, ca&s;t the like length or equality of &s;hadow, they making one &amp; the &s;ame angle with the earth, the Sun being at one and the &s;ame angle of height to al the Gnomons. As in example, let the earth be re|pre&s;ented by the &s;mall circle within the great circle, marked ABCD, and let a Gnomon &s;tand at E of the le&s;&s;er Circle, who&s;e horizon is the line AC, and let an other gnomon of the &s;ame length be &s;et at I, who&s;e horizon
<FIGURE>
</FIGURE>
<PB N="14" REF="15">
is repre&s;ented by the line BD, now if the Sun be at equall angles of height above the&s;e two Horizons, namely, at 60 degrees from C to G, and 60 from B to F, the Gnomons &s;hall give a like equality of &s;hadows, as in example is ma|nife&s;t. Now from the former appears that the earth is of no other form then round, el&s;e could it not give equality of &s;hadows, neither could it be the center to all the other in|ferior Orbs: For if you grant not the earth to be the mid|dle, this mu&s;t nece&s;&s;arily follow, that there is not equality of &s;hadow. For <HI>example,</HI> let the great Circle re|pre&s;ent the hea+vens, and the le&s;&s;e the earth out of the cen|ter of the grea|ter, now the Sunne being a|bove the Hori|zon AC 60 d. and a gnomon at E ca&s;ts his &s;hadow from E to F, and if the &s;ame gnomon of the &s;ame length doth &s;tand till the Sun come to the oppo&s;ite &s;ide of the Horizon AC, and the Sun being 60 degrees above that Horizon, ca&s;ts the &s;hadow from E to H, which are un|equall in length; the rea&s;on of which inequality proves that then it did not &s;tand in the center, and the equality of the other proves that it is in the center. Hence is al&s;o mo&s;t forceably proved that the earth is compleatly round in the re&s;pect of the heavens, as is &s;hewed by the equality
<FIGURE>
</FIGURE>
<PB N="15" REF="15">
of &s;hadows, for if it were not round, one and the &s;ame gnomon could not give one and the &s;ame &s;hadow, the earth being not compleatly round, as in the en&s;uing di&s;cour&s;e and demon&s;tration is more plainly handled and made manife&s;t.</P>
<P>And that the earth is round may appeare, fir&s;t, by the Eclip&s;es, when the &s;hadow of the earth appeareth on the body of the Moon, darkning it in whole or in part, and &s;uch is the body &s;uch is the &s;hadow. Again, it appears to be round by the orderly appearing of the Stars, for as men travell farther North or South they di&s;cover new Stars which they &s;aw not before, and lo&s;e the &s;ight of them they did &s;ee. As al&s;o by the ri&s;ing or &s;etting of the Sun or Stars, which appear not at the &s;ame time to all Countries, but by difference of Meridians, and by the different ob&s;ervations of Eclip&s;es, appearing &s;ooner to the Ea&s;terly Nations then tho&s;e that are farther We&s;t: Neither doe the tops of the highe&s;t hils, nor the &s;inking of the lowe&s;t valleys, though they may &s;eeme to make the earth un-even, yet compared with the whole greatne&s;&s;e, doe not at all hinder the round|ne&s;&s;e of it, and is no bigger then a point or pins head in compari&s;on of the highe&s;t heavens.</P>
<TRAILER>Thus having run over the <HI>Sy&s;teme</HI> of the greater <HI>WORLD,</HI> now let us &s;ay &s;omthing of the <HI>Compendium</HI> thereof, that is <HI>MAN.</HI></TRAILER>
</DIV2>
<DIV2 N="5" TYPE="chapter">
<PB N="16" REF="16">
<HEAD>CHAP V.</HEAD>
<ARGUMENT>
<P>Of Man, or the little World.</P>
</ARGUMENT>
<P>_MAn is the perfection of the Creation, the glory of the Creator, the compendium of the World, the Lord of the Creatures.</P>
<P>He is truly a Co&s;mus of beauty, who&s;e eye is the Sunne of his body, by which he beholds the never re&s;ting motions of the heavens, contem|platively to behold the place of motion; the place of his eternall re&s;t. <HI>Lord, what is man that thou &s;houlde&s;t be &s;o mindefull of him, or the &s;on of man that thou &s;o regarde&s;t him? thou ha&s;t made a World of wonder in his face.</HI> Thou ha&s;t made him to be a rationall creature, endowed&punc; him with rea&s;on, &s;o that his intellect becomes his <HI>Primum mobi|le,</HI> to &s;et his action at work, nevertheles, man neither moves nor reigns in him&s;elfe, and therefore not for him&s;elfe, but is born not to him&s;elfe, but for his Countrey; therefore he ought to employ him&s;elfe in &s;uch Arts as may be, and prove to be profitable for his Countrey.</P>
<LG>
<L>Man is the <HI>Atlas</HI> that &s;upports the Earth,</L>
<L>A perfect World, though in a &s;econd birth:</L>
<L>I know not which the compleat World to call,</L>
<L>The &s;en&s;le&s;&s;e World, or man the rationall:</L>
<L>One claims compleat in bigne&s;&s;e and in birth,</L>
<L>Saith &s;he's compleat, for man was la&s;t brought forth.</L>
<L>Man &s;peaks again, and &s;tands in his defence</L>
<L>Becau&s;e he's rationall, hath compleat &s;en&s;e.</L>
<L>Nature now &s;eeing them to di&s;agree,</L>
<L>Sought for a means that they united be:</L>
<L><PB N="17" REF="16">Concluded man, that he &s;hould guide the Sphears,</L>
<L>Limit their motion in Dayes, and Moneths, and Years:</L>
<L>He thinking now his Office not in vain,</L>
<L>Limits the Sun unto a Diall plain:</L>
<L>Girdles the World in Circles, Zones, and Climes,</L>
<L>To &s;hew his Art unto the after times.</L>
<L>Nature that made him thus compleat in all,</L>
<L>To plea&s;e him more, him <HI>Microco&s;mus</HI> call,</L>
<L>A little world, only in this re&s;pect</L>
<L>Of quantity, and not for his defect:</L>
<L>Pray, Gentle Reader, view but well their feature,</L>
<L>Which being done, pray tell me who's the greater?</L>
</LG>
<P><FIGURE>
</FIGURE></P>
<P>For he hath given me certain knowledge of the things that are, namely to know how the World was made, and the operations of the Elements, the beginning, ending, and mid&s;t of times, the alte|ration of the turning of the Sun, and the change of Sea&s;ons, the circuite of years and po&s;ition of Stars, <HI>Wi&s;d.</HI> 7. 17.</P>
<TRAILER>The ende of the Praecognita Philo&s;ophicall.</TRAILER>
</DIV2>
</DIV1>
<DIV1 TYPE="argument">
<PB REF="17">
<HEAD>THE ARGVMENT OF THE Praecognita A&s;tronomicall.</HEAD>
<LG>
<L>_YOu'r come to &s;ee a &s;ight, the World's the &s;tage,</L>
<L>Perhaps you'l &s;ayt's but a Star-gazing age,</L>
<L>What come you out to &s;ee? one u&s;e an In&s;trument?</L>
<L>Can &s;peculation yeild you &s;uch content?</L>
<L>That you can re&s;t in learning but the name</L>
<L>Of <HI>Pega&s;us,</HI> or of &s;wift <HI>Charle&s;es Wane?</HI></L>
<L>And would you learn to know how he doth move</L>
<L>About his axis, &s;et at work by Jove?</L>
<L>If you would learn the practice, read and then</L>
<L>I need not thus intreat you by my pen</L>
<L>To tread in Arts fair &s;teps, or to attain the way,</L>
<L>Go on, make ha&s;te, <HI>Relinquent</HI> do not &s;tay:</L>
<L>Or will you &s;cale Olympick hils &s;o high?</L>
<L>Be &s;ure you take fa&s;t hold, <HI>ASTRONOMIE:</HI></L>
<L>Then in that fair &s;pread Canopie no way</L>
<L>From thee is hid, no not <HI>Galezia.</HI></L>
<L><HI>They that de&s;cend the waters deepe doe &s;ee</HI></L>
<L><HI>Gods wonders in the deepe, and what they be:</HI></L>
<L>They that contemplate on the &s;tarry skie</L>
<L>Do &s;ee the works that he hath fram'd &s;o high.</L>
<L>Learn fir&s;t divi&s;ion of the World, and how</L>
<L>'Tis &s;eated, I doe come to &s;hew you now.</L>
</LG>
</DIV1>
<DIV1 TYPE="part">
<PB N="19" REF="17">
<HEAD>THE PRAECOGNITA ASTRONOMICAL.</HEAD>
<DIV2 N="1" TYPE="chapter">
<HEAD>CHAP I.</HEAD>
<ARGUMENT>
<P>Of the divi&s;ion of the World, by accidentall &s;cituation of the Circles.</P>
</ARGUMENT>
<P>_COSMUS, the World, is divided by <HI>Microco&s;mus</HI> the little World, into &s;ub&s;tantiall and imaginary parts: Now the &s;ub&s;tantiall are tho&s;e materiall parts or &s;ub&s;tance of which the World is compacted and made a Body, by the inter-folding of one Sphear within another, as is the Sphear of <HI>Saturn, Jupi|ter, Mars, Sol, &amp;c.</HI> And the&s;e of them&s;elves have a gentle and proper motion, but by violence of the fir&s;t mover,
<PB N="20" REF="18">
have a racked motion contrary to their own proper moti|on: whence it appears, that the motion of the heavens are two, one proper to the Sphears as they are different in them&s;elves, the other common to all.</P>
<LG>
<L>By <HI>Phebus</HI> motion plainly doth appear,</L>
<L>How many dayes doe con&s;titute one yeare.</L>
</LG>
<P>Will you know how many days doe con&s;titute a year, he telleth you who &s;aith,</P>
<LG>
<L>Ter centum ter viginti cum quinque diebus</L>
<L>Sex horas, neque plus integer Annus habet.</L>
</LG>
<LG>
<L>Three hundred &s;ixty five dayes, as appear,</L>
<L>With &s;ix houres added, make a compleat Year.</L>
</LG>
<P>The ju&s;t period of the Suns proper revolution.</P>
<Q>Perpetuus Solis di&s;tinguit tempora motus.</Q>
<P>The Imaginary part traced out by mans imagination, are Circles, &s;uch is the <HI>Horizon,</HI> the <HI>Equator,</HI> the <HI>Meridi|an,</HI> the&s;e Circles have of them&s;elves no proper motion, but by alteration of place have an accidentall divi&s;ion, di|viding the World into a right Sphear, cutting the paral|lels of the Sun equally or oblique, making unequall dayes and nights: whence two ob&s;ervations ari&s;e:</P>
<P>Fir&s;t, Where the parallels of the Sun are cut equally, there is al&s;o the dayes and nights equall.</P>
<P>Secondly, Where they are cut oblique, there al&s;o the dayes and nights are unequall.</P>
<P>The variety of the heavens are diver&s;ly divided into Sphears, or &s;everall Orbs, and as the Poets have found
<PB N="21" REF="18">
out a <HI>Galazia,</HI> the milkie way of <HI>Juno</HI> her bre&s;ts, or the way by which the gods goe to their Palaces, &s;o they will a&s;&s;igne to each Sphear his &s;everall god.</P>
<LIST>
<HEAD>Godde&s;&s;e of</HEAD>
<LABEL>Heralts.</LABEL>
<ITEM><HI>Caliope</HI> in the highe&s;t Sphears doth dwell,</ITEM>
<LABEL>A&s;trologie.</LABEL>
<ITEM>Among&s;t the Stars <HI>Urania</HI> doth excell,</ITEM>
<LABEL>Philo&s;ophie.</LABEL>
<ITEM><HI>Polimnia,</HI> the Sphear of <HI>Saturn</HI> guides,</ITEM>
<LABEL>Gladne&s;&s;e,</LABEL>
<ITEM><HI>Sterp&s;icore</HI> with <HI>Jupiter</HI> abides.</ITEM>
<LABEL>Hi&s;torie,</LABEL>
<ITEM>And <HI>Clio</HI> raigneth in mans fixed Sphear.</ITEM>
<LABEL>Tragedic.</LABEL>
<ITEM><HI>Melpomine</HI> guides him that gvids the year</ITEM>
<LABEL>Solace.</LABEL>
<ITEM>Yea, and <HI>Erata</HI> doth fair <HI>Venus</HI> &s;way.</ITEM>
<LABEL>Loud In&s;truments.</LABEL>
<ITEM><HI>Mercury</HI> his Orbe <HI>Euturpe</HI> doth obey.</ITEM>
<LABEL>Ditty.</LABEL>
<ITEM>And horned <HI>Cynthia</HI> is become the Court Of <HI>Thalia</HI> to &s;ing and laugh at &s;port.</ITEM>
</LIST>
<P>Where they take their places as they come in order.</P>
<P>The Sphear is &s;aid to be right where the Poles have no elevation, but lie in the Horizon, &s;o that to them the E|quinoctiall is in the Zenith, that is, the point ju&s;t over their heads.</P>
<P>The Sphear is oblique in regard of its accidentall divi|&s;ion, accidentally divided in regard of its orbicular form; orbicular in regard of its accidentall, equall variation orbi|cular, it appears before in the <HI>Praecognita Philo&s;ophicall,</HI> his equall variation is &s;een by the equall proportion of the earth an&s;wering to a Coele&s;tiall degree, for Circles are in proportion one to another, and parallel one to another are cut equally, &s;o is the earth to the heavens; having con&s;idered them as before, we will now con&s;ider another &s;ort of Sphear, which is called parallel.</P>
<P><PB N="22" REF="19">This parallel Sphear is &s;o that the parallels of the Sun are parallel to the Horizon, having the Poles in their Ze|nith, being the extream intemperate, colde, and frozen Zone: <HI>Ovid</HI> in his bani&s;hment complaines thus thereof.</P>
<LG>
<L>Hard is the fright in <HI>Scythia</HI> I &s;u&s;tain,</L>
<L>Over my head heavens Axis doth remain.</L>
</LG>
</DIV2>
<DIV2 N="2" TYPE="chapter">
<HEAD>CHAP II.</HEAD>
<ARGUMENT>
<P>Of the Circles of the Horizon, the Equator, and the Meridian.</P>
</ARGUMENT>
<P>_THe greate&s;t Circle of a Sphear is that which divides it in two equall parts, and that be|cau&s;e it cro&s;&s;eth diametrically, and the dia|meter is the longe&s;t line as can be &s;truck in a Circle, and therefore the greate&s;t, which great Circles are repre&s;ented in the follow|ing figure, repre&s;enting the Circles of a Sphear in an ob|lique Latitude, according to the Latitude or elevation of the Pole here at <HI>London,</HI> which is 51 <HI>deg. 32 min.</HI> being North Latitude, becau&s;e the North Pole is elevated.</P>
<P>The <HI>Horizon</HI> is a great Circle dividing the part of hea|uen &s;een, from where we imagine an Antipodes, the inha|bitants being to us an <HI>Antipheri&s;ta&s;in,</HI> our direct oppo&s;ites, &s;o that while the Sun continues vi&s;ible to us, it is above our Horizon, and &s;o continues day with us, while it is night with our oppo&s;ites; and when the Sun goes down with us it appears to them, making day with them while it remain|eth night with us, and according to the demon&s;tration, is expre&s;&s;ed by the greot Circle marked NSEW, &s;ignifying
<PB N="23" REF="19">
the Ea&s;t, We&s;t, North, and South parts of the Horizon. So now if you imagine a Circle to be drawn from the Suns leaving our &s;ight, through tho&s;e Azimuth points of heaven, then that Circle there imagined is the Horizon, and is accidentally divided as a man changes his place, and divides the World in a right or oblique Sphear.</P>
<P><FIGURE>
</FIGURE></P>
<P>The <HI>Meridian</HI> is a great Circle &s;cituated at right angles to the Horizon, equally pa&s;&s;ing between the Ea&s;t and We&s;t points, and con&s;equently running due North and South, and pa&s;&s;eth through the Poles of the World, being &s;ted|fa&s;tly fixed, it is repre&s;ented by the great Circle marked NDSC, and is accidentally divided, if we travell Ea&s;t
<PB N="24" REF="20">
or We&s;t, but in travailing North or South altereth not, &amp; when the Sun touches this Circle, it is then mid-day or Noon: Now if you imagine a Circle to pa&s;&s;e from the North to the South parts of the Horizon, through your Zenith, that Circle &s;o imagined is your Meridian, from which Meridian we account the di&s;tance of houres.</P>
<P>The Aequinoctiall likewi&s;e divides the World in two equall parts, cro&s;&s;ing at right angles between the two Poles, and is therefore di&s;tant from each Pole 90 degrees, and is elevated from the Horizon on the contrary &s;ide of the Poles elevation, &s;o much as the Pole wants of 90 deg. elevation, demon&s;trated in the Scene by the Circle pa&s;&s;ing from A to B, and is accidentally elevated with the Poles as we change our Horizon, and when the Sun touches this Circle, the dayes and nights are then equall, and to tho&s;e that live under this Citcle the dayes and nights hang in <HI>equilibra</HI> continually, and the Sun doth move every houre 15 degrees of this Circle, making the houre lines equall, pa&s;&s;ing 15 degrees in one houre, 30 degrees in two houres, 45 degrees in three houres, 60 degrees for four, and &s;o in|crea&s;ing 15 degrees as you increa&s;e in houres. This I note to the intent you may know my meaning at &s;uch time as I &s;hall have occa&s;ion ro mention the Aequinoctiall di&s;tances.</P>
<P>The Axis of the World is that which the Stile in every Diall repre&s;ents, being a line imaginary, &s;uppo&s;ed to pa&s;&s;e through the center of the World, from the South to the North part of the Meridian, who&s;e outmo&s;t ends are the Poles of the World, this becomes the Diameter, about which the World is imagined to be turned in a right Sphear having no elevation, in an oblique to be elevated above the Horizon and the angle at the center, numbred on the arch of the Meridian between the apparent Pole and the Hori|zon,
<PB N="25" REF="20">
is the elevation thereof, repre&s;ented by the &s;treight line pa&s;&s;ing from E to F, the arch EN being accounted the elevation thereof, which according to our demon&s;tration is the Latitude of <HI>London.</HI></P>
<P><FIGURE>
</FIGURE></P>
<P>The Stars that doe attend the Artick or North Pole, are the greater and le&s;&s;er Beare, the la&s;t &s;tar in the le&s;&s;er Bears tale is called the Pole Star, by rea&s;on of its neerne&s;s to it: this is the guide of Mariners, as appeareth by <HI>Ovid</HI> in his exile, thus</P>
<LG>
<L>You great and le&s;&s;er Bear who&s;e Stars doe guide</L>
<L><HI>Sydonian</HI> and <HI>Graecian</HI> &s;hips that glide</L>
</LG>
<LG>
<PB N="26" REF="21">
<L>Even you who&s;e Poles doe view this le&s;&s;er Ball,</L>
<L>Under the We&s;tern Sea neere &s;et at all.</L>
</LG>
<P>The &s;tars that attend the Southern Pole is the Cro&s;s, as is &s;een in the Globes.</P>
<LG>
<L>Lord be my Pole, make me thy Style, Lord then</L>
<L>Thy name &s;hall be my <HI>terminus ad quem.</HI></L>
</LG>
<P><HI>Video Coelos opera manuum tuarum, lunam &amp; &s;tellas que tu funda&s;ti.</HI></P>
</DIV2>
<DIV2 N="3" TYPE="chapter">
<HEAD>CHAP III.</HEAD>
<ARGUMENT>
<P>Of the &s;everall &s;orts of Planes, and how they are known.</P>
</ARGUMENT>
<P>_DYals are the dayes limiters, and the bounders of time, whereof there are three &s;orts: <HI>Hori|zontall, Erect, Inclining:</HI> Horizontall are al|wayes parallel to the Horizon: Erect, &s;ome are erect direct, others erect declining: Incli|ning al&s;o are direct or declining: for more explanation the figure following &s;hall give you better &s;atisfaction, where the Horizon marked with diver&s;e points of the Compa&s;&s;e &s;hall explain the demon&s;tration: Now if you imagine Cir|cles to pa&s;&s;e through the Zenith A, cro&s;&s;ing the Horizon in his oppo&s;ite points, as from SW through the verticall point A, pa&s;&s;ing to the oppo&s;ite point of South-we&s;t to North-Ea&s;t, tho&s;e, or the like circles, are called Azimuthes, parallel to which Azimuthes all erect Sciothericals doe &s;tand.</P>
<P><PB N="27" REF="21">Tho&s;e Planes that lie parallel to the Horizontall Circle are called Horizontall planes, and his Style makes an angle with the Pole equall to the elevation thereof; then the ele|vation of the Pole is the elevation of the Style.</P>
<P><FIGURE>
</FIGURE></P>
<P>Erect Verticals are &s;uch which make right angles with the Horizon, and lie parallel to the Verticall point, and the&s;e, as I told you before, were either direct or declining.</P>
<P>Direct are tho&s;e that &s;tand in a direct Azimuth, behold|ing one of the four Cardinall Quarters of the World, as either direct Ea&s;t, We&s;t, North, or South, marked with the&s;e letters NEWS, or declining from them to &s;ome other indirect Azimuth or &s;ide-lying points.</P>
<P><PB N="28" REF="22">Erect North and South are &s;uch as behold tho&s;e Quar|ters, and cuts the Meridian at right angles, &s;o that the planes cro&s;&s;e the Meridian due Ea&s;t and We&s;t, and the Poles are their Styles, equally elevated according to the aequino|ctiall altitude, being the complement of the Poles ele|vation. For in all North Faces, Planes, or Dials, the Style beholds the North Pole, and in all South faces, the Style beholds the South Pole: therefore, where the North Pole is elevated, there the North Pole mu&s;t be pointed out by the Style, and where the South Pole is elevated <HI>vice ver&s;a.</HI></P>
<P>The &s;econd &s;ort of Verticals are declining, which ate &s;uch that make an acute angle with the Quarter from which they decline; for an acute angle is le&s;&s;e then a right angle, and a right angle is 90 degrees: the&s;e declining Planes ly|ing in &s;ome accidentall Azimuthe.</P>
<P>For &s;uppo&s;ing a Diall to turn from the South or North towards the Ea&s;t or We&s;t, the Meridian line of the South declines Ea&s;tward, happening in the&s;e Azimuthes or be|tween them.</P>
<LIST>
<ITEM>South declining Ea&s;t</ITEM>
<ITEM>South declining We&s;t</ITEM>
<ITEM><P><TABLE>
<ROW>
<CELL>S by E</CELL>
<CELL>11</CELL>
<CELL>15</CELL>
<CELL ROWS="8">Or to the&s;e points of the We&s;t decli|ners, or be|tween them.</CELL>
<CELL>S by W</CELL>
<CELL>11</CELL>
<CELL>15</CELL>
</ROW>
<ROW>
<CELL>S S E</CELL>
<CELL>22</CELL>
<CELL>30</CELL>
<CELL>S S W</CELL>
<CELL>22</CELL>
<CELL>30</CELL>
</ROW>
<ROW>
<CELL>S E by S</CELL>
<CELL>33</CELL>
<CELL>45</CELL>
<CELL>S W by S</CELL>
<CELL>33</CELL>
<CELL>45</CELL>
</ROW>
<ROW>
<CELL>South-Ea&s;t</CELL>
<CELL>45</CELL>
<CELL>00</CELL>
<CELL>South We&s;t</CELL>
<CELL>45</CELL>
<CELL>00</CELL>
</ROW>
<ROW>
<CELL>S. E by E</CELL>
<CELL>56</CELL>
<CELL>15</CELL>
<CELL>S W by W</CELL>
<CELL>56</CELL>
<CELL>15</CELL>
</ROW>
<ROW>
<CELL>E S E</CELL>
<CELL>67</CELL>
<CELL>30</CELL>
<CELL>W S W</CELL>
<CELL>67</CELL>
<CELL>30</CELL>
</ROW>
<ROW>
<CELL>E by S</CELL>
<CELL>78</CELL>
<CELL>45</CELL>
<CELL>W by S</CELL>
<CELL>78</CELL>
<CELL>45</CELL>
</ROW>
<ROW>
<CELL>Ea&s;t</CELL>
<CELL>90</CELL>
<CELL>00</CELL>
<CELL>We&s;t.</CELL>
<CELL>90</CELL>
<CELL>00</CELL>
</ROW>
</TABLE></P></ITEM>
</LIST>
<P>Again, North decliners, declining toward the Ea&s;t and We&s;t, doe happen in the&s;e Azimuthes or between them.</P>
<LIST>
<PB N="29" REF="22">
<ITEM>North declining Ea&s;t</ITEM>
<ITEM>North declining We&s;t</ITEM>
<ITEM><P><TABLE>
<ROW>
<CELL>N by E</CELL>
<CELL>11</CELL>
<CELL>15</CELL>
<CELL ROWS="8">Or to the&s;e points of the We&s;t decli|ners, or be|tween them.</CELL>
<CELL>N by W</CELL>
<CELL>11</CELL>
<CELL>15</CELL>
</ROW>
<ROW>
<CELL>N N E</CELL>
<CELL>22</CELL>
<CELL>30</CELL>
<CELL>N N W</CELL>
<CELL>22</CELL>
<CELL>30</CELL>
</ROW>
<ROW>
<CELL>N E by N</CELL>
<CELL>33</CELL>
<CELL>45</CELL>
<CELL>N W by N</CELL>
<CELL>33</CELL>
<CELL>45</CELL>
</ROW>
<ROW>
<CELL>North-Ea&s;t</CELL>
<CELL>45</CELL>
<CELL>00</CELL>
<CELL>North We&s;t</CELL>
<CELL>45</CELL>
<CELL>00</CELL>
</ROW>
<ROW>
<CELL>N E by E</CELL>
<CELL>56</CELL>
<CELL>15</CELL>
<CELL>N W by W</CELL>
<CELL>56</CELL>
<CELL>15</CELL>
</ROW>
<ROW>
<CELL>E N E</CELL>
<CELL>67</CELL>
<CELL>30</CELL>
<CELL>W N W</CELL>
<CELL>67</CELL>
<CELL>30</CELL>
</ROW>
<ROW>
<CELL>E by N</CELL>
<CELL>78</CELL>
<CELL>45</CELL>
<CELL>W by N</CELL>
<CELL>78</CELL>
<CELL>45</CELL>
</ROW>
<ROW>
<CELL>Ea&s;t.</CELL>
<CELL>90</CELL>
<CELL>00</CELL>
<CELL>We&s;t.</CELL>
<CELL>90</CELL>
<CELL>00</CELL>
</ROW>
</TABLE></P></ITEM>
</LIST>
<P>By which it appeareth that every point of the Compa&s;&s;e is di&s;tant from the Meridian 11 degrees 15 minutes.</P>
<P>The third &s;ort of planes are inclining, or rather reclining, who&s;e upper face beholds the Zenith, and in that re&s;pect is called Reclining, but if a Diall be made on the nether &s;ide, and thereby re&s;pect the Horizon, it is then called an incliner, &s;o that the one is the oppo&s;ite to the other.</P>
<P>The&s;e planes are likewi&s;e accidentally divided, for they are either direct recliners, reclining from the direct points of Ea&s;t, We&s;t, North; and South, and in this &s;ort happens the direct Polar and Aequinoctiall planes, as infinite more according to the inclination or reclination of the plane, or they are as erect planes doe become declining recliners, which looke oblique to the Cardinall parts of the World, and obtu&s;ely to the parts they re&s;pect.</P>
<P>Suppo&s;e a plane to fall backward from the Zenith, and by con&s;equence it falls towards the Horizon; then that repre&s;ents a Reclining plane, &s;uch you &s;hall you &s;uppo&s;e the Aequinoctiall Circle in the figure to repre&s;ent, reclining from the North Southwards 51 degrees from the Zenith, or &s;uppo&s;e the Axis to repre&s;ent a plane lying parallel to it, which falls from the Zenith Northward reclining 38 de|grees, one being Aequinoctiall, the other a Polar plane.</P>
<P><PB N="30" REF="23">But for the inclining decliners you &s;hall know them thus, fora&s;much as the Horizon is the limiter of our &s;ight, and being cut at right angles repre&s;enteth the Ea&s;t, We&s;t, North, and South points, it may happen &s;o that a plane may lie between two of the&s;e quarters in an accidentall Azimuth, and &s;o not beholding one of the Cardinall Quar|ters is &s;aid to decline: Again, the &s;aid plain may happen not to &s;tand Verticall, which is either Inclining or Recli|ning, and &s;o are &s;aid to be Inclining Decliners: Fir&s;t, be|cau&s;e they make no right angle with the Cardinal Quarters: Secondly, becau&s;e they are not Verticall or upright.</P>
<P>There are other Polar planes, which lie parallel to the Poles under the Meridian, which may ju&s;tly be called Me|ridian plains, and the&s;e are erect direct Ea&s;t and We&s;t Dials, where the poles of the plane remain, which planes if they recline, are called Po&s;ition planes, cutting the Horizon in the North and South points, for Circles of po&s;ition are nothing but Circles cro&s;&s;ing the Horizon in tho&s;e points.</P>
</DIV2>
<DIV2 N="4" TYPE="chapter">
<HEAD>CHAP IV.</HEAD>
<ARGUMENT>
<P>Shewing the finding out of a Meridian Line after many wayes, and the Declination of a Plane.</P>
</ARGUMENT>
<P>_A Meridian Line is nothing el&s;e but a line who&s;e outmo&s;t ends point due North and South, and con&s;equently lying under the Meridian Circle, and the Sun comming to the Meridian doth then ca&s;t the &s;hadow of all things Northward in our Latitude;
<PB N="31" REF="23">
&s;o that a line drawn through the &s;hadow of any thing per|pendicularly erai&s;ed, the Sun being in the Meridian, that line &s;o drawn is a Meridian line, the u&s;e whereof is to place planes in a due &s;cituation to their points re&s;pective, as in the definition of this Circle I &s;hewed there was acci|dentall Meridians as many as can be imagined between place and place, which difference of Meridians is the Lon|gitude, or rather difference of Longitude, which is the &s;pace of two Meridians, which &s;hews why noon is &s;ooner to &s;ome then others.</P>
<P>The Meridian may be found divers wayes, as mo&s;t com|monly by the Mariners compa&s;&s;e, but by rea&s;on the needle hath a point attractive &s;ubject to errour, and &s;o overthrow|eth the labour, I cea&s;e to &s;peake any further.</P>
<P>It may be found in the night, for when the &s;tarre called <HI>Aliot,</HI> &s;eems to be over the Pole-&s;tarre, they are then true North, the manner of finding it, Mr. <HI>Fo&s;ter&punc;</HI> hath plainly laid down in his book of Dyalling, performed by a Qua|drant, which is the fourth part of a circle, being parted into 90 degrees.</P>
<P>It may al&s;o be fouhd as Ma&s;ter <HI>Blundevile</HI> in his Booke for the Sea teacheth, being indeed a thing very nece&s;&s;ary for the Sea, which way is thus: Strike a Circle on a plain Superficies, and rai&s;e a wire, or &s;uch like, in the center to ca&s;t a &s;hadow, then ob&s;erve in the forenoon when the &s;hadow is &s;o that it ju&s;t touches the circumference or edge of the Circle, and there make a mark; doe &s;o again in the afternoon, and at the edge where the &s;hadow goes out make another mark, between which two marks draw a line; which part in halfe, then from that middle point to the center draw a line which is a true Meridian.</P>
<P>Or thus, Draw a great many Circles concentricall one
<PB N="32" REF="24">
within another, then ob&s;erve by the Circles about noone when the Sun ca&s;ts the &s;horte&s;t &s;hadow, and that then &s;hall repre&s;ent a true Meridian, the rea&s;on why you mu&s;t ob&s;erve the length of the &s;hadow by circles &amp; not by lines is, becau&s;e if the Sun have not attained to the true Meridian it wil ca&s;t its &s;hadow from a line, and &s;o my eye may deceive me, when as by Circles the Sun ca&s;ting &s;hadow round about, &s;till meetes with one circumference or other, and &s;o we may ob&s;erve diligently. Secondly, it is proved that the &s;hadow in the Meridian is the &s;horte&s;t, becau&s;e the Sun is neere&s;t the Verticall point. Thirdly, it is proved that it is a true Meridian for this cau&s;e, the Sun, as all other Lumi|nous bodies, ca&s;ts his &s;hadow diametrically, and &s;o being in the South part ca&s;ts his &s;hadow northward, and is there|fore a true Meridian.</P>
<P>But now to finde the declination of a wall, if it be an erect wall draw a perpendicular line, but if it be a declining reclining plane, draw fir&s;t an horizontall line, and then draw a perpendicular to that, and in the perpendicular line &s;trike a Style or &s;mall Wyre to make right angles with the plane, then note when the &s;hadow of the Style falleth in one line with the perpendicular, and at that in&s;tant take the altitude of the Sun, and &s;o get the Azimuthe reckoned from the South, for that is the true declination of the wall from the South. The di&s;tance of the Azimuthes from the South, or other points, are mentioned in degrees and minutes in the third Chapter, in the definition of the &s;eve|rall &s;orts of planes: or by holding the &s;treight &s;ide of any thing again&s;t the wall, as is the long Square ABCD, who&s;e edge AB &s;uppo&s;e to be held to a wall, and &s;uppo&s;e again that you hold a thrid and plummet in your hand at E, the Sun &s;hining, and it ca&s;t &s;hadow the line EF, and at the
<PB N="33" REF="24">
&s;ame in&s;tant take the alti|tude of the Sun, thereby getting the Azimuthe as is taught following, then from the point F, as the center of the Horizon., and from the line FE, reckon the di&s;tance of the South, which &s;uppo&s;e I finde the Azimuthe to be 60 degrees from the Ea&s;t or We&s;t, by the propo&s;itions that are delivered in the end of this Booke, and becau&s;e there is a Quadrant of a Circle between the South, and the Ea&s;t or We&s;t points, I &s;ub&s;tract the di&s;tance of the Azimuthe from 90 degrees, and it &s;hall leave 30, which is the declination of the wall, equall to the angle EFG: but to finde the inclination or reclination, I &s;hall &s;hew when I come to the u&s;e of the Univer&s;all Qua|drant, or having fir&s;t found the Meridian line, you may prick down the Azimuthe.</P>
<P><FIGURE>
</FIGURE></P>
</DIV2>
<DIV2 N="5" TYPE="chapter">
<HEAD>CHAP V.</HEAD>
<ARGUMENT>
<P>Shewing what houre-lines may be drawn upon any Plane.</P>
</ARGUMENT>
<P>_LIght being the cau&s;e primary of &s;hadows, &s;ha|dows being but the imitation of the &s;econdary cau&s;e, that is &s;ub&s;tance, doth delineate unto us the pa&s;&s;ing away of time, by receiving light on the &s;ub&s;tance ca&s;ting &s;hadow.</P>
<P><PB N="34" REF="25">Neverthele&s;&s;e, &s;ub&s;tance receives not light, if either they want the immediate beame or reflecting light, which is the rea&s;on that &s;ome Dials are vacant of diver&s;e houres, or el&s;e are vacant for a certain Sea&s;on of the year, wherefore we will &s;hew &s;ome rea&s;ons why the Sun beams cannot be re|ceived
<FIGURE>
</FIGURE>
on diver&s;e planes, which is cau&s;ed by the acciden|tall &s;cituation thereof, which we will con&s;ider by this fi|gurative demon&s;tration, by the <HI>Analemma,</HI> de&s;cribed in Mr. <HI>Gunters</HI> Book.</P>
<P>The Sun, though he never moves from the line Eclip|tique wherein he hath his annuall or yearly motion, yet
<PB N="35" REF="25">
have a declination from the Aequinoctiall North or South, making his diurnall or daily motion, altering the dayes and nights according to all the diver&s;ities thereof: for the Sun being in the Aequinoctiall hath no declination, but in his diurnall motion &s;till declyning from the Aequinocti|all makes his progre&s;&s;e towards the North or South, de&s;cri|beth many parallel Circles, being parallel to the Aequino|ctiall, who&s;e farthe&s;t di&s;tance from either &s;ide is 23 deg. 30 minutes, &s;o that &s;o many degrees that the Sun is di&s;tant from the Aequinoctiall, &s;o much is its declination.</P>
<P>Now if you imagine the Circle before de&s;cribed to re|pre&s;ent the Meridian Circle which cro&s;&s;ed diametrically, which diameter &s;hall repre&s;ent the Aequinoctiall, then lay|ing down the greate&s;t declination, on either &s;ide of it, drawing two lines at that di&s;tance, on either &s;ide of the Aequinoctiall, parallel to it, repre&s;ent the Tropicks, the upper repre&s;enting the Tropick of Cancer, marked with GE, the other the Tropick of Capricorn, marked with HI: and if from each &s;everall degree you draw parallels too, they doe repre&s;ent the parallels of the Sun, which &s;hall &s;hew the diurnall motion of the Sun: now if you cro&s;&s;e the&s;e parallels with a line from E to H, that then repre&s;ents the Ecliptique; now if you cro&s;&s;e the Aequino-Ctiall at right angles with another line, that line repre&s;ents the Axis of the World: then if you lay down from the Poles the elevation thereof, to wit, the North and South Poles, according to the elevation of the North Pole down|ward, where the number of degrees end make a mark; then account the &s;ame elevation from the South Pole up|ward, and there al&s;o make a mark, from which two marks draw a right line, which &s;hall repre&s;ent your Horizon, and cuts the parallels of the Sun according to the time of his abiding above the Horizon.</P>
<P><PB N="36" REF="26">As in example, they that live under the Aequinoctiall have their dayes and nights equall, for under the Aequi|noctiall the Poles lie in the Horizon, and have no elevation, &s;o that you &s;ee the Axis AB cuts the Aequinoctiall at right
<FIGURE>
</FIGURE>
angles, and then mu&s;t needes cut the parallels of the Sun equall, &s;o that the continuing of the Sun above the Poles or Horizon, is equall to his continuance under the Poles or Horizon; &s;o that there is repre&s;ented a right Sphear where the dayes and nights are equall. But if the Pole hath ele|vation,
<PB N="37" REF="26">
as here at <HI>London,</HI> 51 degrees 30 minutes, then the Horizon is repre&s;ented by CD, where you &s;ee that then the horizon cuts the parallel of the Sun oblique, repre&s;ent|ing an oblique Sphear, &s;o that now the lines grow longer while the Sun declines in them towards the North pole A, then the day is repre&s;ented by the parallel EF, and the night by FG, when the Sun is in his greate&s;t North decl|nation, &s;o that you &s;ee that then in the night the Sun is no lower under the Horizon then from C to G, and then 'tis twi-light all night. Again, the Sun having his greate&s;t de|clination towards B the South Pole, then he continues but the arch ID above the Horizon, then the day is repre&s;ent|ed by KI: and the night by HK: Thus you &s;ee the rea&s;on of the dayes and nights inequality in an oblique Sphear, and equality in a right, you may likewi&s;e perceive by tho&s;e parallels, why the Sun cannot &s;hine on all Diall Planes, as we will now &s;hew.</P>
<P>Fir&s;t, An Ea&s;t and We&s;t Diall lies parallel to the Me|ridian, therefore the Sun in the Meridian cannot &s;hine on them; neverthele&s;&s;e, though an Ea&s;t and We&s;t Diall cannot have the houre of 12 on it, yet an Ea&s;t or We&s;t po&s;ition may, becau&s;e it cro&s;&s;eth the Horizon in the North and South.</P>
<P>Secondly, A direct North Diall can have but morning and evening houres on it, and then of no u&s;e but when the Sun hath North declination, for then his Amplitude or di&s;tance from the Ea&s;t and We&s;t is Northward, and &s;o at morning or night &s;hines on the face thereof.</P>
<P>Thirdly, A North reclining may &s;hew all the houres all the year, if it recline from the North Southward, the quantity of the complement of the lea&s;t Meridian altitude, but if but the complement of the elevation of the Aequi|noctiall,
<PB N="38" REF="27">
and &s;o become a Polar Plane, it can then but &s;hew while the Sun is in the North Signes, for the Dyall lying parallel to the Aequinoctiall while the Sun is in South de|clination cannot &s;hine on the plane becau&s;e it lies under.</P>
<P>All upright planes declining from the South may have the houre line of 12, &s;o al&s;o may all North decliners, but not in the Temperate Zone, which is contained between the degrees. South incliners al&s;o may have the line of 12, who&s;e upper face is not below the lea&s;t Meridian altitude, as al&s;o if greater then the greate&s;t Meridian altitude, then doth the upper face want it.</P>
<P>Fifthly, all North recliners reclining more then the great|e&s;t meridian altitudes complement, may have all the houres but will &s;hew but one part of the yeare.</P>
<P>Sixthly, All South declinets or recliners may have the line of 12 on them. And now having proceeded thus far in &s;ome theoricall demon&s;tration or grounds of Dials for the Geometricall projection, we will in the next Chapter lay down the theoricall demon&s;tration for the Arithmeticall Calculation, and &s;o proceed to our practicall way of opera|tion as en&s;ueth.</P>
</DIV2>
<DIV2 N="6" TYPE="chapter">
<HEAD>CHAP VI.</HEAD>
<ARGUMENT>
<P>Being the definition of the &s;everall lines of Sines, Tangents, and Secants, to be under&s;tood before we can come to Arithmeticall Calculation.</P>
</ARGUMENT>
<P>_THe Arithmeticall part for calculation is thus to be under&s;tood, there are certain right lines from e|very degree of a Quadrant, named by certain words of art, which for illu&s;tration we will con|&s;ider in their nomination and definition, who&s;e names are
<PB N="39" REF="27">
the&s;e, <HI>Sines, Tangents,</HI> and <HI>Secants,</HI> which have certain arches of degrees and minutes of a Quadrant an&s;wering thereto, and how&s;oever the Que&s;tion is propounded, are re&s;olved by the&s;e numbers as in the Golden Rule, by &s;till adding the &s;econd and third number together in &s;tead of Multiplication, and &s;ub&s;tracting the fir&s;t in&s;tead of Divi&s;i|on, doth leave the arch of the Que&s;tion as it was propoun|ded, which well con&s;idered, nothing &s;hall &s;eeme difficult.
<FIGURE>
</FIGURE>
A right Sine is halfe the &s;ubten&s;e of the double arch, which &s;ubten&s;es are repre&s;ented by the lines pa&s;&s;ing from D to D&punc; and from E to E, and from F to F, the halfe of which lines &s;ubtending the arches are the right Sines.</P>
<P>A Tangent is a right line without the peripherie to the extremity of the Secant to the Radius being perpendicu|lar erai&s;ed, &s;uch is repre&s;ented by the line BC.</P>
<P>A Secant is a right line drawn from the center through the circumference to the Tangent, &s;uch is repre&s;ented by the line AB, the Semidiameter of the &s;ame Circle is called the Radius.</P>
<P><PB N="40" REF="28">You may furthermore for very convenient u&s;es have tho&s;e lines placed on a Ruler, for if from one degree of one Quadrant of a Semicircle you draw lines to the &s;ame degree of the other Quadrant, cutting the line GA, that line &s;o cut &s;hall be a line of Sines, and if from the centre you draw lines to the Tangent line through every degree of the Quadrant, that line &s;o cut is a Tangent line, who&s;e u&s;e is mo&s;t exqui&s;ite and infinite for the &s;olution of many excel|lent propo&s;itions.</P>
</DIV2>
<DIV2 N="7" TYPE="chapter">
<HEAD>CHAP VII.</HEAD>
<ARGUMENT>
<P>Being the fundamentall Diagram for the Geometricall projection of Dials.</P>
</ARGUMENT>
<P>_THe Style being the repre&s;entation of the Axis of the World, doth become the Gnomon or &s;ub&s;tance ca&s;ting &s;hadow on all Planes lying parallel to &s;ome Circle or other, as to circles of Azimuthes in all Verticall Dials.</P>
<P>So that the figure following is a repre&s;entation of divers &s;emidiameters, doth plainly &s;hew the theoricall ground of the practick part hereof.</P>
<P>Where the line in the demon&s;tration, noted the &s;emidi|ameter of the Horizon, &s;ignifies the Horizon, for &s;o &s;up|po&s;ing it to repre&s;ent an Horizontall Diall, the &s;tyle or Axis mu&s;t be elevated above it, according to the Poles ele|vation above the Horizon, and then the &s;emidiameter or Axis of the World repre&s;ents the &s;tyle or Axis ca&s;ting &s;ha|dow being the line AC.</P>
<DIV3 TYPE="section">
<PB N="41" REF="28">
<HEAD>The Geometricall projection of Dials.</HEAD>
<P><FIGURE>
</FIGURE></P>
<P>Where note by the way, that if you &s;et one foot of the Compa&s;&s;es in B, and with the Semidiameter of the Equa|tor, fix the other foot in the line BC, keeping that la&s;t foot fa&s;t, and at that center draw a Quadrant divided into &s;ix parts, &amp; a ruler from the center of the Equator through each divi&s;ion, &s;hall divide the line AB as a contingent line, and if from C to the&s;e marks on the line AB you draw lines, it &s;hall be the houre lines of a Verticall Diall.</P>
<P>But &s;uppo&s;ing a Diall to &s;tand verticall, or upright to the Horizon AB, as the line BC, then that is repre&s;ented by the &s;emidiameter of the Verticall, and his &s;tyle again repre&s;ented by the &s;emidiameter or Axis AC, being di|&s;tant
<PB N="42" REF="29">
from the Verticall equall to the complement of the Poles elevation, and again, the Aequinoctiall cro&s;&s;ing the Axis at right angles, the &s;emidiameter thereof is repre&s;ent|ed by the line BD, the rea&s;on why the angle at A hath to his oppo&s;ite angle at C, the complement of the angle at A, is grounded on this, the three angles of any right lined triangle are equall to two right angles, and a right angle con&s;i&s;ts of 90 degrees: now the angle at B is 90 degrees, being one right angle, and the angle at A being an angle of 51 degrees, which wants of 90 39 degrees, which is the angle at C, all which being added together doe make 180 degrees, being two right angles: here you &s;ee that having two angles, the third is the complement of 180 degrees.</P>
</DIV3>
</DIV2>
<DIV2 N="8" TYPE="chapter">
<HEAD>CHAP VIII.</HEAD>
<ARGUMENT>
<P>Of the proportion of &s;hadows to their Bodies.</P>
</ARGUMENT>
<P>_SEeing the Zenith makes right angles with the Horizon, and a right angle con&s;i&s;teth of 90 degrees, the middle point betwixt both is 45 degrees, the Sun being at that height, the &s;hadow of all things perpen|dicularly rai&s;ed, are equal to their bodies, &s;o al&s;o is the Radius of a Circle equall to the Tangent of 45 degrees: and if the Sunne be lower then 45 degrees it mu&s;t nece&s;&s;ary follow the &s;hadow mu&s;t exceed the &s;ub&s;tance, becau&s;e the Sun is nigh the Horizon, and this is called the adver&s;e or contrary &s;hadow.</P>
<P>Contrarily, if the Sun exceed this middle point, the &s;ub&s;tance then exceeds the &s;hadow, becau&s;e the Sun is neerer
<PB N="43" REF="29">
the verticall point. Mr. <HI>Diggs</HI> in his <HI>Pantometria</HI> laying down the manifold u&s;es of his Quadrant Geometricall, doth there &s;hew, that having received the Sun beams through the Pinacides or Sights, that when the Suns alti|tude cuts the parts of right &s;hadow, then the &s;hadow ex|ceeds the &s;ub&s;tance erected ca&s;ting &s;hadow as 12 exceeds the parts cut: But in contrary &s;hadow contrary effects.</P>
</DIV2>
<DIV2 N="9" TYPE="chapter">
<HEAD>CHAP IX.</HEAD>
<ARGUMENT>
<P>To finde the Declination of the Sun.</P>
</ARGUMENT>
<P>_TO give you <HI>Orontius</HI> his words, it is con|venient to take the beginning from the greate&s;t obliquation of the Sun, becau&s;e on that almo&s;t the whole harmony of all A&s;tronomicall matters &s;eeme to depend, as &s;hall be manife&s;t from the di&s;cour&s;e of the &s;ucceeding Canons.</P>
<P>Wherefore prepare of commodious and elect &s;ub&s;tance, a Quadrant of a Circle parted into 90 equall parts, on who&s;e right angled Radius let be placed two pinacides or &s;ights to receive the beams of the Sun.</P>
<P>Then erect it toward the South in the time of the Sol&s;ti|cials, either in <HI>Cancer</HI> the highe&s;t annuall Almicanther, or in <HI>Capricorn</HI> the lowe&s;t annuall&punc; meridian altitude, al&s;o ob|&s;erve the equilibra, or equality of day and night in the time of the Aequinoctials, from the Meridian altitude thereof &s;ub&s;tract the lea&s;t Meridian altitude, which is, when the Sun enters in the fir&s;t minute of <HI>Capricorn,</HI> the remainer is the Declination, or &s;ub&s;tract the Aequinoctiall altitude from
<PB N="44" REF="30">
the greate&s;t Meridian altitude, the remainer is the Decli|nation of the greate&s;t obliquity of the Sun in the Zodiaque.</P>
<P>The height of the Sun is ob&s;erved by the Quadrant when the beames are received through the &s;ights by a plum|met proceeding from the center, noting the degree of alti|tude by the thrid falling thereon.</P>
<P>You may al&s;o take notice that for the continuall variati|on of the Suns greate&s;t declination it ought to be ob&s;erved by faithful In&s;truments: for as <HI>Orontius</HI> notes that <HI>Claudius, Ptolomie</HI> found it to be 23 degrees 51 minutes and 20 &s;e|conds, but in the time of <HI>Albatigine</HI> the &s;ame number of degrees yet but 35 minutes, <HI>Alcmeon</HI> found it of little le&s;&s;e, to wit 33 minutes, <HI>Purbachi</HI> and &s;ome of his Di&s;ciples doe affirme the &s;ame to be 23 degrees only 28 minutes, yet <HI>Jo|hanes Regiomontan.</HI> in the tables of Directions, hath alotted the minutes to be 30, but &s;ince <HI>Dominick Maria</HI> an Italian, and <HI>Johannes Varner</HI> of <HI>Norimburg</HI> te&s;tifie to have found it to be 29 minutes, to which ob&s;ervation our works doe ex|actly agree. Albeit all did ob&s;erve the &s;ame well neere by like In&s;truments, neverthele&s;&s;e, not ju&s;tly by exact con&s;tru|ction, or by in&s;ufficient dexterity of ob&s;ervation &s;ome &s;mall difference might happen, but not &s;o much as from <HI>Ptolo|mie</HI> to our time.</P>
<P>Having this greate&s;t Declination, to finde the pre&s;ent Declination is thus, by calculation: As the Radius, is to the Sine of the greate&s;t Declination; &s;o is the Sine of the Suns di&s;tance from the next Aequinoctiall point, that is <HI>Aries</HI> or <HI>Libra,</HI> to the declination required: wherefore in the Naturall Sines, as in the Rule of Proportion, multiply the &s;econd by the third, divide by the fir&s;t, the Quotient is the Sine of the Declination. Or by the naturall Sines, adde the &s;econd and third, and &s;ub&s;tract the fir&s;t, the remainer is the Sine of the pre&s;ent Declination.</P>
<P><PB N="45" REF="30">
<TABLE>
<ROW ROLE="label">
<CELL ROWS="2">Degre.</CELL>
<CELL>&Aries;</CELL>
<CELL>&Libra;</CELL>
<CELL>&Taurus;</CELL>
<CELL>&Scorp;</CELL>
<CELL>&Gemini;</CELL>
<CELL>&Sagitt;</CELL>
<CELL ROWS="2">Degre.</CELL>
</ROW>
<ROW ROLE="label">
<CELL>D</CELL>
<CELL>m</CELL>
<CELL>D</CELL>
<CELL>m</CELL>
<CELL>D</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL>11</CELL>
<CELL>29</CELL>
<CELL>20</CELL>
<CELL>10</CELL>
<CELL>30</CELL>
</ROW>
<ROW>
<CELL>1</CELL>
<CELL>0</CELL>
<CELL>24</CELL>
<CELL>11</CELL>
<CELL>50</CELL>
<CELL>20</CELL>
<CELL>23</CELL>
<CELL>29</CELL>
</ROW>
<ROW>
<CELL>2</CELL>
<CELL>0</CELL>
<CELL>47</CELL>
<CELL>12</CELL>
<CELL>11</CELL>
<CELL>20</CELL>
<CELL>35</CELL>
<CELL>28</CELL>
</ROW>
<ROW>
<CELL>3</CELL>
<CELL>1</CELL>
<CELL>11</CELL>
<CELL>12</CELL>
<CELL>31</CELL>
<CELL>20</CELL>
<CELL>47</CELL>
<CELL>27</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>1</CELL>
<CELL>35</CELL>
<CELL>12</CELL>
<CELL>52</CELL>
<CELL>20</CELL>
<CELL>58</CELL>
<CELL>26</CELL>
</ROW>
<ROW>
<CELL>5</CELL>
<CELL>1</CELL>
<CELL>59</CELL>
<CELL>13</CELL>
<CELL>12</CELL>
<CELL>21</CELL>
<CELL>9</CELL>
<CELL>25</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>2</CELL>
<CELL>23</CELL>
<CELL>13</CELL>
<CELL>32</CELL>
<CELL>21</CELL>
<CELL>20</CELL>
<CELL>24</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>2</CELL>
<CELL>47</CELL>
<CELL>13</CELL>
<CELL>52</CELL>
<CELL>21</CELL>
<CELL>30</CELL>
<CELL>23</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>3</CELL>
<CELL>10</CELL>
<CELL>14</CELL>
<CELL>11</CELL>
<CELL>21</CELL>
<CELL>40</CELL>
<CELL>22</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>3</CELL>
<CELL>34</CELL>
<CELL>14</CELL>
<CELL>30</CELL>
<CELL>21</CELL>
<CELL>49</CELL>
<CELL>21</CELL>
</ROW>
<ROW>
<CELL>10</CELL>
<CELL>3</CELL>
<CELL>58</CELL>
<CELL>14</CELL>
<CELL>50</CELL>
<CELL>21</CELL>
<CELL>58</CELL>
<CELL>20</CELL>
</ROW>
<ROW>
<CELL>11</CELL>
<CELL>4</CELL>
<CELL>21</CELL>
<CELL>15</CELL>
<CELL>8</CELL>
<CELL>22</CELL>
<CELL>7</CELL>
<CELL>19</CELL>
</ROW>
<ROW>
<CELL>12</CELL>
<CELL>4</CELL>
<CELL>45</CELL>
<CELL>15</CELL>
<CELL>27</CELL>
<CELL>22</CELL>
<CELL>15</CELL>
<CELL>18</CELL>
</ROW>
<ROW>
<CELL>13</CELL>
<CELL>5</CELL>
<CELL>8</CELL>
<CELL>15</CELL>
<CELL>45</CELL>
<CELL>22</CELL>
<CELL>23</CELL>
<CELL>17</CELL>
</ROW>
<ROW>
<CELL>14</CELL>
<CELL>5</CELL>
<CELL>31</CELL>
<CELL>16</CELL>
<CELL>3</CELL>
<CELL>22</CELL>
<CELL>30</CELL>
<CELL>16</CELL>
</ROW>
<ROW>
<CELL>15</CELL>
<CELL>5</CELL>
<CELL>55</CELL>
<CELL>16</CELL>
<CELL>21</CELL>
<CELL>22</CELL>
<CELL>37</CELL>
<CELL>15</CELL>
</ROW>
<ROW>
<CELL>16</CELL>
<CELL>6</CELL>
<CELL>18</CELL>
<CELL>16</CELL>
<CELL>38</CELL>
<CELL>22</CELL>
<CELL>43</CELL>
<CELL>14</CELL>
</ROW>
<ROW>
<CELL>17</CELL>
<CELL>6</CELL>
<CELL>41</CELL>
<CELL>16</CELL>
<CELL>56</CELL>
<CELL>22</CELL>
<CELL>50</CELL>
<CELL>13</CELL>
</ROW>
<ROW>
<CELL>18</CELL>
<CELL>7</CELL>
<CELL>4</CELL>
<CELL>17</CELL>
<CELL>12</CELL>
<CELL>22</CELL>
<CELL>55</CELL>
<CELL>12</CELL>
</ROW>
<ROW>
<CELL>19</CELL>
<CELL>7</CELL>
<CELL>27</CELL>
<CELL>17</CELL>
<CELL>29</CELL>
<CELL>23</CELL>
<CELL>0</CELL>
<CELL>11</CELL>
</ROW>
<ROW>
<CELL>20</CELL>
<CELL>7</CELL>
<CELL>49</CELL>
<CELL>17</CELL>
<CELL>45</CELL>
<CELL>23</CELL>
<CELL>5</CELL>
<CELL>10</CELL>
</ROW>
<ROW>
<CELL>21</CELL>
<CELL>8</CELL>
<CELL>12</CELL>
<CELL>18</CELL>
<CELL>1</CELL>
<CELL>23</CELL>
<CELL>9</CELL>
<CELL>9</CELL>
</ROW>
<ROW>
<CELL>22</CELL>
<CELL>8</CELL>
<CELL>34</CELL>
<CELL>18</CELL>
<CELL>17</CELL>
<CELL>23</CELL>
<CELL>13</CELL>
<CELL>8</CELL>
</ROW>
<ROW>
<CELL>23</CELL>
<CELL>8</CELL>
<CELL>57</CELL>
<CELL>18</CELL>
<CELL>32</CELL>
<CELL>23</CELL>
<CELL>17</CELL>
<CELL>7</CELL>
</ROW>
<ROW>
<CELL>24</CELL>
<CELL>9</CELL>
<CELL>19</CELL>
<CELL>18</CELL>
<CELL>47</CELL>
<CELL>23</CELL>
<CELL>20</CELL>
<CELL>6</CELL>
</ROW>
<ROW>
<CELL>25</CELL>
<CELL>9</CELL>
<CELL>41</CELL>
<CELL>19</CELL>
<CELL>2</CELL>
<CELL>23</CELL>
<CELL>22</CELL>
<CELL>5</CELL>
</ROW>
<ROW>
<CELL>26</CELL>
<CELL>10</CELL>
<CELL>3</CELL>
<CELL>19</CELL>
<CELL>16</CELL>
<CELL>23</CELL>
<CELL>24</CELL>
<CELL>4</CELL>
</ROW>
<ROW>
<CELL>27</CELL>
<CELL>10</CELL>
<CELL>25</CELL>
<CELL>19</CELL>
<CELL>30</CELL>
<CELL>23</CELL>
<CELL>26</CELL>
<CELL>3</CELL>
</ROW>
<ROW>
<CELL>28</CELL>
<CELL>10</CELL>
<CELL>46</CELL>
<CELL>19</CELL>
<CELL>44</CELL>
<CELL>23</CELL>
<CELL>27</CELL>
<CELL>2</CELL>
</ROW>
<ROW>
<CELL>29</CELL>
<CELL>11</CELL>
<CELL>8</CELL>
<CELL>19</CELL>
<CELL>57</CELL>
<CELL>23</CELL>
<CELL>27</CELL>
<CELL>1</CELL>
</ROW>
<ROW>
<CELL>30</CELL>
<CELL>11</CELL>
<CELL>29</CELL>
<CELL>20</CELL>
<CELL>10</CELL>
<CELL>23</CELL>
<CELL>28</CELL>
<CELL>0</CELL>
</ROW>
<ROW ROLE="label">
<CELL>De</CELL>
<CELL>&Pisces;</CELL>
<CELL>&Virgo;</CELL>
<CELL>&Aquar;</CELL>
<CELL>&Leo;</CELL>
<CELL>&Capri;</CELL>
<CELL>&Cancer;</CELL>
<CELL>De</CELL>
</ROW>
</TABLE></P>
<P>But I have here ad|ded a Table of Decli|nation of the part of the Ecliptique from the Aequinoctiall, the u&s;e whereof you may di&s;|cern is very plain, for if you finde the Signe on the top, and the de|grees downward, the common angle &s;hall be the Declination of the Sun that day. As if the Sun being in the 10 degree of <HI>Taurus</HI> or <HI>Scorpio,</HI> the declina|tion &s;hall bee 14 de|grees 50 minutes, and if you finde the Signe in the bottome, you &s;hall &s;eeke the degrees on the right hand up|ward, &s;o the 20 de|greee of <HI>Leo</HI> or <HI>Aqua|rius</HI> hath the &s;ame de|clination with the for|mer.</P>
<TRAILER>The ende of the Praecog|nita <HI>A&s;tronomicall.</HI></TRAILER>
</DIV2>
</DIV1>
<DIV1 TYPE="argument">
<PB REF="31">
<HEAD>THE ARGVMENT OF Practicall Sciothericy Optical.</HEAD>
<LG>
<L>_REader, read this, for I dare this defend,</L>
<L>Thy po&s;ting life on Dials doth depend,</L>
<L>Con&s;ider thou how quick the houre's gone,</L>
<L>Alive to day, to morrow life is done:</L>
<L>Then u&s;e thy time, and alwayes beare in minde,</L>
<L>Times hary forehead, yet he's ball'd behinde,</L>
<L>Here's that that will deline to thee and &s;hew</L>
<L>How quick time runs, how fa&s;t thy life doth goe:</L>
<L>Yet <HI>(fe&s;tina lente)</HI> learn the praecognit part,</L>
<L>And &s;o attain to practice of this art,</L>
<L>Whereby you &s;hall be able for to trace</L>
<L>Out &s;uch a path, where <HI>Sol</HI> &s;hall run his race,</L>
<L>And make the greater Co&s;mus to appear,</L>
<L>Delineating day and time of year.</L>
</LG>
<DIV2 TYPE="section">
<HEAD>Horologium Vitae.</HEAD>
<LG>
<L>Latus ad occa&s;um, nunquam rediturus ad ortum</L>
<L>Vivo hodie, moriar cras, here natus eram.</L>
</LG>
</DIV2>
</DIV1>
<DIV1 TYPE="part">
<PB N="47" REF="31">
<HEAD>HOROLOGIOGRAPHIA <HI>OPTICA.</HI></HEAD>
<DIV2 N="1" TYPE="chapter">
<HEAD>CHAP I.</HEAD>
<ARGUMENT>
<P>Shewing the making of an Horizontall plane to an Oblique Spheare.</P>
</ARGUMENT>
<P>_FRom the Theoricall Demon&s;tra|tion before, take the &s;emidia|meter of the Horizon with your Compa&s;&s;es, then draw the line AB, repre&s;enting the Meridian or line of 12, and &s;etting one foot in A, de&s;cribe the Qua|drant CAB, and CA mu&s;t be at right angles to AB, to which Quadrant draw the tangent line FA, which is the line of contingence, then take from the Theorical demon&s;tration the &s;emidiameter of the Aequator,
<PB N="48" REF="32">
and placing that on the line AB de&s;ctibe a quadrant touch|ing the line of contingence al&s;o within the other, repre&s;ent|ed by the Quadrant H <HI>e</HI> I which divide into 6 parts, and a Ruler laid to the center <HI>e,</HI> make marks where the Ruler toucheth the line of contingence, which mu&s;t be continued beyond F, that &s;o the houre lines may meet with the line BF, where it cro&s;&s;eth that line make marks: then remo|ving the Ruler to the center A of the horizontall Semi|circle, draw lines through each mark of the line of contin|gence which &s;hall be the houres, number the morning houres from the Meridian towards your left hand, and eve|ning or afternoon houres towards the right. The Style mu&s;t be an angle equall to the elevation of the Pole, the 12 houre mu&s;t lie under the Meridian Circle.</P>
<DIV3 TYPE="calculation">
<HEAD>The Arithmeticall Calculation.</HEAD>
<P>As the Radius, Is to the Tangent of the Aequinoctiall di&s;tance of the houre from the Meridian;</P>
<P>So is the Signe of the elevation of the Pole, To the Tangent of the houres di&s;tance from the Meridian.</P>
<P>The definition of the Aequinoctiall di&s;tance is in the de|finition of the Aequinoctiall Circle, <HI>Chap. 1. Praecognita A&s;tronomicall.</HI></P>
</DIV3>
<DIV3 TYPE="section">
<PB N="49" REF="32">
<HEAD>The figure of an Horizontall Diall, for the Latitude of <HI>London 51^d. 30^m.</HI></HEAD>
<P><FIGURE>
<HEAD>South</HEAD>
</FIGURE></P>
<P>The houres of the afternoon mu&s;t be the &s;ame di&s;tance from the Meridian, 1 and 11, 2 and 10, 3 and 9, and &s;o of the re&s;t, this is very plain, neither wants any expo&s;itor, only you may on the Horizontal plane, prick down beyond the houre of 6 a clock, the morning houres of 4 and 5, and the evening houres of 7 and 8, by rea&s;on that the Sun wil &s;hine on the Horizontall plane as &s;oone as it is above the Horizon.</P>
</DIV3>
<DIV3 TYPE="section">
<PB N="50" REF="33">
<HEAD>The figure of a South Verticall plane, for the Latitude of <HI>London,</HI> which is parallel to the Prime Verticall.</HEAD>
<P><FIGURE>
</FIGURE></P>
<P>The &s;emidiameter of the Verticall is but the Tangent of the elevation of the Pole to the Radius of the Hori|zon.</P>
<P>And the &s;emidiameter of the Horizon, the Tangent of the elevation of the Equator to the Radius of the Ver|ticall.</P>
</DIV3>
</DIV2>
<DIV2 N="2" TYPE="chapter">
<PB N="51" REF="33">
<HEAD>CHAP II.</HEAD>
<ARGUMENT>
<P>Shewing the making of a direct Verticall Diall for an Oblique Sphear, that is, a direct North or South Diall plane.</P>
</ARGUMENT>
<P>_EVery plane hath a Verticall point, and for the making of a Verticall Diall for the Latitude of <HI>London,</HI> out of the theoricall demon&s;trati|on <HI>Chap. 7. Praecog. A&s;tron&punc;</HI> take the &s;emidia|meter of the Verticall, and with that, as with the &s;emidiameter of the Horizon, de&s;cribe a Quadrant, &amp; draw the tangent line FG, and with the &s;emidiameter of the Aequator fini&s;h all as in the Horizontall: the Style mu&s;t proceed from the center A, and be elevated from the Meridian line AF, &s;o much as is the complement of the E|levation of the Pole, and mu&s;t point toward the invi&s;ible Pole, <HI>viz.</HI> the South Pole, and hath but 12 houres on it.</P>
<DIV3 TYPE="calculation">
<HEAD>The Arithmeticall Calculation.</HEAD>
<P>As the Radius,</P>
<P>Is to the tangent of the Aequinoctiall di&s;tance of the houre from the Meridian;</P>
<P>So is the Co-&s;ine, that is, the complement &s;ine of the elevation, to the tangent of the houre di&s;tance from the Me|ridian required.</P>
</DIV3>
</DIV2>
<DIV2 N="3" TYPE="chapter">
<PB N="52" REF="34">
<HEAD>CHAP III.</HEAD>
<ARGUMENT>
<P>Shewing the making of a direct North Verticall Diall for an Oblique Sphear, as al&s;o a more ea&s;ie way of drawing the South or Horizontall Planes.</P>
</ARGUMENT>
<P>_THe North Diall is but the back &s;ide of the South Diall; and differeth little from it, but in naming of the houres, for account|ing the &s;ixth houre from the Meridian in the direct South verticall, to be the &s;ame in the direct North Verticall, and account|ing the fir&s;t houres on the Ea&s;t &s;ide of the South, on the We&s;t &s;ide of the North plane, and &s;o <HI>vice ver&s;a,</HI> the fir&s;t houres on the We&s;t &s;ide of the South, on the Ea&s;t &s;ide of the North plane, as by the figure appeareth.</P>
<P>And becau&s;e the North Pole is elevated, the Style mu&s;t point up toward it the vi&s;ible Pole.</P>
<P>It mu&s;t have but the fir&s;t and la&s;t houres of the South plane, becau&s;e the Sun never &s;hines but at evening or morning on a North wall in an oblique Sphear, and but in Somer, becau&s;e then the Sun hath North Declination, but in a right Sphear, it may &s;hew all the houres as a South Di|all, but for a &s;ea&s;on of the yeare.</P>
<P>But if you will make the Verticall plane or Horizontall in a long angled Parallelogram, you &s;hall take the Secant of the elevation of the Pole, which is the &s;ame with AC in the fundamentall Diagram, and make that your Meridi|an line, and &s;hall take the Sine of the elevation of the Pole above the Meridian, which in a direct South or North is equall to the elevation of the Aequinoctiall, and in the Fun|damentall
<PB N="53" REF="34">
Diagram is the line DE, and prick it down from A and C at right angles with the line AC, and &s;o inclo&s;e the long &s;quare BADBCD, it &s;hall be the bou~ds of a direct North or South Diall; la&s;tly, if from the fundamental di|agram you prick down the &s;everal tangents of 15, 30 45, from Band D on the lines BB and DD, &amp; the &s;ame di&s;tances from C toward B and D, &amp; la&s;tly if from the cen|ter A, you draw lines to every one of tho&s;e marks, they &s;hall be the houre-lines of an erect direct South Diall.</P>
<P><FIGURE>
</FIGURE></P>
<P>To make an Horizontall Diall by the &s;ame projection you &s;hall take the Secant of 38 <HI>deg. 30 min.</HI> the elevation of the Equator, which in the fundamentall Scheme is the line AF, for the Meridian, and the Sine of the elevation of the Pole, which in the fundamentall diagram is the &s;ame with DA, and
<PB N="54" REF="35">
prick that down from the Meridian at right angles both wayes, as in the former planes, and &s;o proceed as before from the &s;ix of clock houre and the Meridian, with the &s;e|verall Tangents of 15, 30, 45, you &s;hall have con&s;tituted a Horizontall plane.</P>
<P>I have cau&s;ed the pricked line that goes cro&s;&s;e, and the other pricked lines which are above the houre line of &s;ix, to be drawn only to &s;ave the making of a figure for the North direct Diall, which is pre&s;ented to you if you turn the Book up&s;ide down, by this figure, contained between the figures of 4, 5, 6, the morning houres, and 6, 7, 8, the evening. And becau&s;e the North pole is elevated a|bove this plane 38 <HI>deg. 30 min.</HI> the Axis mu&s;t be from the center according to that elevation, pointing upward as the South doth downward, &s;o as A is the Zenith of the South, C mu&s;t be in the North.</P>
<P>The Arithmeticall calculation is the &s;ame with the for|mer, al&s;o a North plane may &s;hew all the houres of the South by con&s;ideration of reflection: For by Opticall de|mon&s;tration it is proved, that the angles of incidence is all one to that of reflection: if any be ignorant thereof, I pur|po&s;ely remit to teach it, to whet the ingenious Reader in labouring to finde it.</P>
<DIV3 TYPE="illustration">
<PB N="55" REF="35">
<HEAD>The Figure of a direct <HI>Ea&s;t</HI> and <HI>We&s;t</HI> Diall for the Latitude of <HI>London, &punc;51 deg. 30 min.</HI></HEAD>
<P><FIGURE>
<HEAD>Ea&s;t Diall. We&s;t Diall.</HEAD>
</FIGURE></P>
</DIV3>
</DIV2>
<DIV2 N="4" TYPE="chapter">
<PB N="56" REF="36">
<HEAD>CHAP IV.</HEAD>
<ARGUMENT>
<P>Shewing the making of the Prime Verticall planes, that is, a direct Ea&s;t or We&s;t Diall.</P>
</ARGUMENT>
<P>_FOr the effecting of this Diall, fir&s;t draw the line AD, on one end thereof draw the circle in the figure repre&s;enting the Equator; then draw two touch lines to the Equator, parallel to the line AD, the&s;e are they on which the houres are marked: divide the Equator in the lower &s;emi|circle in 12 equall parts, then apply a ruler to the center, through each part, and where it touches the lines of con|tingence make marks; from each touch point draw lines to the oppo&s;ite touch point, which are the parallels of the houres, and at the end of tho&s;e lines mark the Ea&s;terly houres from 6 to 11, and of the We&s;t from 1 to 6. The&s;e planes, as I told you, want the Meridian houre, becau&s;e it is parallel to the Meridian. Now for the placing of the Ea&s;t Diall, number the elevation of the Axis, to wit, the arch DC, from the line of the Equator, to wit, the line AD: and in the We&s;t Diall number the elevation to B; fa&s;ten a plummet and thrid in the center A, and hold it &s;o that the plummet may fall on the line AC for the Ea&s;t Diall, and AB for the We&s;t Diall, and then the line AD is parallel to the Equator, and the Dial in its right po&s;ition. And thus the We&s;t as well as Ea&s;t, for according to the &s;aying, <HI>Contrariorum eadem e&s;t doctrina,</HI> contraries have one manner of doctrine.</P>
<P>Here you may perceive the u&s;e of Tangent line, for it is evident that every houres di&s;tance is <GAP DESC="illegible" EXTENT="2 letters">t the Tangent of the Aequinoctiall di&s;tance.</P>
<DIV3 TYPE="calculation">
<PB N="57" REF="36">
<HEAD>The Arithmeticall Calculation.</HEAD>
<P>1 Having drawn a line for the houre of 6, whether Ea&s;t or We&s;t, As the tangent of the houre di&s;tance, is to the Radius, &s;o is the di&s;tance of the houre from 6, to the height of the Style.</P>
<P>2 As the Radius is to the height of the Style, &s;o is the tangent of the houre di&s;tance from 6, to the di&s;tance of the &s;ame houre from the &s;ub&s;tyle.</P>
<P>The &s;tyle mu&s;t be equall in height to the &s;emidiameter of the Equator, and fixed on the line of 6.</P>
</DIV3>
</DIV2>
<DIV2 N="5" TYPE="chapter">
<HEAD>CHAP V.</HEAD>
<ARGUMENT>
<P>Shewing the making a direct parallel Polar plane, or oppo&s;ite Aequinoctiall.</P>
</ARGUMENT>
<P>_I Call this a direct parallel Polar plane for this cau&s;e, becau&s;e all planes may be called by their &s;cituation of their Poles, and &s;o an Aequinoctiall parallel plane, may be called a Polar plane, becau&s;e the Poles thereof lie in the poles of the World.</P>
<P>For the projecting of the parallel polar plane, fir&s;t draw the horizontall line AB, then with Scale and Compa&s;&s;es protract an angle of 15 degrees, at each end cro&s;&s;ing as in the following figure: which cro&s;&s;ing is the center of the E|quator, and the lea&s;t di&s;tance between the horizontall line AB and the center of the Equator, is the &s;emidiameter of the Equator circle, then with the turning of the compa&s;&s;es one foot fixed in the center, de&s;cribe an ob&s;cure circle, at the length of the diameter of that circle, draw a parallel line
<PB N="58" REF="37">
<FIGURE>
</FIGURE>
to AB, which is CD, now for the houre di&s;tances, the Equator mu&s;t be divided into 24 parts, the houres of a na|turall day, for the performance of which, you &s;hall thus doe it ea&s;ilie. Fir&s;t, take the &s;emidiameter of the Equator with your Compa&s;&s;es, and place one foot, re&s;ting at that opening, in either the angle ABC or D, which in example is at B, then with the other foot de&s;cribe an arch from the horizontall line to the line BC, which is the &s;mall pricked arch EF, which is the 24 part of the Equator, which parts prick about the circle, numbring from the diameter 12 each way; then lay a ruler through each divi&s;ion and the center, and where it cro&s;&s;eth the horizontall lines AB and BC make marks, then from each oppo&s;ite marks draw lines pa|rallel to the diameter, which are the houre lines, as in the &s;econd figure.</P>
<P>The Gnomon mu&s;t be a quadrangled Parallelogram, who&s;e height is equall to the &s;emidiameter of the Equator, as in the Ea&s;t and We&s;t Dials, &s;o likewi&s;e the&s;e houres are Tangents to the Equator.</P>
<DIV3 TYPE="calculation">
<PB N="59" REF="37">
<HEAD>Arithmeticall calculation.</HEAD>
<P>Draw fir&s;t a line repre&s;enting the Meridian, or 12 a clock line, and another parallel to the &s;aid line for &s;ome houre which may have place on the line, &s;ay, As the tangent of that houre is to the Radius, &s;o is the di&s;tance of that houre from the Meridian to the height of the Style.</P>
<P>2 As the Radius is to the height of the &s;tyle, &s;o the tan|gent of any houre, to the di&s;tance of that houre from the Meridian.</P>
<P><FIGURE>
</FIGURE></P>
</DIV3>
</DIV2>
<DIV2 N="6" TYPE="chapter">
<HEAD>CHAP VI.</HEAD>
<ARGUMENT>
<P>Shewing the making of a direct oppo&s;ite polar plane, or parallel Aequinoctiall Diall.</P>
</ARGUMENT>
<P>_AN Aequinoctiall plane lyeth parallel to the Aequi|noctiall Circle, making an angle at the Horizon e|qual to the elevation of the &s;aid Circle: the poles of which plane lie in the poles of the world. The making of this plane requires little in&s;truction, for by drawing a
<PB N="60" REF="38">
Circle, and divide it into 24 parts the plane is prepared, all fixing a &s;tyle in the center at right angles to the plane.</P>
<P>As the Radins, is to the &s;ine of declination, &s;o is the co|tangent of the Poles height, to the tangent of the di&s;tance of the &s;ub-&s;tile from the Meridian.</P>
<P>If you draw lines from 7 to 5 on each &s;ide, tho&s;e lines &s;o cut &s;hall be the places of the houre lines of a parallel polar plane, now if you draw to each oppo&s;ite from the pricked lines, tho&s;e lines &s;hall be the houre lines of the for|mer plane.</P>
</DIV2>
<DIV2 N="7" TYPE="chapter">
<HEAD>CHAP VII.</HEAD>
<ARGUMENT>
<P>Shewing the making of an erect Verticall declining Diall.</P>
</ARGUMENT>
<P>_IF you will work by the fundamentall Diagram, you &s;hall fir&s;t draw a line, &s;uch is the line AB, repre&s;enting the Meridian, then &s;hall you take out of the fundamentall diagram the Secant of the Latitude, <HI>viz.</HI> AC, and prick it down from A to B, and at B you &s;hall draw a horizontall line at right angles, &s;uch is the line CD, then you &s;hall continue the line AB toward <HI>i,</HI> and from that line, and where the line AB cro&s;&s;eth in CD, de&s;cribe an arch equall to the angle of Declination toward F if it decline Ea&s;tward, and toward G if the plane decline We&s;tward. Then &s;hall you prick down on the line BF, if it bean Ea&s;terly declining plane, or from B to G if contrary; the Secant complement of the Latitude, <HI>viz.</HI> AG in the fundamentall Diagram, and the Sine of 51 degrees, <HI>viz.</HI> DA, which is all one with the &s;emidia|meter of the Equator, and therewithall prick it down at
<PB N="61" REF="38">
<FIGURE>
</FIGURE>
<PB N="62" REF="39">
right angles to the line of declination, <HI>viz.</HI> BF, from B to H and G, and from F towards K and L, then draw the long &s;quare KIKL, and from B toward H and G, prick down the &s;everall tangents of 15, 30, 45, and prick the &s;ame di|&s;tance from K and L towards H and G: la&s;tly, draw lines through each of tho&s;e points from F to the horizontall line CD, and where they end on that line to each point draw the houre lines from the point A, which plane in our ex|ample is a Verticall declining ea&s;tward&punc; 45 degrees, and it is fini&s;hed. But becau&s;e the contingent line will run out &s;o far before it be inter&s;ected, I &s;hall give you one following Ge|ometricall example to prick down a declining Diall in a right angled parallelogram.</P>
<P>Now for the Arithmeticall calculation, the fir&s;t opera|tion &s;hall be thus: <HI>As the Radius, to the co-tangent of the ele|vation, &s;o is the &s;ine of the declination, to the tangent of the &s;ub&s;tiles di&s;tance from the meridian of the place.</HI> then,</P>
<DIV3 N="2" TYPE="operation">
<HEAD>II Operation.</HEAD>
<P>Having the complement of the declination and elevation, finde the &s;tyles height above the &s;ub-&s;tile, thus,</P>
<P><HI>As the Radius, to the co-&s;ine of the declination, &s;o the co-&s;ine of the elevation, to the &s;ine of the &s;tyles height above the &s;ub|&s;tyle.</HI></P>
</DIV3>
<DIV3 N="3" TYPE="operation">
<HEAD>III Operation.</HEAD>
<P>As the &s;ine of elevation, is to the Radius, &s;o the tangent of declination, to the tangent of the inclination of the Meridi|an of the plane to the Meridian of the place.</P>
</DIV3>
<DIV3 N="4" TYPE="operation">
<HEAD>IV Operation.</HEAD>
<P>Having the &s;tyles height above the &s;ub&s;tyle, and the an|gle at the pole comprehended between the houre given and the meridian of the plane &s;ay.</P>
<P><HI>As the Radius, to the &s;ine of the &s;tyles height above the</HI>
<PB N="63" REF="39">
<HI>&s;ub&s;tyle; &s;o is the tangent of the angle at the pole, comprehen|ded between the houre given and the meridian of the plane, to the tangent of the houre di&s;tance from the &s;ub&s;tyle.</HI> Thus the Arithmeticall way being laid down, another Geometricall follows.</P>
<P>YOu &s;hall fir&s;t on the &s;emidiameter of the Horizon, <HI>viz.</HI> AB, de&s;cribe the arch BC the declination of the plane, and BD the complement of the elevation of the pole, then &s;hall you draw the lines AC and AD, and at B you &s;hall rai&s;e the perpendicular DCB.</P>
<P><FIGURE>
</FIGURE></P>
<P>Now if from the fun|damentall diagram, or from a Tangent who&s;e Radius or &s;emidiameter is equal to AB, you prick down the &s;everall Tan|gents of 15, 30, 45, which, as I often repeat, are the &s;everal Aequino|ctiall di&s;tances for the fir&s;t, &s;econd, or third houres from the Meridian or houre line of 6, and at each point rai&s;e perpendiculars to inter&s;ect the lines D and C, they &s;hall divide the line DC, &s;o as by making a Rombus of the lines AD, AC, they &s;hall be the parts to be pricked down from the Meridian and the houre line of 6. Now our example is a South declining Ea&s;tward 30 degrees, which is here propounded to be drawn: You &s;hall fir&s;t draw the perpendicular line and horizontall at right angles one to another, <HI>viz.</HI> the line A and CD. From any part of the line AB, as at E, number the declination of the
<PB N="64" REF="40">
<FIGURE>
<HEAD>The Figure of an upright plane declining from the South Ea&s;tward 30 degrees.</HEAD>
</FIGURE>
<PB N="65" REF="40">
plane, <HI>viz.</HI> the angle FEG, contained by the line EF, then if from the center G, where the Meridian and the Horizon|tall line cro&s;&s;e, you &s;hall again lay down the &s;ame angle to|ward the left hand, &s;uch is the line GH, which inter&s;ects the line EF in H, then &s;hall you take the length of the line HG, and prick it down from G to K, from whence you &s;hall number the elevation of the complement of the eleva|tion of the pole, <HI>viz.</HI> 38 deg. 30 min. and where that line inter&s;ects the Meridian, as at I, there &s;hall be the center of the houre lines, and the point through which from E to I the houre line of 9 mu&s;t pa&s;&s;e: then if you take the two lines divided by the tangent in the former operation, and prick the line AD from the center on the meridian, and the line AC, and prick it down on the &s;ix a clock line from I towards E and L, and la&s;tly, draw the oblique angled pa|rallelogram, and prick down the divided line AD on the two &s;ides, and the line AC from the Meridian both wayes, making marks, to which places, and from the center, draw the houre lines. Now for the placing of the &s;tyle you mu&s;t alwayes note that the &s;tyle is on the contrary &s;ide to that quarter where the plane declineth to, &amp; for the line of the &s;ub&punc; &s;tyle on which it mu&s;t &s;tand, number the length of the line IG, which is the di&s;tance of the center from the hori|zontall line, in as many equall parts as you plea&s;e, as into 5, and at the end thereof draw the line MN perpendicular, then take the di&s;tance between G and the foot of the &s;tyle, and prick down the &s;ame number of parts; &s;o if from the center you draw the line IM it &s;hall be the line of the &s;ub|&s;tyle, for the &s;ame proportion as IG to DG, the &s;ame pro|portion is IN to MN, <HI>as is manife&s;t by the fourth propo&s;ition of the 6 Book of Euclide.</HI> On the line of the &s;tyle IM, draw in any part the perpendicular OQ equal to the height
<PB N="66" REF="41">
of the &s;tyle NO, and to which point the line IQ being drawn, &s;hall be the axis of the world, then if from Q &s;hall be drawn the perpendicular QS, cutting the line of the &s;tyle IM in S, giveth the right line from E to S for the Aequinoctiall line, and &s;hall be perpendicular to IM if you have performed right. By this propo&s;ition which is laid down in <HI>Clavius</HI> his <HI>de&s;criptio Horologiorum,</HI> it is manife&s;t that if a &s;tyle had &s;tood in O, and the length of that &s;tyle had been pricked down perpendicular to the point O, as at H, and if from H we had laid down an angle equall to the complement of the declination of the wall, that line would inter&s;ect the horizontall line drawn at the foot of the &s;tyle at E, and if at R we rai&s;e a perpendicular, it &s;hall inter&s;ect the horizontall line at G, to which if I draw a perpendicu|lar it &s;hall be the meridian of the plane, and if I proceed as before, to finde the center of the houre lines which I found at I, it is manife&s;t that by this means is made a diall from any point a&s;&s;igned, which I leave to your own <HI>genius</HI> till &s;omthing more &s;hall be &s;poken and written of it by a more able pen.</P>
<P>Now good Reader, labour to under&s;tand my plaine meaning in this, labouring only not to confound thy me|mory or capacity, &amp; therefore give you al&s;o to under&s;tand that &s;uch are the houre di&s;tances of a We&s;terly declining plane, as are tho&s;e of an Ea&s;terly, only changing the &s;ide of the plane, and naming it by the complementall houres, the complemental houres I call tho&s;e that added together make 12, as followeth.</P>
<P><PB N="67" REF="41">
<TABLE>
<ROW>
<CELL ROWS="6">Forenoon houres of the declining Ea&s;t plane.</CELL>
<CELL>6</CELL>
<CELL ROWS="6">Complemen|tal houres are</CELL>
<CELL>6</CELL>
<CELL ROWS="6">are afternoon houres of a declining We&s;t plane.</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>5</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>4</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>3</CELL>
</ROW>
<ROW>
<CELL>10</CELL>
<CELL>2</CELL>
</ROW>
<ROW>
<CELL>11</CELL>
<CELL>1</CELL>
</ROW>
</TABLE></P>
<P>So that if the houres of the Ea&s;terly declining plane be 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, the houres of the We&s;terly decli|ning Diall is 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, &s;til keeping the &s;ame di&s;tances of the houre lines in one as the other, &s;o that if an Ea&s;terly declining be but turned the back &s;ide, it repre&s;ents a We&s;terly declining Dial as much, and the &s;tyle mu&s;t &s;tand over his &s;ub&s;tyle, and whereabouts the houre lines are clo|&s;e&s;t or neere&s;t together, thereabout is the &s;ub&s;tyle.</P>
<P>Now having &s;hewed you the making of all Horizontall and Verticall, whether direct or declining, Polar or Aequi|noctiall, I &s;hall proceed to &s;hew the projecting of tho&s;e which are oblique, whether declining reclining, or incli|ning, reclining, &amp;c. whereto, for the more ea&s;e, I have calculated to every degree of a Quadrant the houre arches of the Horizontall planes, from one degree of elevation till the Pole is in the Zenith. The Table and u&s;e followeth in &s;everall Chapters.</P>
<P><PB N="68" REF="42">
<TABLE>
<HEAD>Here followeth the Table of the arches of the houre lines di&s;tance from the Meridian in all Horizons, from one degree of ele|vation, till the Pole is elevated 30 degrees, by which is made all direct Murall, whether upright, or reclining Dials.</HEAD>
<ROW ROLE="label">
<CELL>&nbsp;</CELL>
<CELL COLS="2"><P>1</P> <P>11</P></CELL>
<CELL COLS="2"><P>2</P> <P>10</P></CELL>
<CELL COLS="2"><P>3</P> <P>9</P></CELL>
<CELL COLS="2"><P>4</P> <P>8</P></CELL>
<CELL COLS="2"><P>5</P> <P>7</P></CELL>
<CELL COLS="2"><P>6</P> <P>6</P></CELL>
</ROW>
<ROW>
<CELL ROLE="label">1</CELL>
<CELL>0</CELL>
<CELL>16</CELL>
<CELL>0</CELL>
<CELL>35</CELL>
<CELL>1</CELL>
<CELL>00</CELL>
<CELL>1</CELL>
<CELL>44</CELL>
<CELL>3</CELL>
<CELL>43</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">2</CELL>
<CELL>0</CELL>
<CELL>32</CELL>
<CELL>1</CELL>
<CELL>9</CELL>
<CELL>2</CELL>
<CELL>00</CELL>
<CELL>3</CELL>
<CELL>27</CELL>
<CELL>7</CELL>
<CELL>25</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">3</CELL>
<CELL>0</CELL>
<CELL>48</CELL>
<CELL>1</CELL>
<CELL>44</CELL>
<CELL>3</CELL>
<CELL>00</CELL>
<CELL>5</CELL>
<CELL>11</CELL>
<CELL>11</CELL>
<CELL>3</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">4</CELL>
<CELL>1</CELL>
<CELL>5</CELL>
<CELL>2</CELL>
<CELL>19</CELL>
<CELL>4</CELL>
<CELL>00</CELL>
<CELL>6</CELL>
<CELL>54</CELL>
<CELL>14</CELL>
<CELL>36</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">5</CELL>
<CELL>1</CELL>
<CELL>20</CELL>
<CELL>2</CELL>
<CELL>53</CELL>
<CELL>4</CELL>
<CELL>59</CELL>
<CELL>8</CELL>
<CELL>65</CELL>
<CELL>18</CELL>
<CELL>1</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">6</CELL>
<CELL>1</CELL>
<CELL>36</CELL>
<CELL>3</CELL>
<CELL>27</CELL>
<CELL>5</CELL>
<CELL>58</CELL>
<CELL>10</CELL>
<CELL>16</CELL>
<CELL>21</CELL>
<CELL>19</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">7</CELL>
<CELL>1</CELL>
<CELL>52</CELL>
<CELL>4</CELL>
<CELL>1</CELL>
<CELL>6</CELL>
<CELL>57</CELL>
<CELL>11</CELL>
<CELL>55</CELL>
<CELL>24</CELL>
<CELL>27</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">8</CELL>
<CELL>2</CELL>
<CELL>8</CELL>
<CELL>4</CELL>
<CELL>35</CELL>
<CELL>7</CELL>
<CELL>54</CELL>
<CELL>15</CELL>
<CELL>9</CELL>
<CELL>30</CELL>
<CELL>3</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">9</CELL>
<CELL>2</CELL>
<CELL>24</CELL>
<CELL>5</CELL>
<CELL>9</CELL>
<CELL>8</CELL>
<CELL>54</CELL>
<CELL>15</CELL>
<CELL>9</CELL>
<CELL>30</CELL>
<CELL>3</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>2</CELL>
<CELL>40</CELL>
<CELL>5</CELL>
<CELL>44</CELL>
<CELL>9</CELL>
<CELL>51</CELL>
<CELL>16</CELL>
<CELL>45</CELL>
<CELL>32</CELL>
<CELL>57</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">11</CELL>
<CELL>2</CELL>
<CELL>56</CELL>
<CELL>6</CELL>
<CELL>18</CELL>
<CELL>10</CELL>
<CELL>48</CELL>
<CELL>18</CELL>
<CELL>18</CELL>
<CELL>35</CELL>
<CELL>27</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">12</CELL>
<CELL>3</CELL>
<CELL>11</CELL>
<CELL>6</CELL>
<CELL>51</CELL>
<CELL>11</CELL>
<CELL>44</CELL>
<CELL>19</CELL>
<CELL>48</CELL>
<CELL>37</CELL>
<CELL>49</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">13</CELL>
<CELL>2</CELL>
<CELL>27</CELL>
<CELL>7</CELL>
<CELL>24</CELL>
<CELL>12</CELL>
<CELL>41</CELL>
<CELL>21</CELL>
<CELL>17</CELL>
<CELL>40</CELL>
<CELL>1</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">14</CELL>
<CELL>3</CELL>
<CELL>46</CELL>
<CELL>7</CELL>
<CELL>57</CELL>
<CELL>13</CELL>
<CELL>36</CELL>
<CELL>22</CELL>
<CELL>44</CELL>
<CELL>42</CELL>
<CELL>5</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">15</CELL>
<CELL>3</CELL>
<CELL>59</CELL>
<CELL>8</CELL>
<CELL>30</CELL>
<CELL>14</CELL>
<CELL>31</CELL>
<CELL>24</CELL>
<CELL>9</CELL>
<CELL>44</CELL>
<CELL>0</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">16</CELL>
<CELL>4</CELL>
<CELL>14</CELL>
<CELL>9</CELL>
<CELL>2</CELL>
<CELL>15</CELL>
<CELL>25</CELL>
<CELL>25</CELL>
<CELL>31</CELL>
<CELL>45</CELL>
<CELL>49</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">17</CELL>
<CELL>4</CELL>
<CELL>28</CELL>
<CELL>9</CELL>
<CELL>35</CELL>
<CELL>16</CELL>
<CELL>17</CELL>
<CELL>26</CELL>
<CELL>51</CELL>
<CELL>47</CELL>
<CELL>30</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">18</CELL>
<CELL>4</CELL>
<CELL>44</CELL>
<CELL>10</CELL>
<CELL>7</CELL>
<CELL>17</CELL>
<CELL>10</CELL>
<CELL>28</CELL>
<CELL>9</CELL>
<CELL>49</CELL>
<CELL>4</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">19</CELL>
<CELL>5</CELL>
<CELL>15</CELL>
<CELL>11</CELL>
<CELL>10</CELL>
<CELL>18</CELL>
<CELL>53</CELL>
<CELL>30</CELL>
<CELL>39</CELL>
<CELL>51</CELL>
<CELL>55</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>5</CELL>
<CELL>15</CELL>
<CELL>11</CELL>
<CELL>10</CELL>
<CELL>18</CELL>
<CELL>53</CELL>
<CELL>30</CELL>
<CELL>39</CELL>
<CELL>51</CELL>
<CELL>55</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">21</CELL>
<CELL>5</CELL>
<CELL>29</CELL>
<CELL>11</CELL>
<CELL>41</CELL>
<CELL>19</CELL>
<CELL>43</CELL>
<CELL>31</CELL>
<CELL>50</CELL>
<CELL>53</CELL>
<CELL>13</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">22</CELL>
<CELL>5</CELL>
<CELL>44</CELL>
<CELL>12</CELL>
<CELL>13</CELL>
<CELL>21</CELL>
<CELL>20</CELL>
<CELL>34</CELL>
<CELL>5</CELL>
<CELL>55</CELL>
<CELL>34</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">23</CELL>
<CELL>5</CELL>
<CELL>58</CELL>
<CELL>12</CELL>
<CELL>43</CELL>
<CELL>21</CELL>
<CELL>20</CELL>
<CELL>34</CELL>
<CELL>5</CELL>
<CELL>55</CELL>
<CELL>34</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">24</CELL>
<CELL>6</CELL>
<CELL>13</CELL>
<CELL>13</CELL>
<CELL>13</CELL>
<CELL>22</CELL>
<CELL>8</CELL>
<CELL>35</CELL>
<CELL>10</CELL>
<CELL>56</CELL>
<CELL>37</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">25</CELL>
<CELL>6</CELL>
<CELL>28</CELL>
<CELL>13</CELL>
<CELL>43</CELL>
<CELL>22</CELL>
<CELL>54</CELL>
<CELL>36</CELL>
<CELL>12</CELL>
<CELL>57</CELL>
<CELL>37</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">26</CELL>
<CELL>6</CELL>
<CELL>42</CELL>
<CELL>14</CELL>
<CELL>12</CELL>
<CELL>23</CELL>
<CELL>40</CELL>
<CELL>37</CELL>
<CELL>13</CELL>
<CELL>58</CELL>
<CELL>34</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">27</CELL>
<CELL>6</CELL>
<CELL>57</CELL>
<CELL>14</CELL>
<CELL>41</CELL>
<CELL>24</CELL>
<CELL>25</CELL>
<CELL>38</CELL>
<CELL>11</CELL>
<CELL>59</CELL>
<CELL>27</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">28</CELL>
<CELL>7</CELL>
<CELL>10</CELL>
<CELL>15</CELL>
<CELL>00</CELL>
<CELL>25</CELL>
<CELL>9</CELL>
<CELL>39</CELL>
<CELL>11</CELL>
<CELL>60</CELL>
<CELL>37</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">29</CELL>
<CELL>7</CELL>
<CELL>24</CELL>
<CELL>15</CELL>
<CELL>39</CELL>
<CELL>25</CELL>
<CELL>52</CELL>
<CELL>40</CELL>
<CELL>2</CELL>
<CELL>61</CELL>
<CELL>4</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>7</CELL>
<CELL>38</CELL>
<CELL>16</CELL>
<CELL>6</CELL>
<CELL>26</CELL>
<CELL>36</CELL>
<CELL>40</CELL>
<CELL>54</CELL>
<CELL>61</CELL>
<CELL>49</CELL>
<CELL>&nbsp;</CELL>
</ROW>
</TABLE></P>
<P><PB N="69" REF="42">
<TABLE>
<HEAD>The continuation of the arches of the Horizontall planes, from 30 to 60 deg. of elevation of the Pole</HEAD>
<ROW ROLE="label">
<CELL>&nbsp;</CELL>
<CELL COLS="2"><P>1</P> <P>11</P></CELL>
<CELL COLS="2"><P>2</P> <P>10</P></CELL>
<CELL COLS="2"><P>3</P> <P>9</P></CELL>
<CELL COLS="2"><P>4</P> <P>8</P></CELL>
<CELL COLS="2"><P>5</P> <P>7</P></CELL>
<CELL COLS="2"><P>6</P> <P>6</P></CELL>
</ROW>
<ROW>
<CELL>31</CELL>
<CELL>7</CELL>
<CELL>51</CELL>
<CELL>16</CELL>
<CELL>34</CELL>
<CELL>27</CELL>
<CELL>15</CELL>
<CELL>41</CELL>
<CELL>44</CELL>
<CELL>62</CELL>
<CELL>30</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>32</CELL>
<CELL>8</CELL>
<CELL>5</CELL>
<CELL>17</CELL>
<CELL>1</CELL>
<CELL>27</CELL>
<CELL>55</CELL>
<CELL>42</CELL>
<CELL>32</CELL>
<CELL>63</CELL>
<CELL>11</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>33</CELL>
<CELL>8</CELL>
<CELL>19</CELL>
<CELL>17</CELL>
<CELL>27</CELL>
<CELL>28</CELL>
<CELL>37</CELL>
<CELL>43</CELL>
<CELL>20</CELL>
<CELL>63</CELL>
<CELL>49</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>34</CELL>
<CELL>8</CELL>
<CELL>31</CELL>
<CELL>17</CELL>
<CELL>54</CELL>
<CELL>29</CELL>
<CELL>13</CELL>
<CELL>44</CELL>
<CELL>5</CELL>
<CELL>64</CELL>
<CELL>24</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>35</CELL>
<CELL>8</CELL>
<CELL>44</CELL>
<CELL>18</CELL>
<CELL>20</CELL>
<CELL>29</CELL>
<CELL>50</CELL>
<CELL>44</CELL>
<CELL>49</CELL>
<CELL>64</CELL>
<CELL>58</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>36</CELL>
<CELL>8</CELL>
<CELL>57</CELL>
<CELL>18</CELL>
<CELL>45</CELL>
<CELL>30</CELL>
<CELL>27</CELL>
<CELL>45</CELL>
<CELL>31</CELL>
<CELL>65</CELL>
<CELL>30</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>37</CELL>
<CELL>9</CELL>
<CELL>10</CELL>
<CELL>19</CELL>
<CELL>9</CELL>
<CELL>31</CELL>
<CELL>2</CELL>
<CELL>46</CELL>
<CELL>12</CELL>
<CELL>66</CELL>
<CELL><GAP DESC="illegible" EXTENT="1 letter">0</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>38</CELL>
<CELL>9</CELL>
<CELL>22</CELL>
<CELL>19</CELL>
<CELL>34</CELL>
<CELL>31</CELL>
<CELL>37</CELL>
<CELL>46</CELL>
<CELL>50</CELL>
<CELL>66</CELL>
<CELL>29</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>39</CELL>
<CELL>9</CELL>
<CELL>24</CELL>
<CELL>19</CELL>
<CELL>58</CELL>
<CELL>32</CELL>
<CELL>11</CELL>
<CELL>47</CELL>
<CELL>28</CELL>
<CELL>66</CELL>
<CELL>56</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>40</CELL>
<CELL>9</CELL>
<CELL>47</CELL>
<CELL>20</CELL>
<CELL>22</CELL>
<CELL>32</CELL>
<CELL>44</CELL>
<CELL>48</CELL>
<CELL>4</CELL>
<CELL>67</CELL>
<CELL>23</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>41</CELL>
<CELL>9</CELL>
<CELL>58</CELL>
<CELL>20</CELL>
<CELL>45</CELL>
<CELL>33</CELL>
<CELL>16</CELL>
<CELL>48</CELL>
<CELL>39</CELL>
<CELL>67</CELL>
<CELL>47</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>42</CELL>
<CELL>10</CELL>
<CELL>10</CELL>
<CELL>21</CELL>
<CELL>7</CELL>
<CELL>33</CELL>
<CELL>47</CELL>
<CELL>49</CELL>
<CELL>13</CELL>
<CELL>68</CELL>
<CELL>10</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>43</CELL>
<CELL>10</CELL>
<CELL>21</CELL>
<CELL>21</CELL>
<CELL>30</CELL>
<CELL>34</CELL>
<CELL>18</CELL>
<CELL>49</CELL>
<CELL>45</CELL>
<CELL>68</CELL>
<CELL>33</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>44</CELL>
<CELL>10</CELL>
<CELL>32</CELL>
<CELL>21</CELL>
<CELL>51</CELL>
<CELL>34</CELL>
<CELL>47</CELL>
<CELL>50</CELL>
<CELL>16</CELL>
<CELL>68</CELL>
<CELL>55</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>45</CELL>
<CELL>10</CELL>
<CELL>44</CELL>
<CELL>21</CELL>
<CELL>45</CELL>
<CELL>35</CELL>
<CELL>16</CELL>
<CELL>50</CELL>
<CELL>46</CELL>
<CELL>69</CELL>
<CELL>15</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>46</CELL>
<CELL>10</CELL>
<CELL>54</CELL>
<CELL>22</CELL>
<CELL>33</CELL>
<CELL>35</CELL>
<CELL>53</CELL>
<CELL>51</CELL>
<CELL>15</CELL>
<CELL>69</CELL>
<CELL>34</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>47</CELL>
<CELL>11</CELL>
<CELL>6</CELL>
<CELL>22</CELL>
<CELL>54</CELL>
<CELL>36</CELL>
<CELL>11</CELL>
<CELL>51</CELL>
<CELL>43</CELL>
<CELL>69</CELL>
<CELL>53</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>48</CELL>
<CELL>11</CELL>
<CELL>16</CELL>
<CELL>23</CELL>
<CELL>14</CELL>
<CELL>36</CELL>
<CELL>37</CELL>
<CELL>52</CELL>
<CELL>9</CELL>
<CELL>70</CELL>
<CELL>11</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>49</CELL>
<CELL>11</CELL>
<CELL>26</CELL>
<CELL>23</CELL>
<CELL>33</CELL>
<CELL>37</CELL>
<CELL>2</CELL>
<CELL>52</CELL>
<CELL>35</CELL>
<CELL>70</CELL>
<CELL>27</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>50</CELL>
<CELL>11</CELL>
<CELL>36</CELL>
<CELL>23</CELL>
<CELL>51</CELL>
<CELL>37</CELL>
<CELL>27</CELL>
<CELL>53</CELL>
<CELL>0</CELL>
<CELL>70</CELL>
<CELL>43</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>51</CELL>
<CELL>11</CELL>
<CELL>46</CELL>
<CELL>24</CELL>
<CELL>10</CELL>
<CELL>37</CELL>
<CELL>52</CELL>
<CELL>53</CELL>
<CELL>24</CELL>
<CELL>71</CELL>
<CELL>13</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>52</CELL>
<CELL>11</CELL>
<CELL>55</CELL>
<CELL>24</CELL>
<CELL>57</CELL>
<CELL>38</CELL>
<CELL>14</CELL>
<CELL>53</CELL>
<CELL>46</CELL>
<CELL>71</CELL>
<CELL>24</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>53</CELL>
<CELL>12</CELL>
<CELL>5</CELL>
<CELL>24</CELL>
<CELL>45</CELL>
<CELL>38</CELL>
<CELL>37</CELL>
<CELL>54</CELL>
<CELL>8</CELL>
<CELL>71</CELL>
<CELL>27</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>54</CELL>
<CELL>12</CELL>
<CELL>14</CELL>
<CELL>25</CELL>
<CELL>2</CELL>
<CELL>38</CELL>
<CELL>58</CELL>
<CELL>54</CELL>
<CELL>30</CELL>
<CELL>71</CELL>
<CELL>40</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>55</CELL>
<CELL>12</CELL>
<CELL>23</CELL>
<CELL>25</CELL>
<CELL>19</CELL>
<CELL>39</CELL>
<CELL>19</CELL>
<CELL>54</CELL>
<CELL>49</CELL>
<CELL>71</CELL>
<CELL>53</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>56</CELL>
<CELL>12</CELL>
<CELL>32</CELL>
<CELL>25</CELL>
<CELL>35</CELL>
<CELL>39</CELL>
<CELL>39</CELL>
<CELL>55</CELL>
<CELL>9</CELL>
<CELL>72</CELL>
<CELL>5</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>57</CELL>
<CELL>12</CELL>
<CELL>40</CELL>
<CELL>25</CELL>
<CELL>51</CELL>
<CELL>39</CELL>
<CELL>59</CELL>
<CELL>55</CELL>
<CELL>28</CELL>
<CELL>72</CELL>
<CELL>17</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>58</CELL>
<CELL>12</CELL>
<CELL>48</CELL>
<CELL>26</CELL>
<CELL>5</CELL>
<CELL>40</CELL>
<CELL>18</CELL>
<CELL>55</CELL>
<CELL>45</CELL>
<CELL>72</CELL>
<CELL>28</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>59</CELL>
<CELL>12</CELL>
<CELL>56</CELL>
<CELL>26</CELL>
<CELL>20</CELL>
<CELL>40</CELL>
<CELL>36</CELL>
<CELL>56</CELL>
<CELL>2</CELL>
<CELL>72</CELL>
<CELL>39</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>60</CELL>
<CELL>13</CELL>
<CELL>4</CELL>
<CELL>26</CELL>
<CELL>33</CELL>
<CELL>40</CELL>
<CELL>54</CELL>
<CELL>56</CELL>
<CELL>19</CELL>
<CELL>72</CELL>
<CELL>49</CELL>
<CELL>&nbsp;</CELL>
</ROW>
</TABLE></P>
<P><PB N="70" REF="43">
<TABLE>
<HEAD>The continuation of the arches of the Horizontall planes, from 60 deg. of elevation, till the Pole is in the Zenith.</HEAD>
<ROW ROLE="label">
<CELL>&nbsp;</CELL>
<CELL COLS="2"><P>1</P> <P>11</P></CELL>
<CELL COLS="2"><P>2</P> <P>10</P></CELL>
<CELL COLS="2"><P>3</P> <P>9</P></CELL>
<CELL COLS="2"><P>4</P> <P>8</P></CELL>
<CELL COLS="2"><P>5</P> <P>7</P></CELL>
<CELL COLS="2"><P>6</P> <P>6</P></CELL>
</ROW>
<ROW>
<CELL ROLE="label">61</CELL>
<CELL>13</CELL>
<CELL>11</CELL>
<CELL>26</CELL>
<CELL>48</CELL>
<CELL>41</CELL>
<CELL>10</CELL>
<CELL>56</CELL>
<CELL>34</CELL>
<CELL>72</CELL>
<CELL>58</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">62</CELL>
<CELL>13</CELL>
<CELL>18</CELL>
<CELL>27</CELL>
<CELL>1</CELL>
<CELL>41</CELL>
<CELL>26</CELL>
<CELL>56</CELL>
<CELL>49</CELL>
<CELL>73</CELL>
<CELL>7</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">63</CELL>
<CELL>13</CELL>
<CELL>25</CELL>
<CELL>27</CELL>
<CELL>13</CELL>
<CELL>41</CELL>
<CELL>42</CELL>
<CELL>57</CELL>
<CELL>3</CELL>
<CELL>73</CELL>
<CELL>16</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">64</CELL>
<CELL>13</CELL>
<CELL>32</CELL>
<CELL>27</CELL>
<CELL>26</CELL>
<CELL>41</CELL>
<CELL>57</CELL>
<CELL>57</CELL>
<CELL>17</CELL>
<CELL>73</CELL>
<CELL>24</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">65</CELL>
<CELL>13</CELL>
<CELL>39</CELL>
<CELL>27</CELL>
<CELL>37</CELL>
<CELL>42</CELL>
<CELL>11</CELL>
<CELL>57</CELL>
<CELL>30</CELL>
<CELL>73</CELL>
<CELL>32</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">66</CELL>
<CELL>13</CELL>
<CELL>45</CELL>
<CELL>27</CELL>
<CELL>49</CELL>
<CELL>42</CELL>
<CELL>25</CELL>
<CELL>57</CELL>
<CELL>42</CELL>
<CELL>73</CELL>
<CELL>39</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">67</CELL>
<CELL>13</CELL>
<CELL>52</CELL>
<CELL>27</CELL>
<CELL>59</CELL>
<CELL>42</CELL>
<CELL>38</CELL>
<CELL>57</CELL>
<CELL>54</CELL>
<CELL>73</CELL>
<CELL>46</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">68</CELL>
<CELL>13</CELL>
<CELL>56</CELL>
<CELL>28</CELL>
<CELL>9</CELL>
<CELL>42</CELL>
<CELL>50</CELL>
<CELL>58</CELL>
<CELL>5</CELL>
<CELL>73</CELL>
<CELL>53</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">69</CELL>
<CELL>14</CELL>
<CELL>3</CELL>
<CELL>28</CELL>
<CELL>19</CELL>
<CELL>43</CELL>
<CELL>2</CELL>
<CELL>58</CELL>
<CELL>16</CELL>
<CELL>73</CELL>
<CELL>59</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">70</CELL>
<CELL>14</CELL>
<CELL>8</CELL>
<CELL>28</CELL>
<CELL>29</CELL>
<CELL>43</CELL>
<CELL>13</CELL>
<CELL>58</CELL>
<CELL>26</CELL>
<CELL>74</CELL>
<CELL>5</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">71</CELL>
<CELL>14</CELL>
<CELL>13</CELL>
<CELL>28</CELL>
<CELL>38</CELL>
<CELL>43</CELL>
<CELL>24</CELL>
<CELL>58</CELL>
<CELL>36</CELL>
<CELL>74</CELL>
<CELL>11</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">72</CELL>
<CELL>14</CELL>
<CELL>18</CELL>
<CELL>28</CELL>
<CELL>46</CELL>
<CELL>43</CELL>
<CELL>34</CELL>
<CELL>58</CELL>
<CELL>44</CELL>
<CELL>74</CELL>
<CELL>16</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">73</CELL>
<CELL>14</CELL>
<CELL>22</CELL>
<CELL>28</CELL>
<CELL>55</CELL>
<CELL>43</CELL>
<CELL>43</CELL>
<CELL>58</CELL>
<CELL>53</CELL>
<CELL>74</CELL>
<CELL>21</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">74</CELL>
<CELL>14</CELL>
<CELL>26</CELL>
<CELL>29</CELL>
<CELL>2</CELL>
<CELL>43</CELL>
<CELL>52</CELL>
<CELL>59</CELL>
<CELL>1</CELL>
<CELL>74</CELL>
<CELL>25</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">75</CELL>
<CELL>14</CELL>
<CELL>30</CELL>
<CELL>29</CELL>
<CELL>9</CELL>
<CELL>44</CELL>
<CELL>0</CELL>
<CELL>59</CELL>
<CELL>8</CELL>
<CELL>74</CELL>
<CELL>29</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">76</CELL>
<CELL>14</CELL>
<CELL>34</CELL>
<CELL>29</CELL>
<CELL>5</CELL>
<CELL>44</CELL>
<CELL>8</CELL>
<CELL>59</CELL>
<CELL>15</CELL>
<CELL>74</CELL>
<CELL>34</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">77</CELL>
<CELL>14</CELL>
<CELL>38</CELL>
<CELL>29</CELL>
<CELL>22</CELL>
<CELL>44</CELL>
<CELL>15</CELL>
<CELL>59</CELL>
<CELL>21</CELL>
<CELL>74</CELL>
<CELL>37</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">78</CELL>
<CELL>14</CELL>
<CELL>41</CELL>
<CELL>29</CELL>
<CELL>27</CELL>
<CELL>44</CELL>
<CELL>22</CELL>
<CELL>59</CELL>
<CELL>26</CELL>
<CELL>74</CELL>
<CELL>41</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">79</CELL>
<CELL>14</CELL>
<CELL>44</CELL>
<CELL>29</CELL>
<CELL>32</CELL>
<CELL>44</CELL>
<CELL>28</CELL>
<CELL>59</CELL>
<CELL>32</CELL>
<CELL>74</CELL>
<CELL>44</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">80</CELL>
<CELL>14</CELL>
<CELL>47</CELL>
<CELL>29</CELL>
<CELL>37</CELL>
<CELL>44</CELL>
<CELL>34</CELL>
<CELL>59</CELL>
<CELL>37</CELL>
<CELL>74</CELL>
<CELL>47</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">81</CELL>
<CELL>14</CELL>
<CELL>49</CELL>
<CELL>29</CELL>
<CELL>42</CELL>
<CELL>44</CELL>
<CELL>39</CELL>
<CELL>59</CELL>
<CELL>41</CELL>
<CELL>74</CELL>
<CELL>49</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">82</CELL>
<CELL>14</CELL>
<CELL>51</CELL>
<CELL>29</CELL>
<CELL>44</CELL>
<CELL>44</CELL>
<CELL>43</CELL>
<CELL>59</CELL>
<CELL>43</CELL>
<CELL>74</CELL>
<CELL>50</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">83</CELL>
<CELL>14</CELL>
<CELL>53</CELL>
<CELL>29</CELL>
<CELL>49</CELL>
<CELL>44</CELL>
<CELL>47</CELL>
<CELL>59</CELL>
<CELL>49</CELL>
<CELL>74</CELL>
<CELL>53</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">84</CELL>
<CELL>14</CELL>
<CELL>55</CELL>
<CELL>29</CELL>
<CELL>52</CELL>
<CELL>44</CELL>
<CELL>51</CELL>
<CELL>59</CELL>
<CELL>52</CELL>
<CELL>74</CELL>
<CELL>55</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">85</CELL>
<CELL>14</CELL>
<CELL>57</CELL>
<CELL>29</CELL>
<CELL>54</CELL>
<CELL>44</CELL>
<CELL>53</CELL>
<CELL>59</CELL>
<CELL>54</CELL>
<CELL>74</CELL>
<CELL>57</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">86</CELL>
<CELL>14</CELL>
<CELL>58</CELL>
<CELL>29</CELL>
<CELL>56</CELL>
<CELL>44</CELL>
<CELL>56</CELL>
<CELL>59</CELL>
<CELL>57</CELL>
<CELL>74</CELL>
<CELL>58</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">87</CELL>
<CELL>14</CELL>
<CELL>59</CELL>
<CELL>29</CELL>
<CELL>58</CELL>
<CELL>44</CELL>
<CELL>58</CELL>
<CELL>59</CELL>
<CELL>58</CELL>
<CELL>74</CELL>
<CELL>59</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">88</CELL>
<CELL>14</CELL>
<CELL>59</CELL>
<CELL>29</CELL>
<CELL>59</CELL>
<CELL>44</CELL>
<CELL>59</CELL>
<CELL>59</CELL>
<CELL>58</CELL>
<CELL>74</CELL>
<CELL>59</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">89</CELL>
<CELL>14</CELL>
<CELL>59</CELL>
<CELL>30</CELL>
<CELL>&nbsp;</CELL>
<CELL>44</CELL>
<CELL>59</CELL>
<CELL>59</CELL>
<CELL>59</CELL>
<CELL>75</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL ROLE="label">90</CELL>
<CELL>15</CELL>
<CELL>&nbsp;</CELL>
<CELL>30</CELL>
<CELL>&nbsp;</CELL>
<CELL>45</CELL>
<CELL>&nbsp;</CELL>
<CELL>60</CELL>
<CELL>&nbsp;</CELL>
<CELL>75</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
</TABLE></P>
</DIV3>
</DIV2>
<DIV2 N="8" TYPE="chapter">
<PB N="71" REF="43">
<HEAD>CHAP VIII.</HEAD>
<ARGUMENT>
<P>Shewing the u&s;e of this Table both in Verticall and Horizontall planes.</P>
</ARGUMENT>
<P>_FOr an Horizontall Diall enter the Table with the elevation of the Pole on the left hand, and the arches noted again&s;t the houres and the e|levation found, are the di&s;tance of the houres from the Meridian.</P>
<P>For a Verticall or direct South or North, enter the Ta|ble with the complement of the elevation on the right &s;ide, and the common meeting of the houres at top, and the com|plement of elevation, is the di&s;tance of the houres from the Meridian in the &s;aid plane. For every horizontall plane is a direct Verticall in that place who&s;e Latitude or di&s;tance of their Zenith from the Aequator, is equall to the comple|ment of the elevation of the Horizontall planes Axis or &s;tyle.</P>
<P>As to make an Horizontall Diall for the Latitude of 51 degrees, I enter the Table and finde the&s;e Arches for 1 and 11, for 2 and 10, &amp;c. Now the &s;ame di&s;tances are the di&s;tances of the houre lines of a direct South plane, where the Pole is elevated the complement of 51 degrees, that is 39 degrees, for 51 and 39 together doe make 90.</P>
<P>So to make a Verticall diall, I enter the Table with 39, the complement of the elevation of the pole, and finde the arches an&s;wering to 1 and 11, to 2 and 10, &amp;c. Thus much in generall of the u&s;e of the Table, now followeth the u&s;e in &s;peciall.</P>
</DIV2>
<DIV2 N="9" TYPE="chapter">
<PB N="72" REF="44">
<HEAD>CHAP IX.</HEAD>
<ARGUMENT>
<P>Shewing the u&s;e of the Tables in making any Declining or Inclining direct Dials.</P>
</ARGUMENT>
<P>_LEt the great Circle ABCD repre&s;ent the Meridian, A the North, and C the South, then the line EF repre&s;ents a South reclining plane, while it fals back from the South North|ward, and repre&s;ents an inclining plane while it re&s;pects the Horizon. This is &s;ufficiently di&s;cu&s;&s;ed be|fore.</P>
<P><FIGURE>
</FIGURE></P>
<P><PB N="73" REF="44">So much as the plane reclines northward beyond the complement of the elevation of the Pole, &s;o much is the North pole elevated above the plane, as here the plane is repre&s;ented by EF, the elevation of the &s;tyle or Axis the arch EG, therefore in this ca&s;e &s;ub&s;tract the complement of the reclination of the plane from the elevation of the elevated pole, and the remainer is the arch of the poles elevation above the plane, with which elevation enter the Table in the left margent, and there are the houre arches from the meridian. If the reclination of the plane be le&s;&s;e then the complement, as is IK, &s;ub&s;tract the arch of recli|nation from the complement of the elevation, there is left the elevation of the South pole above the plane, and with the complement of the elevation of the pole above the plane enter the table on the right margent, and there &s;hall you finde the di&s;tance of the houres: and herein Mr. <HI>Faile</HI> failed, for in&s;tead of &s;ub&s;tracting one from the other, he addeth one to another, cau&s;ing a great errour. The di&s;tance of every houre of the North incliner on the back &s;ide of the South incliner as much are equall, &s;aving that the houres on the North &s;ide mu&s;t be named by the complement houres to 12, and as the North pole is above one plane, &s;o is the South pole above the other, you may al&s;o conceive the like in making of all South incliners and recliners, by framing the po&s;ition of the plane on the South &s;ide as the figure is on the North: and in North recliners le&s;&s;e then the eleva|tion of the pole, adde the reclination of the flat, which is the elevation of the North pole above the plane: herein Mr. <HI>Fail</HI> failed al&s;o, as depending on the former, following the doctrine of contraries, which formo&s;t well examined would have &s;aved the opening of a gap to this &s;econd errour: With the &s;aid elevation found enter the Table for the Ho|rizontal
<PB N="72" REF="45">
<GAP DESC="duplicate" EXTENT="1 page">
<PB N="73" REF="45">
<GAP DESC="duplicate" EXTENT="1 page">
<PB N="74" REF="46">
arches, and thereby make a Horizontall&punc; plane as is &s;hewed, &s;o is the Diall al&s;o prepared.</P>
<P>If it recline that it lie between the Horizon and the Equa|tor, then to the elevation of the Pole adde the complement of the reclination, which is the height of the &s;tyle above the plane, and fini&s;h it as a Horizontall plane for that latitude, and not as a Verticall, as Mr. <HI>Faile</HI> would have it, becau&s;e every reclining plane is a Horizontall plane where the pole is elevated according to the &s;tyle.</P>
<DIV3 TYPE="section">
<HEAD>In a given plane oblique to the Meridian, and to the Horizon, and to the prime Verticall, that is, a given plane Inclining declining, to finde as well the Meridian of the place as of the plane, and the elevation of the pole above the plane: <HI>Prob. 3,</HI> Petici, <HI>Liber Gnomonicorum.</HI></HEAD>
<P>TO give you the parallel of <HI>Piti&s;cus</HI> his example, we will pro&s;ecute it according to the naturall Tangents in his example, and give you his words. Let the Meridian of the place be ABCD&punc; the Horizon AEC, the prime Verticall BED, the Orientall point E, the Ver|ticall declined BKD, and right angled at K, the poles of the World G and I: the poles of the planes H, the Meridian GHI, the angle of declination EBF, the arch of inclina|tion BK. But before all things the arch K, or the di&s;tance of the meridian of the place NL is from the Vertical plane KL &s;hould be &s;ought by the &s;econd Axiome, then the arke BN by the third or fourth Axiome, after the&s;e the angle BKN, that is, in one word, the Triangle BKN is found, by which di&s;charged, the arke BN is found either equal to the poles elevation, or greater or le&s;&s;er. If the arke be e|qual to the complement of the poles elevation, by it is a to|ken the plane is oblique under the Meridian, to be inclined
<PB N="75" REF="46">
unto the Pole, in that ca&s;e the meridian of the place and of the plane, and al&s;o the Axis doe concur in the &s;ame line G L&punc; if the plane be &s;uppo&s;ed to fall in the &s;ame great circle KN, but if the plane be not &s;uppo&s;ed, but in &s;ome parallel of the &s;ame, and the Axis be &s;omwhat carryed away, as ne|ce&s;&s;arily it is done if the Sciotericall be ab&s;olved, the Me|ridian of the plane and place are two lines parallel between them&s;elves, and are mutually joyned together according to the difference of longitude of the place and of the plane, which difference is according to the angle HGC, which is the complement of the angle BNK late found, becau&s;e the angle KGH is right by 57. <HI>p.</HI> 1. yea, fora&s;much as the meridian of the plane may goe by the poles of the plane, but concurring at G or N are equall to two right, by 20 <HI>p.</HI> 1.</P>
<P><FIGURE>
</FIGURE></P>
<P><HI>Example,</HI> Let the plane meridionall declined to the right
<PB N="76" REF="47">
hand 29 de. 59 m. inclining toward the pole artick 23 de. 3 m. the elevation of the pole 49 de. 35 m. and there are to be &s;ought in the &s;ame the meridian of the place &amp; the plane, and the elevation of the pole or Axis above the plane. The calculation &s;hall be thus.</P>
<GAP DESC="math">
<P>To 67874 the tangent of the arke KN the di&s;tance of the meridian of the place from the Verticall of the plane, 34 de. 10 m. <HI>per ax.</HI> 2&punc;</P>
<GAP DESC="math">
<P>The &s;ine of the arke NC 49de. 35 m. who&s;e complement is the arke BN 40de. 25 m <HI>per axi.</HI> 4.</P>
<GAP DESC="math">
<P>To 60388 the &s;ine of the angle BNK 37d 9m. who&s;e com|plement is the angle HNC, or HGC 52 de. 51. m. the difference of the longitude of the plane from the longitude of the place, or the di&s;tance of the meridians of the place and plane.</P>
<P>Therefore let the horizon of the place be LC, the verti|call of the plane KL, the circle of the plane of the horizon KNC, in which there is numbred from K towards C 34
<PB N="77" REF="47">
de. 10m. and at the terme of the numeration <HI>N,</HI> draw the right line L <HI>N</HI> E, which &s;hall be the meridian of the plane and place, if the center of the Sciotericie L or F is taken for the center of the World, and the right line L <HI>N</HI> F for the Axis, but becau&s;e in the perfection of the Diall, IG remaineth the Axis, with E the center of the world, not in the right line L <HI>N</HI> F, but above the &s;ame, with props at plea&s;ure, but notwith|&s;tanding it is rai&s;ed e|quall in height with EI and OG, and more|over the plane is &s;om|what withdrawn fro~ the axis of the world, therefore the line L <HI>N</HI> F is now not alto|gether the meridian of the place, but only the meridian of the plane, or as vul|garly they &s;peake, the &s;ub&s;tilar.</P>
<P>But you may finde the meridian of the place thus, draw IH at right angles to the meridian of the plane, which they vulgarly call the Contingence to the common &s;ection of the Equator, which in the plane let E the center of the world be &s;et from the axis IG in the meridian of the plane L <HI>N</HI> F.</P>
<P><FIGURE>
</FIGURE></P>
<P>Then to the center E, con&s;i&s;ting in the line L <HI>N</HI> E, le the circle of the Equator FK be de&s;cribed, and in the &s;ame
<PB N="78" REF="48">
toward the Ea&s;t, becau&s;e the horizon of the plane is more ea&s;terly then the horizon of the place, and moreover the beame is ca&s;t &s;ooner or later upon the meridian of the plane then the place, let there be numbered the difference of lon|gitude of the place and plane 52 de. 51 m. and by K the end of the numeration let a right line be drawn, as it were the certain beams of the Equator EKH, which where it touch|eth the common &s;ection of the Equator with the plane, to wit, the right line FH, by that point let C the meridian of the place be drawn perpendicular.</P>
</DIV3>
<DIV3 TYPE="case">
<HEAD>The &s;econd ca&s;e of the third Probleme of <HI>Piti&s;cus</HI> his <HI>Liber Gnomonicorum.</HI></HEAD>
<P><HI>Sivero arcus BN, repertus fuerit, &amp;c.</HI> But if the arke BN &s;hall be found le&s;&s;e then the complement of the poles e|levation, it is a &s;igne the plane doth con&s;i&s;t on this &s;ide the pole artick, and moreover above &s;uch a plane not the pole Artick, but the pole Antartick &s;hall be extolled to &s;uch an angle as ILM is, who&s;e mea&s;ure is the arke IM, to which, out of the doctrine of oppo&s;ites, the arke GO is equall, which you may certainly finde together with the arke NO thus. As MOG the right angle, to NG the difference between BN and BG, &s;o ONG the angle before found, to OG, <HI>per axi.</HI> 3. As the tangent ONG to Radius, &s;o the tangent OG, to the &s;ine O <HI>N,</HI> by <HI>axi.</HI> 2.</P>
<P><HI>Example;</HI> Let the plane be meridionall declined to the right hand 34 de. 30 m. inclined toward the pole artick 16 de. 10 m. and again, let the elevation of the pole be 49 de. 35 m. and there are &s;ought:</P>
<P>The meridian of the place: the longitude of the countrey</P>
<P>The meridian of the plane: the longitude of the plane?</P>
<P>The elevation of the pole above the plane.</P>
<P><PB N="76" REF="48">
<FIGURE>
</FIGURE></P>
<P><HI>The Calculation.</HI></P>
<P>1. As BF Radius, 100000, to FC tangent comple|ment of declination 55 de. 30 m. 14550, &s;o 27843 the &s;ine of the inclination 16 de. 10 m. to 40511, the tangent of K <HI>N</HI> 22 de. 31 / 3 m. the di&s;tance of the meridian of the place from the Verticall of the plane, <HI>per axi.</HI> 2.</P>
<GAP DESC="math">
<P>The &s;ine of the arke <HI>N</HI> C 62 de, 532 / 3 m. who&s;e complement is B <HI>N</HI> 27 de. 61 / 3 m. by which &s;ub&s;tracted from BG the comple|ment of the poles elevation 40 de. 25 m. there is remaining the arke <HI>N</HI> G 13 de. 182 / 3 m. by <HI>axi.</HI> 4.</P>
<P><PB N="80" REF="49">
<GAP DESC="math"></P>
<P>To 61108 the &s;ine of the angle B <HI>N</HI> K, or O <HI>N</HI> G 37d. 40 m. <HI>per axi. 3. &amp; comp.</HI> 1.</P>
<GAP DESC="math">
<P>To 14069 the &s;ine of the arch OG the di&s;tance of the ax|is GL from the meridian of the plane&punc; OL 8de. 51 / 3m. <HI>by ax.</HI> 3.</P>
<GAP DESC="math">
<P>To 18410 the &s;ine of the arch <HI>N</HI> O, the di&s;tance of the me|ridian of the plane OL, from the meridian of the place <HI>N</HI> L 30 deg. 36&frac12; m, <HI>by axi.</HI> 2.</P>
<P>The calculation being ab&s;olved, let there be drawn the horizon of the place AC, &s;econdly, the verticall of the plane BQ, thirdly, the horizon of the plane ABCQ, in who&s;e Quadrant AQ, to wit, according to the pole antar|tique, which alone appeareth above &s;uch a plane. Fir&s;t, let be numbred the di&s;tance of the meridian of the place from the verticall of the plane 22 de. 3 m. and by the ende of the numeration at P, let the meridian of the plane LP be drawn, then from the point P, let the di&s;tance of the me|ridian of the plane from the meridian of the place be num|bered, by the terme of the numeration M, let the meridi|an of the plane LM be drawn. Finally, from the point M, into what&s;oever part, let the proper elevation of the pole
<PB N="81" REF="49">
be numbered, or the di&s;tance of the axis from the meridian of the plane 8 de&punc; 51 / 3m. and by the term of the numeration I, let the axis&punc; LI be drawn, to be extolled or lifted up on the meridian of the plane LM, to the angle MLN.</P>
<P><FIGURE>
</FIGURE></P>
<P><HI>The third ca&s;e of the third probleme of</HI> Piti&s;cus <HI>his</HI> liber Gnomonicorum.</P>
<P><HI>Si deni&abque; arcus BN repertus fuerit major, &amp;c.</HI> La&s;tly, if the arke BN be found greater then the complement of the poles elevation BG, it is a token the plane to be inclined beyond the pole artique, and moreover the pole artique &s;hould be extolled above &s;uch a plane to &s;o great an angle as the angle GLO, which the arke GO mea&s;ureth, which arke, together with the arke ON in the end you may find in &s;uch &s;ort as in the precedent ca&s;e.</P>
<P><HI>Example,</HI> Let there be a meridian plane declining to the right hand 35 de. 54 m. inclining towards the pole artique
<PB N="82" REF="50">
75 de. 43 m. and let the elevation of the pole be 49 de. 35&frac12; m. but there is &s;ought the meridian of the plane and place, together with the elevation of the pole above the plane, the calculation &s;hall be thus.</P>
<P><FIGURE>
</FIGURE></P>
<GAP DESC="math">
<P>to 133874 tangent of the arke KN, the di&s;tance of the me|ridian of the place from the verticall of the plane, 53 de. 14&frac12; m, by <HI>axi.</HI> 2.</P>
<GAP DESC="math">
<P>The &s;ine of the arke NC 8 de. 29^<GAP DESC="illegible" EXTENT="1 letter"> m. who&s;e complement
<PB N="83" REF="50">
is BN 81 de. 30&frac12; m. from whence if you &s;ub&s;tract BG 40 de. 25 m. there remaineth the arke GN 41 de. 5&frac12; m.</P>
<GAP DESC="math">
<P>to 97982, the &s;ine of the angle BNK, or ONG, by <HI>axi.</HI> 3.</P>
<GAP DESC="math">
<P>to 64399 the &s;ine of the arch OG, the di&s;tance of the ax|is from the meridian of the plane 40 de. 51 / 3 m. by <HI>axi.</HI> 3.</P>
<GAP DESC="math">
<P>to 17483 the &s;ine of the arke O <HI>N</HI> the di&s;tance of the me|ridian of the plane from the meridian of the place, 10 de. 4 m. by <HI>axi. &amp; comp.</HI> 2.</P>
<P><FIGURE>
</FIGURE></P>
<P>The calculation being fini&s;hed, let the horizon of the place be AC, the verticall of the plane KD, the ho|rizon of the plane AKCD, in which let be numbered from the vertical point K toward C the di&s;tance of the meridian of the place from the ver|tical of the plane 53 de. 14&frac12; m. and by the end of the nu|meration
<PB N="84" REF="51">
let be drawn the meridian of the place LN, then from the meridian of the place, to wit, from the point N backward, let the di&s;tance of the meridian of the plane 10 de. 4m. be numbred, and by O the end of the numerati|on, let LO the meridian of the plane be drawn, from which afterwards let the proper elevation of the pole be numbred, or the di&s;tance of the axis from the meridian of the plane 48d. 5&frac12;m. and by the term of the numeration G, let the axis LG be drawn, being extolled above the plane BO, to the angle GLO.</P>
</DIV3>
</DIV2>
<DIV2 N="10" TYPE="chapter">
<HEAD>CHAP X.</HEAD>
<ARGUMENT>
<P>In which is &s;hewed the drawing of the houre-lines in the&s;e la&s;t planes not there mentioned, being al&s;o part of <HI>Piti&s;cus</HI> his example in the fourth Probleme of his <HI>liber Gnom.</HI></P>
</ARGUMENT>
<P>_SO then, &s;aith he, <HI>Si axis, &amp;c.</HI> If the axis be oblique to the plane, as the foregoing are, as in any plane oblique to the Equa|tor many of the houre-lines doe concur at the axis with equal angles, but they are ea&s;ily found thus.</P>
<P>From any point of the axis, as it were from the center of the World, for example in the meridional declining to the right hand 30 de. From the point E of the axis, let be drawn a line at right angles, as it were any radius of the Equator EF, which right line where it doth fall in the me|ridian of the plane, whether the &s;ame be the meridian of the place or not, thereby the meridian of the plane let another
<PB N="85" REF="51">
<FIGURE>
</FIGURE>
right line be drawn at right angles FQ, which &s;hall be the common &s;ection of the Equator with the plane, the Ra|dius of the Equator FE let be &s;et again in the meridian of the plane, as is FG, and from G, as from the center of the world, let the circle of the Equator be de&s;cribed as great as you plea&s;e, and again, let another Radius of the Equator
<PB N="86" REF="52">
be drawn from the center G to the inter&s;ection of the line of the Equator with the meridian of the place, or with the 12 houre line, which Radius, where it &s;hall cut the Equator Circle, which here is in the point K, from thence the begin|ning being made, let the oppo&s;ite &s;emicircle of the Equator be divided into 12 parts, in the common &s;ections of the Equator and plane, and by every one of the divi&s;ions from the center, let right lines be drawn, which may be put out, &s;uch are GP, GQ, &amp;c. which when they &s;hall touch the common &s;ection of the Equator, then the houre lines an|&s;wering to tho&s;e divi&s;ions nece&s;&s;arily &s;hall pa&s;&s;e, and &s;o of every one of the houre lines to be drawn two points &s;hall be obtained, one in the center L of the Diall, where they all meet, the other in the common &s;ection of the Equator and the plane, or in the line FQ, by which they all pa&s;&s;e, by which two points, if the right lines LQ and LP be drawn, tho&s;e &s;o drawn are the houre lines. The like may be done of any other.</P>
<P>But becau&s;e <HI>Piti&s;cus</HI> is mute in defining which part he takes for the right hand and which the left, we mu&s;t &s;earch his meaning.</P>
<P><HI>Piti&s;cus</HI> was a Divine is evident by his own words in his dedication, <HI>Cel&s;itudini tuae tota vita mea prolixe me excu&s;a|rem quod ego homo Theologus&punc; &amp;c.</HI> If we take him as hee was a Divine, we imagine his face to be towards the Ea&s;t, then the South is his right hand, and the North is his left hand.</P>
<P>That he was an A&s;tronomer too, appeareth by his Books both of proper and common motion, then we mu&s;t ima|gine his face repre&s;enting the South, the Ea&s;t on his left hand, which cannot be, as &s;hall appear.</P>
<P><PB N="87" REF="52">Neither mu&s;t we take him according to the Poets, who&s;e face mu&s;t be imagined toward the We&s;t.</P>
<P>In &s;hort, take him according to Geographie, repre&s;ent|ing the Pole, and this &s;hews the right hand was the Ea&s;t, and left the We&s;t, as is evident by the Diall before going, for it is a plane declining from the South to the right hand 30 degrees, that is, the Ea&s;t, becau&s;e it hath the morning houres not the evening, becau&s;e the Sun &s;hines but part of the afternoon on the plane. Thus in briefe I have run throngh all planes, and proceed to &s;hew you farther con|clu&s;ions: But I de&s;ire the Reader to take notice that in the&s;e examples of <HI>Piti&s;cus.</HI> I have followed his own &s;teps, and made u&s;e of the Naturall Sines and Tangents.</P>
</DIV2>
<DIV2 N="11" TYPE="chapter">
<HEAD>CHAP XI.</HEAD>
<ARGUMENT>
<P>Shewing how by the helpe of a Horizontall Diall, or other, to make any Diall in any po&s;ition how ever.</P>
</ARGUMENT>
<P>_HAving prepared a Horizontall Diall as is taught before: on the 12 houre, as far di&s;tant as you plea&s;e from the foot of the &s;tyle, draw a line perpendicular to the line of 12, on that de&s;cribe a Semicircle, pla&s;ing the foot of the Compa&s;&s;es in the cro&s;&s;ing of the lines, this Semicircle divide into 180 parts, each Quadrant into 90, to number the declination thereon, let the arch of the Semicircle be toward the North part of the Diall.
<PB N="88" REF="53">
Then prepare a plane &s;late, &s;uch as will blot out what hath been formerly made thereon, and make it to move perpen|dicularly on the horizontal plane on the center of the &s;emi|circle, which wil repre&s;ent any declining plane by moving it on the &s;emicircle. Now knowing the declination of the plane turn this &s;late towards the ea&s;terly part, if it decline towards the Ea&s;t, if contrary to the We&s;t, if toward the We&s;t, and &s;et it on the &s;emicircle to the degree of declina|tion, then taking a candle and moving the Diall till the &s;ha|dow fall on all the houres of the horizontall plane, mark al|&s;o where the &s;hadow falls on the declining plane, that al&s;o is the &s;ame houre on the plane &s;o &s;cituated, drawn from the joyning of the &s;tyle with the plane. It is &s;o plain it needs no figure.</P>
<P>So may you doe in all manner of declining reclining, or reclining and inclining Dials, by framing your in&s;trument to repre&s;ent the po&s;ition of the plane.</P>
<P>Note al&s;o that the &s;ame angle the axis of the Horizontal Dial makes with the plane, the &s;ame elevation mu&s;t the axis of that plane have, and where it &s;hadows on the repre&s;enting plane when the &s;hadow of the horizontal axis is on 12, that is the meridian of the place.</P>
<P>By the &s;ame al&s;o may you de&s;cribe all the conclu&s;ions A&s;tronomicall, the Almicanthers, circles of height: the parallels of the Sun, &s;hewing the declination: the Azi|muthes, &s;hewing the point of the Compa&s;&s;e the Sun is in: and all the propo&s;itions of the Sphere.</P>
<P>Seeing this is &s;o plain and evident, nay a delightful con|clu&s;ion, I will not give you farther directions in a matter of &s;o great per&s;picuity, as to lay down the &s;everall wayes for projecting the Sphere on every &s;everall plane, but proceed to &s;hew the making of a general Dial for the whole World,
<PB N="89" REF="53">
which we will u&s;e as our Declinatorie to finde the &s;cituati|on of any wall or plane, as &s;hall be required to make a Diall thereon, as followeth in the next Chapter.</P>
</DIV2>
<DIV2 N="12" TYPE="chapter">
<HEAD>CHAP XII.</HEAD>
<ARGUMENT>
<P>Shewing the making of a Diall on a Cro&s;&s;e form, as al&s;o a Univer&s;all Quadrant drawn from the &s;ame projection, as al&s;o to de&s;cribe the Tropicks on Meridian or Polar planes.</P>
</ARGUMENT>
<P>_THis Univer&s;all Diall is de&s;cribed by <HI>Clavi|us</HI> in his eighth Book <HI>de Gnomonicis:</HI> But becau&s;e the Arti&s;ts of the&s;e times have found out a more commodi|ous contrivance of it in the fa|brique, I &s;hall de&s;cribe it ac|cording to this Figure.</P>
<P><FIGURE>
</FIGURE></P>
<P>You &s;hall therefore of com|modious matter prepare in &s;il|ver or bra&s;&s;e a concave Cro&s;s, &s;uch as is repre&s;ented to your eye, who&s;e three limbes EFG &s;hall be equall, then &s;hall you on the limbe 12 E de&s;cribe as before a parallel Polar plane, as accounting that the height of the &s;tyle, again, on the &s;ide
<FIGURE>
</FIGURE>
<PB N="90" REF="54">
of the Cro&s;&s;e AF you &s;hall de&s;cribe an Orientall or Ea&s;t Diall, and on the other &s;ide a We&s;tern Diall, accounting the arms of the Cro&s;&s;e as the height of the &s;tyle, &s;o have you prepared the plane: you &s;hall again provide a Box with a magneticall needle to be within the body of the Cro&s;&s;e, which &s;hall be contrived to move on the &s;houlders of the Cro&s;&s;e, &s;o as by the helpe of the degrees of a Qua|drant numbred on the limbe of the Box; you may depre&s;s or elevate the end of the Cro&s;&s;e E according to the com|plement of the latitude of the place.</P>
<P>Now to know the houre of the day, you &s;hall turn the plane by the helpe of the needle, &s;o as the end A &s;hall be toward the North, and E toward the South, and elevate the end E to the complement of the elevation, then bring|ing the Box to &s;tand in the Meridian, the &s;houlder of the Cro&s;&s;e &s;hall &s;hew you the houre.</P>
<P>Upon this al&s;o is grounded the Univer&s;all Quadrant hereafter de&s;cribed, which In&s;trument is made in Bra&s;&s;e by Mr. <HI>Walter Hayes</HI> as it is here de&s;cribed. Prepare a Qua|drant of Bra&s;&s;e, divide it in the limbe into 90 degrees, and at the end of 45 degrees from the center draw the line A B, which &s;hall repre&s;ent the Equator, divide the limbe into 90 degrees, as other Quadrants are u&s;ually divided, then number both wayes from the line AB the greate&s;t declina|tion of the Sun from the North and South, at the termina|tion whereof draw the arch CD which &s;hall be the Tro|picks, then out of the Table of declina|tion, <HI>pag.</HI> 45, from B both wayes let there be numbered the declinatio~ of the Signes according to this Table.</P>
<P><TABLE>
<ROW ROLE="label">
<CELL COLS="2">&nbsp;</CELL>
<CELL>G</CELL>
<CELL>M</CELL>
<CELL COLS="2">&nbsp;</CELL>
</ROW>
<ROW>
<CELL COLS="2">&Aries;</CELL>
<CELL>00</CELL>
<CELL>00</CELL>
<CELL COLS="2">&Libra;</CELL>
</ROW>
<ROW>
<CELL>&Taurus;</CELL>
<CELL>&Virgo;</CELL>
<CELL>11</CELL>
<CELL>30</CELL>
<CELL>&Scorp;</CELL>
<CELL>&Pisces;</CELL>
</ROW>
<ROW>
<CELL>&Gemini;</CELL>
<CELL>&Leo;</CELL>
<CELL>20</CELL>
<CELL>30</CELL>
<CELL>&Sagitt;</CELL>
<CELL>&Aquar;</CELL>
</ROW>
<ROW>
<CELL COLS="2">&Cancer;</CELL>
<CELL>23</CELL>
<CELL>30</CELL>
<CELL COLS="2">&Capri;</CELL>
</ROW>
</TABLE></P>
<P>Fir&s;t, for <HI>Taurus</HI> and <HI>Virgo,</HI> and his oppo&s;ite Signe 11 deg. 30 m. namely, <HI>Scorpio</HI> and <HI>Pi&s;ces,</HI>
<PB N="91" REF="54">
<FIGURE>
</FIGURE>
<PB N="92" REF="55">
whereby divide the arch CD, which if you &s;hould draw a line from the center A, one &s;hould be the beginning of <HI>Taurus</HI> and <HI>Virgo,</HI> the other the beginning of <HI>Scorpio</HI> and <HI>Pi&s;ces.</HI> Again, if from B both wayes you number 20 de. 30 min. the end of which &s;hall be the beginning of <HI>Gemini</HI> and <HI>Leo,</HI> or <HI>Sagittarius</HI> and <HI>Aquarius,</HI> number it as is de|&s;cribed, together with a letter for the beginning of each moneth. So you have a quarter of the Zodiaque, and a quarter of a year projected on it.</P>
<P>Now the plane it &s;elfe is no other then an Ea&s;t or We&s;t Diall, numbred on one &s;ide with the morning houres, and on the other with the evening houres, the middle line AB repre&s;enting the Equator. And to &s;et it for the houre, you &s;hall project the Tropicks and other intermediate parallels of the Signes upon them as is hereafter &s;hewed, but that the plane may not run out of the Quadrant you &s;hal work thus, opening the Compa&s;&s;es to 15 degrees of the Quadrant, prick that down both wayes, at which di&s;tance draw pa|rallels to the line AB, and with the &s;ame di&s;tance, as if it were the &s;emidiameter of the Equator, de&s;cribe the &s;emi|diameter of the Equator on the top of the line AB, which divide into 12 parts, and laying a ruler through the center and each of tho&s;e divi&s;ions in the &s;emicircle to tho&s;e paral|lel lines on each &s;ide of AB, marke where they cut, and from &s;ide to &s;ide draw the parallel houre lines as is taught in the making of an Ea&s;t and We&s;t Diall, make tho&s;e pa|rallel lines al&s;o divided as a tangent line on each &s;ide AB, &s;o if this Quadrant were held on an Ea&s;t or We&s;t wall, and a plummet let fall from the center of the Equator where the &s;tyle &s;tands (which may be a pin fitted to take out and in, fitted to the height of the di&s;tance between the line A B and the other parallels, which is all one with the Ra|dius
<PB N="93" REF="55">
of the &s;mall Circle) it &s;hall I &s;ay, be in its right &s;ci|tuation on the Ea&s;t or We&s;t wall if you let the plummet and threed fall on the elevation of the Pole in that place.</P>
<P>But becau&s;e we de&s;ire to make it generall, we mu&s;t de|&s;cribe the Tropicks and other parallels of declination upon it, as is u&s;uall to be done on your Polar and Ea&s;t and We&s;t Diall, which how to doe is thus.</P>
<P>Having drawn the houre lines and Equator as is taught from E the height of the &s;tyle, take all the di&s;tances between it and the houre lines where they doe cro&s;&s;e the line AB, and prick them down on the line repre&s;enting the Equator in this figure from the center B. Then de&s;cribe an occult arch of a Circle, whereon de&s;cribe a Chorde of 23 degrees 30 minutes, with &s;uch other declinations as you intend on your plane. Then on the line repre&s;enting the Equator, no|ted here with the figures of the houres they were taken from, 6, 7, 8, 9, 10, 11, at the marks formerly made, that was taken from E the height of the &s;tyle, and every of the houres, from the&s;e di&s;tances I &s;ay rai&s;e perpendiculars to cut the other lines of declination, &s;o tho&s;e perpendiculars &s;hall repre&s;ent tho&s;e houre lines from whence they were taken, and the di&s;tances between the Equator and the &s;e|verall lines of declination &s;hall be the &s;ame di&s;tances from the Equator, and the other parallels of declination upon your plane, through which marks being pricked down upon the &s;everall hourelines from the Equinoctiall.</P>
<P><PB N="94" REF="56">
<FIGURE>
</FIGURE></P>
<P>If you draw tho&s;e Hyper|bolicall lines, you &s;hall have de&s;cribed the parallels of de|clination required.</P>
<P>But if you will performe the &s;ame work a &s;econd and ea&s;ie way, worke by this Ta|ble following, which is uni|ver&s;all, and is compo&s;ed out of the Table of Right &amp; Ver|&s;ed &s;hadow.</P>
<P>Put this Table before thee, &amp; for the point of each houre line whereby the &s;everall pa|rallels of the Signes &s;hall pa&s;s worke thus.</P>
<P>The &s;tyle being divided into known parts&punc; if&punc; into 12, take the parts of &s;hadow out of the Table in the &s;ame known parts by which the &s;tyle is divided, &amp; prick them down on each houre line as you finde it marked in the Table an&s;wering the houre both before and after noon. As &s;uppo&s;e that a Polar plane I finde when the Sun is in <HI>Aries</HI> or <HI>Libra</HI> at 12 a clock the &s;hadow hath no latitude, but at 1 and 11 it hath 3 parts 13 min. of the parts of the &s;tyle, which I prick from the foot of the &s;tyle on the houres of 1 and 11 both above and beneath the Equator: and for 2 and 10 I finde 6 parts 56 min. which I prick down al&s;o from the center to the houre lines of 10 and 2, and &s;o of the other houre lines and parallels, through which if I draw
<PB N="95" REF="56">
tho&s;e lines they &s;hall repre&s;ent the parallels of the Decli|nation.</P>
<P><TABLE>
<HEAD>A Table of the Latitude of &s;hadows.</HEAD>
<ROW ROLE="label">
<CELL COLS="2">&nbsp;</CELL>
<CELL COLS="2"><HI>Cancer.</HI></CELL>
<CELL COLS="2"><HI>Gemini</HI> <LB> <HI>Leo</HI></CELL>
<CELL COLS="2"><HI>Virgo</HI> <LB> <HI>Taurus</HI></CELL>
<CELL COLS="2"><HI>Libra</HI> <LB> <HI>Aries</HI></CELL>
<CELL COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>a</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL COLS="2">12</CELL>
<CELL>5</CELL>
<CELL>13</CELL>
<CELL>4</CELL>
<CELL>25</CELL>
<CELL>2</CELL>
<CELL>26</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL COLS="2">12</CELL>
</ROW>
<ROW>
<CELL COLS="2">1</CELL>
<CELL>6</CELL>
<CELL>17</CELL>
<CELL>5</CELL>
<CELL>35</CELL>
<CELL>4</CELL>
<CELL>5</CELL>
<CELL>3</CELL>
<CELL>13</CELL>
<CELL COLS="2">11</CELL>
</ROW>
<ROW>
<CELL COLS="2">2</CELL>
<CELL>8</CELL>
<CELL>11</CELL>
<CELL>8</CELL>
<CELL>35</CELL>
<CELL>7</CELL>
<CELL>27</CELL>
<CELL>6</CELL>
<CELL>56</CELL>
<CELL COLS="2">10</CELL>
</ROW>
<ROW>
<CELL COLS="2">3</CELL>
<CELL>14</CELL>
<CELL>5</CELL>
<CELL>13</CELL>
<CELL>31</CELL>
<CELL>12</CELL>
<CELL>39</CELL>
<CELL>12</CELL>
<CELL>0</CELL>
<CELL COLS="2">9</CELL>
</ROW>
<ROW>
<CELL COLS="2">4</CELL>
<CELL>23</CELL>
<CELL>15</CELL>
<CELL>22</CELL>
<CELL>45</CELL>
<CELL>21</CELL>
<CELL>21</CELL>
<CELL>20</CELL>
<CELL>27</CELL>
<CELL COLS="2">8</CELL>
</ROW>
<ROW>
<CELL COLS="2">5</CELL>
<CELL>49</CELL>
<CELL>6</CELL>
<CELL>47</CELL>
<CELL>57</CELL>
<CELL>45</CELL>
<CELL>45</CELL>
<CELL>44</CELL>
<CELL>47</CELL>
<CELL COLS="2">7</CELL>
</ROW>
<ROW>
<CELL COLS="2">6</CELL>
<CELL COLS="8"><HI>&V;mbra infinita.</HI></CELL>
<CELL COLS="2">6</CELL>
</ROW>
</TABLE></P>
<P>If you would finde the houre of the day by this Qua|drant, you &s;hall fix the &s;tyle being of a &s;mall pin of the height of the &s;emidiameter of the Equator in the center, then holding up the Quadrant till the thred and plummet fall on the degrees of the latitude of the place on the Tan|gent lines either on the morning or evening houres, and withall turning the Quadrant till you have cau&s;ed the &s;ha|dow to fall on the declination of the Sun for that day a|mong the parallels, the thred &s;till falling on the elevation, the &s;hadow of the Gnomon &s;hall then give the houre of the day: the declination may be &s;ought in the limbe of the Quadrant an&s;wering to the day of the moneth, and this Quadrant may be made u&s;e of diver&s;e wayes for very good u&s;es, e&s;pecially if you cau&s;e to be drawn two lines more between the Equinoctiall line and tangent line, divided on either &s;ide, which &s;hall be very apt for the making of any &s;ort of Diall: but if you de&s;ire you may have the &s;ame
<PB N="96" REF="57">
on a Ruler, together with the u&s;e thereof, by the In&s;tru|ment maker before mentioned: the manner of making whereof is as followeth&punc; and the u&s;e whereof is in part laid down in the Chapter intreating of Declining planes. Let there be a right angled parallelogram ABCD, of what
<FIGURE>
</FIGURE>
magnitude you plea&s;e, on the longer &s;ide BC let be cut off a line equall to the &s;horter AB, which &s;hall be BE, and at E as a center de&s;cribe the arke of a Circle FG, whereon prick down the Radius FG, then draw the line EA cut|ting the arch in H, the arch FH &s;hall be the eight part of the Circle or the halfe of the Quadrant or right angle, and FG &s;hall be foure parts of the whole Circle divided into 24, whereof FH &s;hall be three of tho&s;e parts of which H G is one part, &s;o that if you do divide from H to F in three parts the arke FH &s;hall be divided into three equall houres, let there be drawn from E occult lines cutting the &s;ide AB in L and M, the &s;ame di&s;tances &s;hall be placed in the oppo|&s;ite &s;ide CD, &s;o the right lines CO and CN &s;hall be e|quall to BM and BL, then draw the right lines MO and LN, which are parallel to the &s;ides BC and AD, &s;o BC &s;hall be the houre of 6 and 12, but the line MO of 11 &amp; 1,
<PB N="97" REF="57">
and of 5 and 7, then the line LN is the hours of a and 10, as al&s;o 4 and 8, and AD the hours of 3 and 9; &s;o as BC is the hour of 12 from mid-night, that is mid-day; M O 1 from the meridian, LN 2, AD 3, and again LN 4, MO 5, BC 6; and again NO 7, LN 8, AD 9; and again LN 10, MO 11, and BC 12; for the halfe hours and quarters, you may divide the Arches HI, IK, KF, into 2 or 4 equall parts, now if you divide any &s;ide, as the tangent in the quadrant is divided to the radius AB; this ruler &s;hal be of excellent u&s;e, which al&s;o you may very well put upon a diagonall Scale without prejudice to the other work&punc; the u&s;e of this Ruler you have in <HI>Clavius</HI> his <HI>Gnomonices.</HI> But to conclude this Chapter by rea&s;on I have &s;hewed very many plain ways, I &s;hall now endeavour becau&s;e I have had occa&s;ion to &s;peak in this Chapter of the parallels of declination, and have &s;hewed how they are drawn in meridian and polar planes, I &s;hal here in&s;ert a ta|ble of Shadows, by which you may be able to do the &s;ame on any other plane, but I would have you note that wherein my example was la&s;t upon a polar plane, by the table of the latitude of &s;hadow, the work is however the &s;ame on a meridian plane, onely accounting the hours in this plane from the 6 a clock houre, as in the polar from the meridian, this quadrant as other quadrants is u&s;ed, to take the inclination, or reclination of planes, which I will mention with a few cautions hereafter following.</P>
<P>Having promi&s;ed in the de&s;cription of the u&s;e of this In&s;trument, to &s;hew how to finde the inclination and re|clination of a plane, I &s;hal proceed to give you &s;ome cau|tions; Fir&s;t then, the quadrant is divided in the limbe, as other quadrants are into 90 degrees, by which is mea&s;ured the angles of inclination or reclination, for if it be a decli|ning plane onely, the declination is accounted from the
<PB N="98" REF="58">
North or South toward the Ea&s;t or We&s;t, if it decline from the North, the North Pole is elivated above it, and the meridian-line a&s;cendeth, if it decline from the South, the &s;outh pole is elivated above that plane, if it decline from the South Ea&s;tward, then is the &s;tyle and &s;ub-&s;tyle refered toward the we&s;t &s;ide of the plane, if to the con|trary the contrary, and may have the line of 12 except north decliners in the temperate Zone, you may make u&s;e of the &s;ide of the quadrant to finde the declination, as is taught before <HI>page</HI> 33, ob&s;erving the angle as is cut by the &s;hadow of the thred held by the limbe, &amp; through the cen|ter, and that &s;ide that lieth perpendicular to the Horizon|tal line which &s;hal be the angle, as is before taught: And if the &s;outh point is between the poles of the plane and the Azimuth, then doth the plane decline Ea&s;tward, if it be the afternoon you take the Azimuth in, if it be the fore|noon you take the Azimuth in, and the &s;outh point be between it and the Poles of the planes horizontal line, it doth decline We&s;tward, if contrary it is in the &s;ame quar|ter where the &s;un is: For an inclining plane, which is the angle that it maketh with the Horizon&punc; draw a Horizon|tall line and cro&s;&s;e it again with a &s;quare, or verticall line, then apply the &s;ide of the quadrant to the vertical line at the beginning of the numeration of the deg. on the qua|drant, and the angle contained between the thred &amp; plum|met, and the applyed &s;ide is the inclination; in all north incliners the north part of the meridian a&s;cendeth, in &s;outh incliners the &s;outh part, and in ea&s;t and we&s;t incliners, the meridian lyeth parallel with the Horizon.</P>
<P>And for the reclination it being all one with the inclina|tion, con&s;idered as an upper and under face of the &s;ame plane, if you cannot apply the &s;ide of the quadrant, you may &s;et a &s;quare or ruler at right angles with the verticall
<PB N="99" REF="58">
line drawn on the upper face and apply the &s;ide of the quadrant to the edge of the ruler, and mea&s;ure the quanti|ty of the angle by the thred and plummet: but this is of di|rect, how&s;oever the&s;e are &s;ubject to another pa&s;&s;ion of de|clining and inclining together, which mu&s;t be &s;ought &s;e|verally, and &s;uch are tho&s;e who&s;e Horizontal line declin|eth toward the north or &s;outh and inclination from north or &s;outh, towarde the ea&s;t or we&s;t, which mu&s;t be &s;ought &s;everally.</P>
<Q>Here followeth the Tables of Right and Contrary &s;hadows.</Q>
<DIV3 TYPE="tables">
<PB N="100" REF="59">
<P><TABLE>
<HEAD>A Table of Right and Contrary &s;hadow, to every Degree and tenth minute of the <HI>Quadrant.</HI></HEAD>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&Sun; Alt</CELL>
<CELL COLS="2">0</CELL>
<CELL COLS="2">1</CELL>
<CELL COLS="2">2</CELL>
<CELL COLS="2">3</CELL>
<CELL COLS="2">4</CELL>
<CELL COLS="2">5</CELL>
<CELL COLS="2">6</CELL>
<CELL COLS="2">7</CELL>
<CELL COLS="2">8</CELL>
<CELL COLS="2">9</CELL>
<CELL ROWS="3" COLS="2">&Sun; Alti<GAP DESC="illegible" EXTENT="1 letter"></CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizontal &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>41378,</CELL>
<CELL>54</CELL>
<CELL>687</CELL>
<CELL>34</CELL>
<CELL>143</CELL>
<CELL>44</CELL>
<CELL>229</CELL>
<CELL>0</CELL>
<CELL>171</CELL>
<CELL>37</CELL>
<CELL>137</CELL>
<CELL>10</CELL>
<CELL>114</CELL>
<CELL>11</CELL>
<CELL>97</CELL>
<CELL>44</CELL>
<CELL>85</CELL>
<CELL>23</CELL>
<CELL>75</CELL>
<CELL>46</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadow</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>4137,</CELL>
<CELL>53</CELL>
<CELL>589</CELL>
<CELL>16</CELL>
<CELL>317</CELL>
<CELL>14</CELL>
<CELL>216</CELL>
<CELL>54</CELL>
<CELL>164</CELL>
<CELL>44</CELL>
<CELL>132</CELL>
<CELL>43</CELL>
<CELL>111</CELL>
<CELL>4</CELL>
<CELL>95</CELL>
<CELL>26</CELL>
<CELL>83</CELL>
<CELL>37</CELL>
<CELL>74</CELL>
<CELL>22</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>2065,</CELL>
<CELL>23</CELL>
<CELL>515</CELL>
<CELL>46</CELL>
<CELL>294</CELL>
<CELL>31</CELL>
<CELL>206</CELL>
<CELL>3</CELL>
<CELL>158</CELL>
<CELL>23</CELL>
<CELL>128</CELL>
<CELL>33</CELL>
<CELL>108</CELL>
<CELL>7</CELL>
<CELL>93</CELL>
<CELL>15</CELL>
<CELL>81</CELL>
<CELL>55</CELL>
<CELL>73</CELL>
<CELL>1</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>1376,</CELL>
<CELL>6</CELL>
<CELL>458</CELL>
<CELL>22</CELL>
<CELL>274</CELL>
<CELL>54</CELL>
<CELL>196</CELL>
<CELL>13</CELL>
<CELL>152</CELL>
<CELL>29</CELL>
<CELL>124</CELL>
<CELL>38</CELL>
<CELL>105</CELL>
<CELL>19</CELL>
<CELL>91</CELL>
<CELL>9</CELL>
<CELL>80</CELL>
<CELL>18</CELL>
<CELL>71</CELL>
<CELL>43</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>1031,</CELL>
<CELL>45</CELL>
<CELL>412</CELL>
<CELL>29</CELL>
<CELL>257</CELL>
<CELL>40</CELL>
<CELL>187</CELL>
<CELL>16</CELL>
<CELL>147</CELL>
<CELL>1</CELL>
<CELL>120</CELL>
<CELL>56</CELL>
<CELL>102</CELL>
<CELL>40</CELL>
<CELL>89</CELL>
<CELL>9</CELL>
<CELL>78</CELL>
<CELL>44</CELL>
<CELL>70</CELL>
<CELL>27</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>825,</CELL>
<CELL>13</CELL>
<CELL>374</CELL>
<CELL>55</CELL>
<CELL>242</CELL>
<CELL>28</CELL>
<CELL>179</CELL>
<CELL>6</CELL>
<CELL>141</CELL>
<CELL>56</CELL>
<CELL>117</CELL>
<CELL>28</CELL>
<CELL>100</CELL>
<CELL>8</CELL>
<CELL>87</CELL>
<CELL>14</CELL>
<CELL>77</CELL>
<CELL>13</CELL>
<CELL>69</CELL>
<CELL>14</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>687,</CELL>
<CELL>34</CELL>
<CELL>343</CELL>
<CELL>54</CELL>
<CELL>229</CELL>
<CELL>0</CELL>
<CELL>171</CELL>
<CELL>37</CELL>
<CELL>137</CELL>
<CELL>10</CELL>
<CELL>114</CELL>
<CELL>11</CELL>
<CELL>97</CELL>
<CELL>44</CELL>
<CELL>85</CELL>
<CELL>23</CELL>
<CELL>75</CELL>
<CELL>46</CELL>
<CELL>68</CELL>
<CELL>3</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><PB N="101" REF="59">
<TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">10</CELL>
<CELL COLS="2">11</CELL>
<CELL COLS="2">12</CELL>
<CELL COLS="2">13</CELL>
<CELL COLS="2">14</CELL>
<CELL COLS="2">15</CELL>
<CELL COLS="2">16</CELL>
<CELL COLS="2">17</CELL>
<CELL COLS="2">18</CELL>
<CELL COLS="2">19</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tall &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>68</CELL>
<CELL>3</CELL>
<CELL>61</CELL>
<CELL>44</CELL>
<CELL>56</CELL>
<CELL>27</CELL>
<CELL>51</CELL>
<CELL>59</CELL>
<CELL>48</CELL>
<CELL>8</CELL>
<CELL>44</CELL>
<CELL>47</CELL>
<CELL>41</CELL>
<CELL>51</CELL>
<CELL>39</CELL>
<CELL>15</CELL>
<CELL>36</CELL>
<CELL>57</CELL>
<CELL>34</CELL>
<CELL>51</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadow.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>66</CELL>
<CELL>55</CELL>
<CELL>60</CELL>
<CELL>47</CELL>
<CELL>55</CELL>
<CELL>40</CELL>
<CELL>51</CELL>
<CELL>18</CELL>
<CELL>47</CELL>
<CELL>32</CELL>
<CELL>44</CELL>
<CELL>16</CELL>
<CELL>41</CELL>
<CELL>24</CELL>
<CELL>38</CELL>
<CELL>51</CELL>
<CELL>36</CELL>
<CELL>34</CELL>
<CELL>34</CELL>
<CELL>31</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>65</CELL>
<CELL>49</CELL>
<CELL>95</CELL>
<CELL>52</CELL>
<CELL>54</CELL>
<CELL>53</CELL>
<CELL>50</CELL>
<CELL>38</CELL>
<CELL>46</CELL>
<CELL>58</CELL>
<CELL>43</CELL>
<CELL>46</CELL>
<CELL>40</CELL>
<CELL>57</CELL>
<CELL>38</CELL>
<CELL>27</CELL>
<CELL>36</CELL>
<CELL>13</CELL>
<CELL>34</CELL>
<CELL>12</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>64</CELL>
<CELL>45</CELL>
<CELL>85</CELL>
<CELL>59</CELL>
<CELL>54</CELL>
<CELL>8</CELL>
<CELL>49</CELL>
<CELL>59</CELL>
<CELL>46</CELL>
<CELL>24</CELL>
<CELL>43</CELL>
<CELL>16</CELL>
<CELL>40</CELL>
<CELL>31</CELL>
<CELL>38</CELL>
<CELL>4</CELL>
<CELL>35</CELL>
<CELL>52</CELL>
<CELL>33</CELL>
<CELL>53</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>63</CELL>
<CELL>43</CELL>
<CELL>85</CELL>
<CELL>7</CELL>
<CELL>53</CELL>
<CELL>24</CELL>
<CELL>49</CELL>
<CELL>21</CELL>
<CELL>45</CELL>
<CELL>51</CELL>
<CELL>42</CELL>
<CELL>47</CELL>
<CELL>40</CELL>
<CELL>5</CELL>
<CELL>37</CELL>
<CELL>41</CELL>
<CELL>35</CELL>
<CELL>31</CELL>
<CELL>33</CELL>
<CELL>35</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>62</CELL>
<CELL>43</CELL>
<CELL>57</CELL>
<CELL>16</CELL>
<CELL>52</CELL>
<CELL>41</CELL>
<CELL>48</CELL>
<CELL>44</CELL>
<CELL>45</CELL>
<CELL>19</CELL>
<CELL>42</CELL>
<CELL>19</CELL>
<CELL>39</CELL>
<CELL>40</CELL>
<CELL>37</CELL>
<CELL>18</CELL>
<CELL>35</CELL>
<CELL>11</CELL>
<CELL>33</CELL>
<CELL>16</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>61</CELL>
<CELL>44</CELL>
<CELL>56</CELL>
<CELL>27</CELL>
<CELL>51</CELL>
<CELL>59</CELL>
<CELL>48</CELL>
<CELL>8</CELL>
<CELL>44</CELL>
<CELL>47</CELL>
<CELL>41</CELL>
<CELL>51</CELL>
<CELL>39</CELL>
<CELL>15</CELL>
<CELL>36</CELL>
<CELL>56</CELL>
<CELL>34</CELL>
<CELL>51</CELL>
<CELL>32</CELL>
<CELL>58</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">20</CELL>
<CELL COLS="2">21</CELL>
<CELL COLS="2">22</CELL>
<CELL COLS="2">23</CELL>
<CELL COLS="2">24</CELL>
<CELL COLS="2">25</CELL>
<CELL COLS="2">26</CELL>
<CELL COLS="2">27</CELL>
<CELL COLS="2">28</CELL>
<CELL COLS="2">29</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tall &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>32</CELL>
<CELL>58</CELL>
<CELL>31</CELL>
<CELL>16</CELL>
<CELL>29</CELL>
<CELL>42</CELL>
<CELL>28</CELL>
<CELL>16</CELL>
<CELL>26</CELL>
<CELL>57</CELL>
<CELL>25</CELL>
<CELL>44</CELL>
<CELL>24</CELL>
<CELL>36</CELL>
<CELL>23</CELL>
<CELL>33</CELL>
<CELL>22</CELL>
<CELL>34</CELL>
<CELL>21</CELL>
<CELL>39</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadow.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>32</CELL>
<CELL>40</CELL>
<CELL>31</CELL>
<CELL>0</CELL>
<CELL>29</CELL>
<CELL>27</CELL>
<CELL>28</CELL>
<CELL>3</CELL>
<CELL>26</CELL>
<CELL>45</CELL>
<CELL>25</CELL>
<CELL>52</CELL>
<CELL>24</CELL>
<CELL>25</CELL>
<CELL>23</CELL>
<CELL>23</CELL>
<CELL>22</CELL>
<CELL>25</CELL>
<CELL>21</CELL>
<CELL><GAP DESC="illegible" EXTENT="1 letter">0</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>32</CELL>
<CELL>23</CELL>
<CELL>30</CELL>
<CELL>44</CELL>
<CELL>29</CELL>
<CELL>13</CELL>
<CELL>27</CELL>
<CELL>49</CELL>
<CELL>26</CELL>
<CELL>32</CELL>
<CELL>25</CELL>
<CELL>21</CELL>
<CELL>24</CELL>
<CELL>15</CELL>
<CELL>23</CELL>
<CELL>13</CELL>
<CELL>22</CELL>
<CELL>15</CELL>
<CELL>21</CELL>
<CELL>21</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>32</CELL>
<CELL>6</CELL>
<CELL>30</CELL>
<CELL>28</CELL>
<CELL>28</CELL>
<CELL>58</CELL>
<CELL>27</CELL>
<CELL>36</CELL>
<CELL>26</CELL>
<CELL>20</CELL>
<CELL>25</CELL>
<CELL>10</CELL>
<CELL>24</CELL>
<CELL>4</CELL>
<CELL>23</CELL>
<CELL>3</CELL>
<CELL>22</CELL>
<CELL>6</CELL>
<CELL>21</CELL>
<CELL>13</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>31</CELL>
<CELL>49</CELL>
<CELL>30</CELL>
<CELL>12</CELL>
<CELL>28</CELL>
<CELL>44</CELL>
<CELL>27</CELL>
<CELL>23</CELL>
<CELL>26</CELL>
<CELL>8</CELL>
<CELL>24</CELL>
<CELL>58</CELL>
<CELL>23</CELL>
<CELL>54</CELL>
<CELL>22</CELL>
<CELL>53</CELL>
<CELL>21</CELL>
<CELL>57</CELL>
<CELL>21</CELL>
<CELL>4</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>31</CELL>
<CELL>32</CELL>
<CELL>29</CELL>
<CELL>57</CELL>
<CELL>28</CELL>
<CELL>30</CELL>
<CELL>27</CELL>
<CELL>10</CELL>
<CELL>25</CELL>
<CELL>56</CELL>
<CELL>24</CELL>
<CELL>47</CELL>
<CELL>23</CELL>
<CELL>43</CELL>
<CELL>22</CELL>
<CELL>44</CELL>
<CELL>21</CELL>
<CELL>48</CELL>
<CELL>20</CELL>
<CELL>56</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>31</CELL>
<CELL>16</CELL>
<CELL>29</CELL>
<CELL>42</CELL>
<CELL>28</CELL>
<CELL>16</CELL>
<CELL>26</CELL>
<CELL>57</CELL>
<CELL>25</CELL>
<CELL>44</CELL>
<CELL>24</CELL>
<CELL>36</CELL>
<CELL>23</CELL>
<CELL>33</CELL>
<CELL>22</CELL>
<CELL>34</CELL>
<CELL>21</CELL>
<CELL>39</CELL>
<CELL>20</CELL>
<CELL>47</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><PB N="102" REF="60">
<TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">30</CELL>
<CELL COLS="2">31</CELL>
<CELL COLS="2">32</CELL>
<CELL COLS="2">33</CELL>
<CELL COLS="2">34</CELL>
<CELL COLS="2">35</CELL>
<CELL COLS="2">36</CELL>
<CELL COLS="2">37</CELL>
<CELL COLS="2">38</CELL>
<CELL COLS="2">39</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tall &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>20</CELL>
<CELL>47</CELL>
<CELL>19</CELL>
<CELL>58</CELL>
<CELL>19</CELL>
<CELL>12</CELL>
<CELL>18</CELL>
<CELL>29</CELL>
<CELL>17</CELL>
<CELL>47</CELL>
<CELL>17</CELL>
<CELL>8</CELL>
<CELL>16</CELL>
<CELL>31</CELL>
<CELL>15</CELL>
<CELL>55</CELL>
<CELL>15</CELL>
<CELL>22</CELL>
<CELL>14</CELL>
<CELL>49</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadow.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>20</CELL>
<CELL><GAP DESC="illegible" EXTENT="1 letter">9</CELL>
<CELL>19</CELL>
<CELL>50</CELL>
<CELL>19</CELL>
<CELL>5</CELL>
<CELL>18</CELL>
<CELL>21</CELL>
<CELL>17</CELL>
<CELL>41</CELL>
<CELL>17</CELL>
<CELL>2</CELL>
<CELL>16</CELL>
<CELL>25</CELL>
<CELL>15</CELL>
<CELL>50</CELL>
<CELL>15</CELL>
<CELL>16</CELL>
<CELL>14</CELL>
<CELL>44</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>20</CELL>
<CELL>31</CELL>
<CELL>19</CELL>
<CELL>43</CELL>
<CELL>18</CELL>
<CELL>57</CELL>
<CELL>18</CELL>
<CELL>15</CELL>
<CELL>17</CELL>
<CELL>34</CELL>
<CELL>16</CELL>
<CELL>56</CELL>
<CELL>16</CELL>
<CELL>19</CELL>
<CELL>15</CELL>
<CELL>44</CELL>
<CELL>15</CELL>
<CELL>11</CELL>
<CELL>14</CELL>
<CELL>39</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>20</CELL>
<CELL>22</CELL>
<CELL>19</CELL>
<CELL>35</CELL>
<CELL>18</CELL>
<CELL>50</CELL>
<CELL>18</CELL>
<CELL>8</CELL>
<CELL>17</CELL>
<CELL>28</CELL>
<CELL>16</CELL>
<CELL>49</CELL>
<CELL>16</CELL>
<CELL>13</CELL>
<CELL>15</CELL>
<CELL>38</CELL>
<CELL>15</CELL>
<CELL>5</CELL>
<CELL>14</CELL>
<CELL>33</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>20</CELL>
<CELL>14</CELL>
<CELL>19</CELL>
<CELL>27</CELL>
<CELL>18</CELL>
<CELL>43</CELL>
<CELL>18</CELL>
<CELL>1</CELL>
<CELL>17</CELL>
<CELL>21</CELL>
<CELL>16</CELL>
<CELL>43</CELL>
<CELL>16</CELL>
<CELL>7</CELL>
<CELL>15</CELL>
<CELL>33</CELL>
<CELL>15</CELL>
<CELL>0</CELL>
<CELL>14</CELL>
<CELL>28</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>20</CELL>
<CELL>6</CELL>
<CELL>19</CELL>
<CELL>20</CELL>
<CELL>18</CELL>
<CELL>36</CELL>
<CELL>17</CELL>
<CELL>54</CELL>
<CELL>17</CELL>
<CELL>15</CELL>
<CELL>16</CELL>
<CELL>37</CELL>
<CELL>16</CELL>
<CELL>1</CELL>
<CELL>15</CELL>
<CELL>27</CELL>
<CELL>14</CELL>
<CELL>54</CELL>
<CELL>14</CELL>
<CELL>23</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>19</CELL>
<CELL>58</CELL>
<CELL>19</CELL>
<CELL>12</CELL>
<CELL>18</CELL>
<CELL>29</CELL>
<CELL>17</CELL>
<CELL>47</CELL>
<CELL>17</CELL>
<CELL>8</CELL>
<CELL>16</CELL>
<CELL>31</CELL>
<CELL>15</CELL>
<CELL>55</CELL>
<CELL>15</CELL>
<CELL>22</CELL>
<CELL>14</CELL>
<CELL>49</CELL>
<CELL>14</CELL>
<CELL>18</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">40</CELL>
<CELL COLS="2">41</CELL>
<CELL COLS="2">42</CELL>
<CELL COLS="2">43</CELL>
<CELL COLS="2">44</CELL>
<CELL COLS="2">45</CELL>
<CELL COLS="2">46</CELL>
<CELL COLS="2">47</CELL>
<CELL COLS="2">48</CELL>
<CELL COLS="2">49</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tall &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>14</CELL>
<CELL>18</CELL>
<CELL>13</CELL>
<CELL>48</CELL>
<CELL>13</CELL>
<CELL>20</CELL>
<CELL>12</CELL>
<CELL>52</CELL>
<CELL>12</CELL>
<CELL>26</CELL>
<CELL>12</CELL>
<CELL>0</CELL>
<CELL>11</CELL>
<CELL>35</CELL>
<CELL>11</CELL>
<CELL>11</CELL>
<CELL>10</CELL>
<CELL>48</CELL>
<CELL>10</CELL>
<CELL>26</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadow.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>14</CELL>
<CELL>13</CELL>
<CELL>13</CELL>
<CELL>43</CELL>
<CELL>13</CELL>
<CELL>15</CELL>
<CELL>12</CELL>
<CELL>48</CELL>
<CELL>12</CELL>
<CELL>21</CELL>
<CELL>11</CELL>
<CELL>56</CELL>
<CELL>11</CELL>
<CELL>31</CELL>
<CELL>11</CELL>
<CELL>8</CELL>
<CELL>10</CELL>
<CELL>45</CELL>
<CELL>10</CELL>
<CELL>22</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>14</CELL>
<CELL>8</CELL>
<CELL>13</CELL>
<CELL>39</CELL>
<CELL>13</CELL>
<CELL>10</CELL>
<CELL>12</CELL>
<CELL>42</CELL>
<CELL>12</CELL>
<CELL>17</CELL>
<CELL>11</CELL>
<CELL>52</CELL>
<CELL>11</CELL>
<CELL>27</CELL>
<CELL>11</CELL>
<CELL>4</CELL>
<CELL>10</CELL>
<CELL>41</CELL>
<CELL>10</CELL>
<CELL>19</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>14</CELL>
<CELL>3</CELL>
<CELL>13</CELL>
<CELL>34</CELL>
<CELL>13</CELL>
<CELL>6</CELL>
<CELL>12</CELL>
<CELL>39</CELL>
<CELL>12</CELL>
<CELL>13</CELL>
<CELL>11</CELL>
<CELL>48</CELL>
<CELL>11</CELL>
<CELL>23</CELL>
<CELL>11</CELL>
<CELL>0</CELL>
<CELL>10</CELL>
<CELL>37</CELL>
<CELL>10</CELL>
<CELL>15</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>13</CELL>
<CELL>58</CELL>
<CELL>13</CELL>
<CELL>29</CELL>
<CELL>13</CELL>
<CELL>1</CELL>
<CELL>12</CELL>
<CELL>34</CELL>
<CELL>12</CELL>
<CELL>8</CELL>
<CELL>11</CELL>
<CELL>43</CELL>
<CELL>11</CELL>
<CELL>19</CELL>
<CELL>10</CELL>
<CELL>56</CELL>
<CELL>10</CELL>
<CELL>33</CELL>
<CELL>10</CELL>
<CELL>11</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>13</CELL>
<CELL>53</CELL>
<CELL>13</CELL>
<CELL>24</CELL>
<CELL>12</CELL>
<CELL>57</CELL>
<CELL>12</CELL>
<CELL>30</CELL>
<CELL>12</CELL>
<CELL>4</CELL>
<CELL>11</CELL>
<CELL>39</CELL>
<CELL>11</CELL>
<CELL>15</CELL>
<CELL>10</CELL>
<CELL>52</CELL>
<CELL>10</CELL>
<CELL>30</CELL>
<CELL>10</CELL>
<CELL>8</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>13</CELL>
<CELL>48</CELL>
<CELL>13</CELL>
<CELL>20</CELL>
<CELL>12</CELL>
<CELL>52</CELL>
<CELL>12</CELL>
<CELL>26</CELL>
<CELL>12</CELL>
<CELL>0</CELL>
<CELL>11</CELL>
<CELL>35</CELL>
<CELL>11</CELL>
<CELL>11</CELL>
<CELL>10</CELL>
<CELL>48</CELL>
<CELL>10</CELL>
<CELL>26</CELL>
<CELL>10</CELL>
<CELL>4</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><PB N="103" REF="60">
<TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">50</CELL>
<CELL COLS="2">51</CELL>
<CELL COLS="2">52</CELL>
<CELL COLS="2">53</CELL>
<CELL COLS="2">54</CELL>
<CELL COLS="2">55</CELL>
<CELL COLS="2">56</CELL>
<CELL COLS="2">57</CELL>
<CELL COLS="2">58</CELL>
<CELL COLS="2">59</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tal &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>10</CELL>
<CELL>4</CELL>
<CELL>9</CELL>
<CELL>43</CELL>
<CELL>9</CELL>
<CELL>23</CELL>
<CELL>9</CELL>
<CELL>3</CELL>
<CELL>8</CELL>
<CELL>43</CELL>
<CELL>8</CELL>
<CELL>24</CELL>
<CELL>8</CELL>
<CELL>6</CELL>
<CELL>7</CELL>
<CELL>48</CELL>
<CELL>7</CELL>
<CELL>30</CELL>
<CELL>7</CELL>
<CELL>13</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadovv.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>10</CELL>
<CELL>1</CELL>
<CELL>9</CELL>
<CELL>40</CELL>
<CELL>9</CELL>
<CELL>19</CELL>
<CELL>8</CELL>
<CELL>59</CELL>
<CELL>8</CELL>
<CELL>40</CELL>
<CELL>8</CELL>
<CELL>21</CELL>
<CELL>8</CELL>
<CELL>3</CELL>
<CELL>7</CELL>
<CELL>45</CELL>
<CELL>7</CELL>
<CELL>27</CELL>
<CELL>7</CELL>
<CELL>10</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>9</CELL>
<CELL>57</CELL>
<CELL>9</CELL>
<CELL>36</CELL>
<CELL>9</CELL>
<CELL>16</CELL>
<CELL>8</CELL>
<CELL>56</CELL>
<CELL>8</CELL>
<CELL>37</CELL>
<CELL>8</CELL>
<CELL>18</CELL>
<CELL>8</CELL>
<CELL>0</CELL>
<CELL>7</CELL>
<CELL>42</CELL>
<CELL>7</CELL>
<CELL>24</CELL>
<CELL>7</CELL>
<CELL>7</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>9</CELL>
<CELL>54</CELL>
<CELL>9</CELL>
<CELL>33</CELL>
<CELL>9</CELL>
<CELL>12</CELL>
<CELL>8</CELL>
<CELL>53</CELL>
<CELL>8</CELL>
<CELL>34</CELL>
<CELL>8</CELL>
<CELL>15</CELL>
<CELL>7</CELL>
<CELL>57</CELL>
<CELL>7</CELL>
<CELL>39</CELL>
<CELL>7</CELL>
<CELL>21</CELL>
<CELL>7</CELL>
<CELL>4</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>9</CELL>
<CELL>50</CELL>
<CELL>9</CELL>
<CELL>29</CELL>
<CELL>9</CELL>
<CELL>9</CELL>
<CELL>8</CELL>
<CELL>50</CELL>
<CELL>8</CELL>
<CELL>30</CELL>
<CELL>8</CELL>
<CELL>12</CELL>
<CELL>7</CELL>
<CELL>54</CELL>
<CELL>7</CELL>
<CELL>36</CELL>
<CELL>7</CELL>
<CELL>18</CELL>
<CELL>7</CELL>
<CELL>1</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>9</CELL>
<CELL>47</CELL>
<CELL>9</CELL>
<CELL>26</CELL>
<CELL>9</CELL>
<CELL>6</CELL>
<CELL>8</CELL>
<CELL>46</CELL>
<CELL>8</CELL>
<CELL>27</CELL>
<CELL>8</CELL>
<CELL>9</CELL>
<CELL>7</CELL>
<CELL>51</CELL>
<CELL>7</CELL>
<CELL>33</CELL>
<CELL>7</CELL>
<CELL>15</CELL>
<CELL>6</CELL>
<CELL>59</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>9</CELL>
<CELL>43</CELL>
<CELL>9</CELL>
<CELL>23</CELL>
<CELL>9</CELL>
<CELL>3</CELL>
<CELL>8</CELL>
<CELL>43</CELL>
<CELL>8</CELL>
<CELL>24</CELL>
<CELL>8</CELL>
<CELL>6</CELL>
<CELL>7</CELL>
<CELL>48</CELL>
<CELL>7</CELL>
<CELL>30</CELL>
<CELL>7</CELL>
<CELL>13</CELL>
<CELL>6</CELL>
<CELL>56</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">60</CELL>
<CELL COLS="2">61</CELL>
<CELL COLS="2">62</CELL>
<CELL COLS="2">63</CELL>
<CELL COLS="2">64</CELL>
<CELL COLS="2">65</CELL>
<CELL COLS="2">66</CELL>
<CELL COLS="2">67</CELL>
<CELL COLS="2">68</CELL>
<CELL COLS="2">69</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tall &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>6</CELL>
<CELL>56</CELL>
<CELL>6</CELL>
<CELL>39</CELL>
<CELL>6</CELL>
<CELL>23</CELL>
<CELL>6</CELL>
<CELL>7</CELL>
<CELL>5</CELL>
<CELL>51</CELL>
<CELL>5</CELL>
<CELL>36</CELL>
<CELL>5</CELL>
<CELL>21</CELL>
<CELL>5</CELL>
<CELL>6</CELL>
<CELL>4</CELL>
<CELL>51</CELL>
<CELL>4</CELL>
<CELL>36</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadow.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>6</CELL>
<CELL>53</CELL>
<CELL>6</CELL>
<CELL>36</CELL>
<CELL>6</CELL>
<CELL>20</CELL>
<CELL>6</CELL>
<CELL>4</CELL>
<CELL>5</CELL>
<CELL>49</CELL>
<CELL>5</CELL>
<CELL>33</CELL>
<CELL>5</CELL>
<CELL>18</CELL>
<CELL>5</CELL>
<CELL>3</CELL>
<CELL>4</CELL>
<CELL>48</CELL>
<CELL>4</CELL>
<CELL>34</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>6</CELL>
<CELL>50</CELL>
<CELL>6</CELL>
<CELL>34</CELL>
<CELL>6</CELL>
<CELL>17</CELL>
<CELL>6</CELL>
<CELL>2</CELL>
<CELL>5</CELL>
<CELL>46</CELL>
<CELL>5</CELL>
<CELL>31</CELL>
<CELL>5</CELL>
<CELL>16</CELL>
<CELL>5</CELL>
<CELL>1</CELL>
<CELL>4</CELL>
<CELL>46</CELL>
<CELL>4</CELL>
<CELL>32</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>6</CELL>
<CELL>47</CELL>
<CELL>6</CELL>
<CELL>31</CELL>
<CELL>6</CELL>
<CELL>15</CELL>
<CELL>5</CELL>
<CELL>59</CELL>
<CELL>5</CELL>
<CELL>43</CELL>
<CELL>5</CELL>
<CELL>28</CELL>
<CELL>5</CELL>
<CELL>13</CELL>
<CELL>4</CELL>
<CELL>58</CELL>
<CELL>4</CELL>
<CELL>44</CELL>
<CELL>4</CELL>
<CELL>29</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>6</CELL>
<CELL>45</CELL>
<CELL>6</CELL>
<CELL>28</CELL>
<CELL>6</CELL>
<CELL>12</CELL>
<CELL>5</CELL>
<CELL>56</CELL>
<CELL>5</CELL>
<CELL>41</CELL>
<CELL>5</CELL>
<CELL>26</CELL>
<CELL>5</CELL>
<CELL>11</CELL>
<CELL>4</CELL>
<CELL>56</CELL>
<CELL>4</CELL>
<CELL>41</CELL>
<CELL>4</CELL>
<CELL>27</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>6</CELL>
<CELL>42</CELL>
<CELL>6</CELL>
<CELL>26</CELL>
<CELL>6</CELL>
<CELL>10</CELL>
<CELL>5</CELL>
<CELL>54</CELL>
<CELL>5</CELL>
<CELL>38</CELL>
<CELL>5</CELL>
<CELL>23</CELL>
<CELL>5</CELL>
<CELL>8</CELL>
<CELL>4</CELL>
<CELL>53</CELL>
<CELL>4</CELL>
<CELL>39</CELL>
<CELL>4</CELL>
<CELL>24</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>6</CELL>
<CELL>39</CELL>
<CELL>6</CELL>
<CELL>23</CELL>
<CELL>6</CELL>
<CELL>7</CELL>
<CELL>5</CELL>
<CELL>51</CELL>
<CELL>5</CELL>
<CELL>36</CELL>
<CELL>5</CELL>
<CELL>21</CELL>
<CELL>5</CELL>
<CELL>6</CELL>
<CELL>4</CELL>
<CELL>51</CELL>
<CELL>4</CELL>
<CELL>36</CELL>
<CELL>4</CELL>
<CELL>22</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><PB N="104" REF="61">
<TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">70</CELL>
<CELL COLS="2">71</CELL>
<CELL COLS="2">72</CELL>
<CELL COLS="2">73</CELL>
<CELL COLS="2">74</CELL>
<CELL COLS="2">75</CELL>
<CELL COLS="2">76</CELL>
<CELL COLS="2">77</CELL>
<CELL COLS="2">78</CELL>
<CELL COLS="2">79</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tal &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>4</CELL>
<CELL>22</CELL>
<CELL>4</CELL>
<CELL>8</CELL>
<CELL>3</CELL>
<CELL>54</CELL>
<CELL>3</CELL>
<CELL>40</CELL>
<CELL>3</CELL>
<CELL>26</CELL>
<CELL>3</CELL>
<CELL>13</CELL>
<CELL>3</CELL>
<CELL>0</CELL>
<CELL>2</CELL>
<CELL>46</CELL>
<CELL>2</CELL>
<CELL>33</CELL>
<CELL>2</CELL>
<CELL>20</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadovv.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>4</CELL>
<CELL>20</CELL>
<CELL>4</CELL>
<CELL>6</CELL>
<CELL>3</CELL>
<CELL>52</CELL>
<CELL>3</CELL>
<CELL>38</CELL>
<CELL>3</CELL>
<CELL>24</CELL>
<CELL>3</CELL>
<CELL>11</CELL>
<CELL>2</CELL>
<CELL>56</CELL>
<CELL>2</CELL>
<CELL>44</CELL>
<CELL>2</CELL>
<CELL>31</CELL>
<CELL>2</CELL>
<CELL>18</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>4</CELL>
<CELL>17</CELL>
<CELL>4</CELL>
<CELL>3</CELL>
<CELL>3</CELL>
<CELL>49</CELL>
<CELL>3</CELL>
<CELL>36</CELL>
<CELL>3</CELL>
<CELL>22</CELL>
<CELL>3</CELL>
<CELL>8</CELL>
<CELL>2</CELL>
<CELL>55</CELL>
<CELL>2</CELL>
<CELL>42</CELL>
<CELL>2</CELL>
<CELL>29</CELL>
<CELL>2</CELL>
<CELL>16</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>4</CELL>
<CELL>15</CELL>
<CELL>4</CELL>
<CELL>1</CELL>
<CELL>3</CELL>
<CELL>47</CELL>
<CELL>3</CELL>
<CELL>33</CELL>
<CELL>3</CELL>
<CELL>20</CELL>
<CELL>3</CELL>
<CELL>6</CELL>
<CELL>2</CELL>
<CELL>53</CELL>
<CELL>2</CELL>
<CELL>40</CELL>
<CELL>2</CELL>
<CELL>26</CELL>
<CELL>2</CELL>
<CELL>13</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>4</CELL>
<CELL>13</CELL>
<CELL>3</CELL>
<CELL>59</CELL>
<CELL>3</CELL>
<CELL>45</CELL>
<CELL>3</CELL>
<CELL>31</CELL>
<CELL>3</CELL>
<CELL>17</CELL>
<CELL>3</CELL>
<CELL>4</CELL>
<CELL>2</CELL>
<CELL>51</CELL>
<CELL>2</CELL>
<CELL>37</CELL>
<CELL>2</CELL>
<CELL>24</CELL>
<CELL>2</CELL>
<CELL>11</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>4</CELL>
<CELL>10</CELL>
<CELL>3</CELL>
<CELL>56</CELL>
<CELL>3</CELL>
<CELL>42</CELL>
<CELL>3</CELL>
<CELL>29</CELL>
<CELL>3</CELL>
<CELL>15</CELL>
<CELL>3</CELL>
<CELL>2</CELL>
<CELL>2</CELL>
<CELL>48</CELL>
<CELL>2</CELL>
<CELL>35</CELL>
<CELL>2</CELL>
<CELL>22</CELL>
<CELL>2</CELL>
<CELL>9</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>4</CELL>
<CELL>8</CELL>
<CELL>3</CELL>
<CELL>54</CELL>
<CELL>3</CELL>
<CELL>40</CELL>
<CELL>3</CELL>
<CELL>22</CELL>
<CELL>3</CELL>
<CELL>13</CELL>
<CELL>3</CELL>
<CELL>0</CELL>
<CELL>2</CELL>
<CELL>46</CELL>
<CELL>2</CELL>
<CELL>33</CELL>
<CELL>2</CELL>
<CELL>20</CELL>
<CELL>2</CELL>
<CELL>7</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
<P><TABLE>
<ROW ROLE="label">
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
<CELL COLS="2">80</CELL>
<CELL COLS="2">81</CELL>
<CELL COLS="2">82</CELL>
<CELL COLS="2">83</CELL>
<CELL COLS="2">84</CELL>
<CELL COLS="2">85</CELL>
<CELL COLS="2">86</CELL>
<CELL COLS="2">87</CELL>
<CELL COLS="2">88</CELL>
<CELL COLS="2">89</CELL>
<CELL ROWS="3" COLS="2">&nbsp;</CELL>
</ROW>
<ROW ROLE="label">
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
<CELL COLS="2">S</CELL>
</ROW>
<ROW ROLE="label">
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
<CELL>p</CELL>
<CELL>m</CELL>
</ROW>
<ROW>
<CELL ROLE="label" ROWS="7">Horizo~tall &s;hadow</CELL>
<CELL ROLE="label">0</CELL>
<CELL>2</CELL>
<CELL>7</CELL>
<CELL>1</CELL>
<CELL>54</CELL>
<CELL>1</CELL>
<CELL>41</CELL>
<CELL>1</CELL>
<CELL>28</CELL>
<CELL>1</CELL>
<CELL>16</CELL>
<CELL>1</CELL>
<CELL>3</CELL>
<CELL>0</CELL>
<CELL>50</CELL>
<CELL>0</CELL>
<CELL>38</CELL>
<CELL>0</CELL>
<CELL>25</CELL>
<CELL>0</CELL>
<CELL>13</CELL>
<CELL ROLE="label">60</CELL>
<CELL ROLE="label" ROWS="7">Verticall &s;hadow.</CELL>
</ROW>
<ROW>
<CELL ROLE="label">10</CELL>
<CELL>2</CELL>
<CELL>5</CELL>
<CELL>1</CELL>
<CELL>52</CELL>
<CELL>1</CELL>
<CELL>39</CELL>
<CELL>1</CELL>
<CELL>26</CELL>
<CELL>1</CELL>
<CELL>14</CELL>
<CELL>1</CELL>
<CELL>1</CELL>
<CELL>0</CELL>
<CELL>48</CELL>
<CELL>0</CELL>
<CELL>36</CELL>
<CELL>0</CELL>
<CELL>23</CELL>
<CELL>0</CELL>
<CELL>10</CELL>
<CELL ROLE="label">50</CELL>
</ROW>
<ROW>
<CELL ROLE="label">20</CELL>
<CELL>2</CELL>
<CELL>3</CELL>
<CELL>1</CELL>
<CELL>50</CELL>
<CELL>1</CELL>
<CELL>37</CELL>
<CELL>1</CELL>
<CELL>24</CELL>
<CELL>1</CELL>
<CELL>11</CELL>
<CELL>0</CELL>
<CELL>50</CELL>
<CELL>0</CELL>
<CELL>46</CELL>
<CELL>2</CELL>
<CELL>34</CELL>
<CELL>0</CELL>
<CELL>21</CELL>
<CELL>0</CELL>
<CELL>8</CELL>
<CELL ROLE="label">40</CELL>
</ROW>
<ROW>
<CELL ROLE="label">30</CELL>
<CELL>2</CELL>
<CELL>0</CELL>
<CELL>1</CELL>
<CELL>48</CELL>
<CELL>1</CELL>
<CELL>35</CELL>
<CELL>1</CELL>
<CELL>22</CELL>
<CELL>1</CELL>
<CELL>9</CELL>
<CELL>0</CELL>
<CELL>57</CELL>
<CELL>0</CELL>
<CELL>44</CELL>
<CELL>0</CELL>
<CELL>31</CELL>
<CELL>0</CELL>
<CELL>19</CELL>
<CELL>0</CELL>
<CELL>6</CELL>
<CELL ROLE="label">30</CELL>
</ROW>
<ROW>
<CELL ROLE="label">40</CELL>
<CELL>1</CELL>
<CELL>58</CELL>
<CELL>1</CELL>
<CELL>45</CELL>
<CELL>1</CELL>
<CELL>33</CELL>
<CELL>1</CELL>
<CELL>20</CELL>
<CELL>1</CELL>
<CELL>7</CELL>
<CELL>0</CELL>
<CELL>55</CELL>
<CELL>0</CELL>
<CELL>42</CELL>
<CELL>0</CELL>
<CELL>29</CELL>
<CELL>0</CELL>
<CELL>17</CELL>
<CELL>0</CELL>
<CELL>4</CELL>
<CELL ROLE="label">20</CELL>
</ROW>
<ROW>
<CELL ROLE="label">50</CELL>
<CELL>1</CELL>
<CELL>56</CELL>
<CELL>1</CELL>
<CELL>43</CELL>
<CELL>1</CELL>
<CELL>31</CELL>
<CELL>1</CELL>
<CELL>18</CELL>
<CELL>1</CELL>
<CELL>5</CELL>
<CELL>0</CELL>
<CELL>32</CELL>
<CELL>0</CELL>
<CELL>40</CELL>
<CELL>0</CELL>
<CELL>27</CELL>
<CELL>0</CELL>
<CELL>15</CELL>
<CELL>0</CELL>
<CELL>2</CELL>
<CELL ROLE="label">10</CELL>
</ROW>
<ROW>
<CELL ROLE="label">60</CELL>
<CELL>1</CELL>
<CELL>54</CELL>
<CELL>1</CELL>
<CELL>41</CELL>
<CELL>1</CELL>
<CELL>28</CELL>
<CELL>1</CELL>
<CELL>16</CELL>
<CELL>1</CELL>
<CELL>3</CELL>
<CELL>0</CELL>
<CELL>50</CELL>
<CELL>0</CELL>
<CELL>38</CELL>
<CELL>0</CELL>
<CELL>25</CELL>
<CELL>0</CELL>
<CELL>13</CELL>
<CELL>0</CELL>
<CELL>0</CELL>
<CELL ROLE="label">0</CELL>
</ROW>
</TABLE></P>
</DIV3>
</DIV2>
<DIV2 N="13" TYPE="chapter">
<PB N="105" REF="61">
<HEAD>CHAP XIII.</HEAD>
<ARGUMENT>
<P>Of the generall de&s;cription and u&s;e of the preceding Tablein, the pricking down and drawing the circles of decli|nation and Aximuths in any planes.</P>
</ARGUMENT>
<P>_THe Table you &s;ee con&s;i&s;teth of 11 columns, the fir&s;t being the minutes of the Suns altitude, and the greater figures on the top are the de|grees of altitude, all the other columns con&s;i&s;t of the parts of &s;hadow, and minutes of &s;hadow, noted above with S for &s;hadow, and p m for parts and minutes of &s;hadow, an&s;werable to a gnomon divided into 12 equall parts, and it is, <HI>As the &s;ine of a known altitude of the &s;un, is to the &s;ine complement of the &s;ame altitude; &s;o the length of the Gnomon in 10 or 12 parts, to the parts of right &s;hadow:</HI> or for the ver&s;ed &s;hadow, <HI>as the &s;ine complement of the given altitude of the &s;un, to the right &s;ine of the &s;ame altitude; &s;o the &s;tyle in parts, to the length of the ver&s;ed &s;hadow</HI> So if we enter the Table with the given altitude of the Sun in the great figures, and if we &s;eeke the mi|nutes in the &s;ides, either noted with horizontall or verti|call &s;hadow, according as your plane is, it &s;hall give you the length of the &s;hadow in parts and minutes in the com|mon angle of meeting together. As if we look for 50 de. 40 m. the meeting of both in the Table &s;hall be 9 parts 50 min. for the length of the right &s;hadow on a horizontall plane: But for the ver&s;ed &s;hadow, take the complement of the altitude of the Sun, and the minutes in the right &s;ide of the Table, titled verticall &s;hadow, and the common area of both &s;hall give your de&s;ire. By this Table it appeareth
<PB N="106" REF="62">
fir&s;t, that the circles of altitude either on the horizontall or verticall planes are ea&s;ily drawn, con&s;icering they are no|thing el&s;e but circles of altitude, which by knowing the al|titude you will know the length of the &s;hadow, which in the horizontall Diall are perfect circles, and have the &s;ame re&s;pect unto the Horizon, as the parallels of declination have to the Equator, but in all upright planes they wil be conicall Sections, and by having the length of the &s;tyle, the altitude of the Sun may be computed by the foregoing Table with much facility, but for the more expediating of the work in pricking down the parallels of declination with the Tropicks, I have here added a Table of the altitude of the Sun for every houre of the day when the Sun enters into any of the 12 Signes.</P>
<P><TABLE>
<HEAD>A Table for the altitude of the <HI>Sun</HI> in the beginning of each <HI>Signe,</HI> for all the houres of the day for the Latitude of <HI>London.</HI></HEAD>
<ROW ROLE="label">
<CELL COLS="2">Hours.</CELL>
<CELL COLS="2"><HI>Cancer.</HI></CELL>
<CELL COLS="2"><HI>Gemini</HI> <LB><HI>Leo</HI></CELL>
<CELL COLS="2"><HI>Taurus</HI> <LB><HI>Virgo</HI></CELL>
<CELL COLS="2"><HI>Aries</HI> <LB><HI>Libra</HI></CELL>
<CELL COLS="2"><HI>Pi&s;ces</HI> <LB><HI>Scorpio</HI></CELL>
<CELL COLS="2"><HI>Aquar</HI> <LB><HI>Sagitta.</HI></CELL>
<CELL COLS="2"><HI>Capric.</HI></CELL>
</ROW>
<ROW>
<CELL COLS="2">12</CELL>
<CELL>62</CELL>
<CELL>0</CELL>
<CELL>58</CELL>
<CELL>43</CELL>
<CELL>50</CELL>
<CELL>0</CELL>
<CELL>38</CELL>
<CELL>30</CELL>
<CELL>27</CELL>
<CELL>0</CELL>
<CELL>18</CELL>
<CELL>18</CELL>
<CELL>15</CELL>
<CELL>0</CELL>
</ROW>
<ROW>
<CELL>11</CELL>
<CELL>1</CELL>
<CELL>59</CELL>
<CELL>43</CELL>
<CELL>56</CELL>
<CELL>34</CELL>
<CELL>48</CELL>
<CELL>12</CELL>
<CELL>36</CELL>
<CELL>58</CELL>
<CELL>25</CELL>
<CELL>40</CELL>
<CELL>17</CELL>
<CELL>6</CELL>
<CELL>13</CELL>
<CELL>52</CELL>
</ROW>
<ROW>
<CELL>10</CELL>
<CELL>2</CELL>
<CELL>53</CELL>
<CELL>45</CELL>
<CELL>50</CELL>
<CELL>55</CELL>
<CELL>43</CELL>
<CELL>12</CELL>
<CELL>32</CELL>
<CELL>37</CELL>
<CELL>21</CELL>
<CELL>51</CELL>
<CELL>13</CELL>
<CELL>38</CELL>
<CELL>10</CELL>
<CELL>30</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>3</CELL>
<CELL>45</CELL>
<CELL>42</CELL>
<CELL>43</CELL>
<CELL>6</CELL>
<CELL>36</CELL>
<CELL>0</CELL>
<CELL>26</CELL>
<CELL>7</CELL>
<CELL>15</CELL>
<CELL>58</CELL>
<CELL>8</CELL>
<CELL>12</CELL>
<CELL>5</CELL>
<CELL>15</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>4</CELL>
<CELL>36</CELL>
<CELL>41</CELL>
<CELL>34</CELL>
<CELL>13</CELL>
<CELL>27</CELL>
<CELL>31</CELL>
<CELL>18</CELL>
<CELL>8</CELL>
<CELL>8</CELL>
<CELL>33</CELL>
<CELL>1</CELL>
<CELL>15</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>5</CELL>
<CELL>27</CELL>
<CELL>17</CELL>
<CELL>24</CELL>
<CELL>56</CELL>
<CELL>18</CELL>
<CELL>18</CELL>
<CELL>9</CELL>
<CELL>17</CELL>
<CELL>0</CELL>
<CELL>6</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>6</CELL>
<CELL>18</CELL>
<CELL>11</CELL>
<CELL>15</CELL>
<CELL>40</CELL>
<CELL>9</CELL>
<CELL>0</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
</ROW>
<ROW>
<CELL>5</CELL>
<CELL>7</CELL>
<CELL>9</CELL>
<CELL>32</CELL>
<CELL>6</CELL>
<CELL>50</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>11</CELL>
<CELL>37</CELL>
</ROW>
<ROW>
<CELL>4</CELL>
<CELL>8</CELL>
<CELL>1</CELL>
<CELL>32</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>&nbsp;</CELL>
<CELL>21</CELL>
<CELL>40</CELL>
</ROW>
</TABLE></P>
<P>This Table is in Mr. <HI>Gunters</HI> Book, <HI>page</HI> 240 which if you de&s;ire to have the point of the Equinoctiall for a Ho|rizontall
<PB N="107" REF="62">
plane on the houre of 12, enter the Table of &s;ha|dows with 38 de. 30 m. and you &s;hall finde the length of the &s;hadow to be 15 parts 5 m. of the length of the &s;tyle di|vided into 12, which prick down on the line of 12 for the Equinoctiall point, from the foot of the &s;tyle. So if I de&s;ire the points of the Tropick of <HI>Cancer,</HI> I finde by this Table that at 12 of the clock the Sun is 62 de. high, with which I enter the Table of &s;hadows, finding the length of the &s;hadow, which I prick down on the 12 a clock line for the point of the Tropick of <HI>Cancer</HI> at the houre of 12. If for the houre of 1, I de&s;ire the point through which the parallel mu&s;t pa&s;s, looke for the houre of 1 and 11, in this la&s;t table under <HI>Cancer,</HI> and I finde the Sun to have the height of 59 de. 43 m. with which I enter the table of &s;ha|dows, and prick down the length thereof from the bottome of the &s;tyle reaching till the other foot of the Compa&s;&s;es fall on the houre for which it was intended. Doe &s;o in all the other houres, till you have pricked down the points of the parallels of declination, through which points they mu&s;t be drawn Hyperbolically. Proceed thus in the making of a Horizontall Diall, but if it be a direct verticall Diall, you &s;hall then take the length of the verticall &s;hadow out of the &s;aid Table, or work it as an Horizontal plane, only account|ing the complement of the elevation in &s;tead of the whole elevation.</P>
<P>For a declining plane you may con&s;ider it as a verticall direct in &s;ome other place, and having found out the E|quator of the plane and the &s;ub&s;tyle, you may proceed in the &s;ame manner from the foot of the &s;tyle, accounting where the &s;tyle &s;tands to be no other wayes then the me|ridian line or line of 12 in a Horizon who&s;e pole is elevated according to the complement height of the &s;tyle above
<PB N="108" REF="63">
the &s;ub&s;tyle, and &s;o prick down the length of the &s;hadows, from the foot of the &s;tyle, on every one of the Houre lines, as if it were a horizontal or Verticall plane.</P>
<P>But in this you mu&s;t be wary, remembring that you have the height of the &s;un calculated for every houre of that Latitude in the entrance of the 12 &s;ignes, in that Place where your Plane is a Horizontall plane, or otherwayes, by con|&s;idering of it as a horizontall or Verricallplane in another latitude</P>
<P>For the Azimuths, or verticall circles, &s;hewing one what point of the compa&s;&s;e the &s;un is in every houre of the day it is performed with a great deale of facility, if fir&s;t, when the &s;un is in the Equator, we doe know by the la&s;t Table of the height of the &s;un for every houre of the day and by his meridian altitude with the help of the table of &s;hadows, find out the Equinoctiall line, whether it be a Horizontall or upright direct plane, for having drawn that line at right angles with the meridian, and having the place of the Style, and length thereof in parts, and the parts of &s;hadow to all altitudes of the &s;un, being pricked down from the foot of the Style, on the Equinoctiall line, through each of tho&s;e points draw parallel lines to the meridian, or 12 a clock line on each &s;ide, which &s;hall be the Azimuths, which you mu&s;t have a care how you denominate according to the quarter of heaven in which the &s;un is in, for if the Sun be in the ea&s;terly points, the Azimuths mu&s;t be on the We&s;tern &s;ide of the plane, &s;o al&s;o the morning houres mu&s;t be on the oppo&s;ite &s;ide.</P>
<P>There are many other A&s;tronomical conclu&s;ions that are u&s;ed to be put upon planes, as the diurnall arches, &s;hewing the length of the day and night, as al&s;o the Jewi&s;h or old
<PB N="109" REF="63">
unequal houres together with the circles of po&s;ition, which with the meridian and horizon di&s;tingui&s;heth the upper he|mi&s;pheare into 6 parts commonly called the hou&s;es of Hea|ven: which if this I have writ beget any de&s;ire of the reader, I &s;hall endeavour to inlarge my &s;elf much more, in &s;hewing a demon&s;trative way, in the&s;e particulars I have la&s;t in&s;i&s;ted upon. I might heare al&s;o &s;hew you the exceeding u&s;e of the table of Right and ver&s;ed &s;hadow in the taking of heights of buildings as it may very wel appear in the &s;everall u&s;es of the quadrant in <HI>Diggs</HI> his <HI>Pantometria,</HI> &amp; in Mr. <HI>Gunters</HI> qua|drant, having the parts of right and ver&s;ed &s;hadow gradu|ated on them, to which Books I refer you.</P>
</DIV2>
<DIV2 N="14" TYPE="chapter">
<HEAD>CHAP XIV.</HEAD>
<ARGUMENT>
<P>Shewing the drawing of the Seeling Diall.</P>
</ARGUMENT>
<P>_IT is an Axiom pronounced long &s;ince, by tho&s;e who have writ of Opticall conceipts of Light and Shadow, that <HI>Omnis reflectio Luminis e&s;t &s;ecundum li|neas &s;en&s;ibiles, latitudinem habentes.</HI> And it hath with as great rea&s;on bin pro|nounced by Geometricians, that the Angles of Inci|dence and Reflection is all one; as appeareth to us by <HI>Euclides</HI> Catoptriques; and on this foundation is this conceipt of which we are now &s;peaking.</P>
<P><PB N="110" REF="64">Wherefore becau&s;e the direct beams cannot fall on the face of this plane, we mu&s;t by help of a piece of gla&s;&s;e apt to receive and reflect the light, placed &s;omwhere horizon|tally in a window, proceed to the work, which indeed is no other then a Horizontall Diall rever&s;ed, to which required a Meridian line, which you mu&s;t endeavour to draw and finde according as you are before taught, or by the helpe of the Meridian altitude of the Sun, your gla&s;&s;e being fixed marke the &s;pot that reflects upon the &s;eeling ju&s;t at 12 a clock, make that one point, and for the other point through which you mu&s;t draw your meridian line, you may finde by holding up a threed and plummet till the plummet fall perpendicular on the gla&s;&s;e, and at the other end of the line held on the &s;eeling make another mark, through both which draw the Meridian line. Now for &s;o much as the center of the Diall is a point without, and the di&s;tance be|tween the gla&s;&s;e and the &s;eeling is to be con&s;idered as the height of the &s;tyle, the gla&s;&s;e it &s;elfe repre&s;enting the cen|ter of the world, or the very apex of the &s;tyle, wee mu&s;t finde out tho&s;e two Tangents at right angles with the Me|ridian, the one neere the window, the other farther in, through &s;everall points whereof we mu&s;t draw the houre|lines. Let AB be the Meridian line found on the &s;eeling, now &s;uppo&s;e the Sun being in the highe&s;t degree of <HI>Cancer</HI> &s;hould &s;hine into the Gla&s;&s;e that is fixed in C, it &s;hall again reflect unto D, where I make a mark, then letting a plum|met fall from the top of the &s;eeling till it fall ju&s;t on C the gla&s;&s;e, from the point E, from which draw the line A B through D and E, which &s;hall be the Meridian required, if you do this ju&s;t at noon: Now if you would finde out the places where the hour-lines &s;hall cro&s;&s;e the Meridian, the Center lying without the window EC, you may work thus</P>
<P><PB N="111" REF="64">Divide the line EC into 12 parts, then may you en|ter the Table of right &amp; ver&s;ed &s;hadow, &s;eeking the degrees and minutes of Elevation of the Equator, <HI>viz.</HI> 38 deg. 30&prime;, to which an&s;wereth 15 parts 5 minutes of the parts of the Style, which prick down from E to F, and at that point draw the line FG, at right angles to the Meridian A
<FIGURE>
</FIGURE>
B, which &s;hall repre&s;ent the Equator. Now to know the center of the hour-lines, if you look again in the Table of &s;hadows 51 deg. 30 min. the elevation of the Pole, you &s;hall finde 9 parts 33 min. of &s;hadow, which added to FE, 15 parts 5 m. &s;hall give the center at B, making the whole line from F to B to be 24 parts 38 primes, and at 6 &s;hall the center of the hour-lines meet. La&s;tly, &s;uppo&s;ing the former work to be done upon the floare, for the more ea|&s;ie working, and having drawn a line repre&s;enting the Me|ridian AB if from B you prick down 9 parts 33 min. of the radius EC, and at E draw it perpendicular to AB, &amp; 15 parts 5 min. from E to F, where if you draw the line FG perpendicular to AB, al&s;o, if from the Center B you &s;hall
<PB N="112" REF="65">
proceed to make a horizontal Dial as is above taught: it &s;hall divide the lines EC and FG in &s;uch parts by draw|ing the hour-lines from the Center through tho&s;e lines, which if they are transferred from thence to the &s;eeling on each &s;ide the Meridian, upon the &s;ame line EC and FG, you have fini&s;hed, for FB &s;hal be the &s;ame as in the funda|mental Diagram I call the Semidiameter of the Horizon; and FC &s;hal be the &s;emidiameter of the Equator: by the &s;ame meanes al&s;o may be made hour-lines, on a Wall re|ceiving it's light only through &s;ome hole in a gla&s;&s;e win|dow: as al&s;o very recreative Dials on the &s;ides of Build|ings, having water or gla&s;&s;e &s;o placed, as that it may reflect the Beames according to &s;everal Azimuths: but the be&s;t way for the placing the gla&s;&s;e is, by preparing the hour|lines fir&s;t, and by a known altitude of the Sun at &s;ome known houre of the day, to mark out on that hour-line where the reflection ought to fal, and expect that houre preci&s;ely, and depre&s;&s;e or elevate the gla&s;&s;e til it fal on that &s;pot or mark a&s;&s;igned.</P>
</DIV2>
<DIV2 N="10" TYPE="chapter">
<HEAD>CHAP X.</HEAD>
<ARGUMENT>
<P>Shewing the making and u&s;e of the Cylinder Dial, who&s;e hour-lines are &s;traight, as al&s;o a Diall drawn from the &s;ame form, having no Style.</P>
</ARGUMENT>
<P>_THis may be u&s;ed on a Staff or other round, made like a Cylinder being drawn as is here de&s;cri|bed, where the right &s;ide repre&s;ent the Tro|picks, and the left &s;ide the Equinoctial: or it may be u&s;ed flat as it is in the Book; the In&s;trument as you &s;ee, is divided into months, and the bottom into
<PB N="113" REF="65">
&s;igns, and the line on the right &s;ide is a tangent to the radius of the breadth of the Pa|rallelogram, &s;er|ving to take the height of the Sun, the &s;everal Paral|lels downward running through the pricked line, in the midle, are the lines of Alti|tude, and the Pa|rallels to the E|quator are the Parallels of De|clination, num|bred on the bot|tom on a Sine of 23 de. and a half.</P>
<P><FIGURE>
</FIGURE></P>
<DIV3 TYPE="section">
<HEAD><PB N="114" REF="66">For the Altitude of the Sun.</HEAD>
<P>The u&s;e of it is fir&s;t, if it be de&s;cribed on the head of a &s;taff, to have a gnomon on the top, equal to the radius, and ju&s;t over the tangent of Altitudes, to turn it till you bring the &s;hadow of it at right angles to it &s;elf, which &s;hal denote the height required.</P>
</DIV3>
<DIV3 TYPE="section">
<HEAD>For the Houre of the Day.</HEAD>
<P>Seek the Altitude of the Sun in the midle prick't line, and the Declination in the Parallels from the Equator, and mark where the traver&s;e lines cro&s;&s;e; through the cro&s;&s;ing of the two former lines, and at the end, you &s;hal finde the figures of 2 or 10, 3 or 9, &amp;c. only the &s;ummer Houres are &s;ought in the right &s;ide&punc; where the Sun is highe&s;t, and the traver&s;e lines longe&s;t; and in the winter, the Hour is &s;ought on the left &s;ide, where the traver&s;e lines are &s;horter.</P>
</DIV3>
<DIV3 TYPE="section">
<HEAD>For the Declination and degree of the Signe.</HEAD>
<P>Seek the day of the moneth on the top marked with <HI>J.</HI> for <HI>January, F</HI> for <HI>February,</HI> &amp;c. and by the help of a hor&s;e hair or threed extended from that all along of Paral|lel of Declination, till it cut on the bottom where the &s;ignes are numbred: the down right lines that are parallel to the Equator counted toward the right hand, is the degree of the Declination of that part of the Ecliptick which is in the bottom, right again&s;t the day of the moneth &s;ought on the top.</P>
<P>The pricked line pa&s;&s;ing through the 18 degree of the Parallel of Altitude, is the line of Twy-light; this pro|jection I had of my very good friend <HI>John Hulet,</HI> Ma&s;ter of Arts&punc; and Teacher of the Mathematicks.</P>
<P>You may al&s;o make a Dyal, by preparing of a hollow
<PB N="115" REF="66">
Cylinder, and if you doe number on both ends of the Circle, on top and bottom, 15 de. from line to line; or di|vide it into 24 parts, and if from top to bottom you draw &s;treight lines, fir&s;t, by dividing the Cylinder through the middle, and only making u&s;e of one half, it &s;hal have 12 houres upon it. La&s;tly, if you cut off a piece from the bottom at an angle according to the Elevation, and turn the half Cylinder horizontal on that bottom, til the &s;hadow of one of the &s;ides fal parallel with any one of tho&s;e lines from top to bottom: which numbred as they ought, &s;hal &s;hew the hour without the u&s;e of a Style; So al&s;o may you project a Dyal on a Globe, having a round brim on the top, who&s;e projection will &s;eem &s;trange to tho&s;e that look upon it, who are ignorant of the&s;e Arts.</P>
</DIV3>
</DIV2>
<DIV2 N="16" TYPE="chapter">
<HEAD>CHAP XVI.</HEAD>
<ARGUMENT>
<P>Shewing the making of a univer&s;all Dyall on a Globe, and how to cover it, if it be required.</P>
</ARGUMENT>
<P>_A Globe (&s;aith <HI>Euclide</HI>) is made by the turning about of a &s;emicircle, &amp; the Dia|meter fixed; this Dyal if univer&s;al, will want the aide of a magnetical Needle to &s;et it, and it mu&s;t move on an Axis in an horizon as the u&s;ual Globes doe; in who&s;e Equator, let be divided into 24 houres, the proporion of the day natural, then on the Axis let a &s;emicircle move. The figure is plain in the top of the Title, &s;upported by the boy: this Globe &s;et to the ele|vation of the Pole, &amp; in the Meridian, let be placed the 12
<PB REF="67">
<FIGURE>
</FIGURE>
12 a clock line: then turne the Semicircle till it &s;ha|dow not: then doth it cro&s;&s;e the houre: which houres are drawn from the poles to each of the 24 divi&s;ions.</P>
<P>If you de&s;ire to cover the Globes, and make other inventions thereon, fir&s;t learn here to cover it ex|actly, with a pair of com|pa&s;&s;es bowed toward the points, mea&s;ure the Dia|meter of the Globe you intend to cover, which had, finde the Circumference thus; Multiply the Dia|meter by 22, and divide that product by 7, and you have your de&s;ire.</P>
<P>That Circumference, let be the line A B, which di|vide into 12 equal parts, and at the di&s;tance of three of tho&s;e parts, draw the Parallel C D, and E F,</P>
<P>A Parallel is thus drawn, take the di&s;tance you would have it a&s;under, as here it is; three of tho&s;e 12 divi&s;ions: &s;et one foot in
<PB N="117" REF="67">
A, and make the Arch at E, &amp; another at B, and make the Arch with the other foot at F, the compa&s;&s;es at the wide|ne&s;s taken, then by the outward bulks of tho&s;e Arches, draw the line E F, &s;o al&s;o draw the line C D.</P>
<P>And to divide the Circumference into parts as our ex|ample is into 12, work thus, &s;et your compa&s;&s;es in A, make the Ark B F, the compa&s;&s;es &s;o opened, &s;et again in B, and make the Ark A C, then draw the line from A to F, then mea&s;ure the di&s;tance from F to B, on the Ark, and place it on the other Arch from A to C, thence draw the line C B, then your compa&s;&s;es open at any di&s;tance, prick down one part le&s;s on both tho&s;e &s;lanting lines; then you intend to divide thereon, which is here 11: becau&s;e we would divide the line A B into 12, then draw lines from each divi&s;ion to the oppo&s;ite, that cuts the line A B in the parts of divi&s;ion.</P>
<P>But to proceed, continue the Circumference at length, to G and H, numbring from A toward G9 of tho&s;e equal parts, and from B toward H as many, which &s;hal be the Centers for each Arch.</P>
<P>So tho&s;e quarters &s;o cut out, &s;hall exactly cover the Globe, who&s;e Circumference is equal to the line A B. Thus have you a glance of the Mathematicks, &s;triking at one thing through the &s;ide of an other: for I here made one figure &s;erve for three &s;everal operations, becau&s;e I would not charge the Pre&s;s with multiplicity of figures.</P>
</DIV2>
<DIV2 N="17" TYPE="chapter">
<HEAD>CHAP XVII.</HEAD>
<ARGUMENT>
<P>Shewing the finding of the Elevation of the Pole, and there|withall a Meridian without the Declination of Sun or Starre.</P>
</ARGUMENT>
<P>_THis is done by erecting a gnomon horizontal, and at 3 times of the day to give a mark at the end of the
<PB N="118" REF="68">
Shadows: now it is certain, that repre&s;ents the Parallel of the Sunne for that day; then take three thin &s;ticks or the like, and lay them from the top of the gnomon, to the places where the &s;hadows fell, and on the&s;e three &s;o &s;tanding, lay a board to ly on all three flat, and a gno|mon in the midle of that board points to the Pole: be|cau&s;e every Parallel the Snn moves in, is parallel to the Equinoctial, and that is at right Angles, with the pole of the World.</P>
<P>Now the Meridian pa&s;&s;eth through the mo&s;t elevated place of that board or circle &s;o laid, neither can the Sun's Declination make any &s;en&s;ible difference in the &s;o &s;mall proportion of 3 or 4 houres time.</P>
</DIV2>
<DIV2 N="18" TYPE="chapter">
<HEAD>CHAP XVIII.</HEAD>
<ARGUMENT>
<P>Shewing how to finde the Altitude of the Sun, only by Scale and Compa&s;&s;es.</P>
</ARGUMENT>
<P>_WIth your Compa&s;&s;es de&s;cribe the Circle A B C D place it horizontal, with a gnomon in the Cen|ter, cro&s;&s;e it with two Diameters; then turn the board till the &s;hadow be on one of the Dia|meters, at the end of the &s;hadow, mark, as here at E, lay down al&s;o, the length of the gonmon from the Center on the other Diameter to F, from E to F drawe a right line: then take your Compa&s;&s;es, and on the
<FIGURE>
</FIGURE>
<PB N="119" REF="68">
chord of 90, take out the Radius the Ark of 60, &s;et the compa&s;&s;es &s;o in E, de&s;cribe an Arch, then take the di|&s;tance between the line E F, and the Diameter D B; which mea&s;ure on the chord of 90, and &s;o many degrees as the compa&s;&s;es extend over; &s;uch a quantity is the height of the Sun, in like manner any Angles being given, you mu&s;t mea&s;ure it by the parts of a circle.</P>
<DIV3 TYPE="section">
<HEAD>Here followeth the problematical Propo&s;itions of the Of|fice of &s;hadow, and the benefit we receive thereof.</HEAD>
<P><HI>Prop.</HI> 1 By &s;hadow, we have a plain demon&s;tration that the Sphere of <HI>Sol</HI> is higher than the Sphere of <HI>Lu|na,</HI> to confirm &s;uch as think they move in one Orbe.</P>
<P>Let the Sun be at A, in the great Circle, and the Moon at B, in the le&s;&s;er, let the Horizon be C D, now, they make one Angle of height, in re&s;pect of the Center of the Earth, not|with&s;tanding though they &s;o equally re&s;pect the Earth, as one may hinder the &s;ight of the other: yet the &s;hadow of the Sun &s;hall pa&s;&s;e by the head of the gnomon E, and ca&s;t it to F, and the beames of the Moon &s;hall pa&s;&s;e by E to G much long|er, which &s;hewes &s;hee is much lower, for the higher the light is, the &s;horter is the &s;hadow. I call the Moon a feminine, if you ask my rea&s;on, &s;hee is cold and moi&s;t, par|ticipating of the nature of Women; and we call her the Mother of moi&s;ture, but that's not all, for I have a rule for it, <HI>Nomen non cre&s;cens.</HI></P>
<P><FIGURE>
</FIGURE></P>
<P><PB N="120" REF="69"><HI>Prop.</HI> 2. By &s;hadow, we are taught the Earth is big|ger then the Moon; &s;eeing in time of a total Ob&s;curi|ty, the Moone is quite over&s;hadowed; for the &s;hadow is ca&s;t in this manner.</P>
<P><FIGURE>
</FIGURE></P>
<P>By the &s;ame we learn al&s;o, that &s;eeing the &s;hadow comes to a point, the Earth is le&s;s then the Sun: for if the o|pacous body be equal to the luminous body, then like two parallels they will never meet, but concurre in <HI>infinitum,</HI> as the&s;e following figures &s;hew.</P>
<P><FIGURE>
</FIGURE></P>
<P>Or if the luminous body were le&s;s then the opacous bo|dy: then the &s;hadow would be &s;o great in &s;o long a way, as from the Earth to the Starry Firmament, that mo&s;t of the Starres as were in oppo&s;ition to the Sun, would not ap|pear: &s;eeing they borrow their light of the Sun.</P>
<P><PB N="121" REF="69">It is al&s;o &s;ufficiently proved by &s;hadow, in the <HI>Praecognita Philo&s;ophical,</HI> that the Earth is round, and that it po&s;&s;e&s;&s;eth the middle as <HI>proprius locus</HI> from which it cannot pa&s;&s;e, and to which all heavie things tend in a right line, as their <HI>terminus ad quem.</HI></P>
<P><HI>Prop.</HI> 3. By &s;hadow we know the altitude of the Sun, as was &s;hewed partly before; but here according to <HI>Piti&s;cus</HI> his example after this manner, let the plane of the Hori|zon be GADEF&punc; and in that let a gnem<GAP DESC="illegible" EXTENT="1 letter">m be perpen|dicularly erected AB, the end B repre&s;enting the center of the World, which gnomon let be divided into equal parts, which here let be 100, and let there be ob&s;erved the right &s;ha|dow of the Sunne, AD &s;truck from the highe&s;t part of the Sunnes body at C, for the &s;hadow AD is &s;truck from the center; I cannot con|ceive by rea|&s;on that part of that &s;ha|dow DE, from the upper bowing of the Sun is perpendicularly il|luminated, I &s;ay let the right &s;hadow ob&s;erved of the up|per bowing of the Sun 83 parts, al&s;o let the Angle A DB be inquired equal to the Angle of the Altitude IBC,
<FIGURE>
</FIGURE>
<PB N="122" REF="70">
as AD the right &s;hadow 83, to AB the gnomon 100, &s;o the Radius 100000, to AD 12040 the tangent of the angle ADB or IBC the Altitude required 50 deg. 18.</P>
<P>From which the &s;emidiameter of the Sun 15 min. &s;ub|&s;tracted doth remain the Altitude of the center of the Sun 50 de. 3 m. the Altitude required, or</P>
<P>Let the verticall Plane be CED, and in the &s;ame the Gnomon EF perpendicularly fixed, touching his extream end, the center of the World F, and divi|ded into 100 equal parts, and let the ver&s;ed &s;hadow of the Sunne be EG 103 432 / 10000 parts, &s;hewing the Al|titude of the lower part of the Sun: for the total &s;hadow EH, again, I cannot per|ceive be|cau&s;e the part HG s illumina|ted from the lower bow|ing of the Sun I, but let the An|gle of the Altitude H FG or IL G be requi|red, I &s;ay as FE, the Gnomon 100, to EG the ver&s;ed &s;hadow 103 234 / 1000, &s;o FE the Radi|us 100000, to EG 103432 the Tangent of the Angle E
<FIGURE>
</FIGURE>
<PB N="123" REF="70">
FG or IFA, that is the Ark IA 45 deg. 58 m. to which if you doe adde the &s;emidiameter of the Sun IL 15 min. there is made the Altitude of the center of the Sun, 46 deg. 13 min.</P>
<P>From this or the former Propo&s;ition we may take no|tice that there is no Dial can &s;hew the exact time without the allowance of the Suns &s;emidiameter: which in a &s;trict acception is true, but hereto Mr. <HI>Wells</HI> hath an&s;wered in the 85 <HI>page</HI> of his Art of &s;hadows, where &s;aith he, becau&s;e the &s;hadow of the center is hindered by the &s;tyle, the &s;hadow of the hour-line proceeds from the limbe which alwayes precedeth the center one min. of time an&s;werable to 15 min. the &s;emidiameter of the Sun (which to allow in the height of the Style were erroneous) wherefore let the al|<GAP DESC="illegible" EXTENT="1 letter">owance be made in the hour-lines, detracting from the true Equinoctial di&s;tances of every 15 deg. 15 primes, and &s;o the Arches of the horizontall plane from the Meridian &s;hall &s;tand thus.</P>
<P><HI>Prop.</HI> 4. By &s;hadow we may finde the natural Tangent of every degree of a quadrant, as appeares by the former exam|ple.</P>
<P><TABLE>
<ROW ROLE="label">
<CELL COLS="2">Houres.</CELL>
<CELL COLS="2">Equino|ctial di|&s;tances.</CELL>
<CELL COLS="3">True hour di&s;tances.</CELL>
</ROW>
<ROW>
<CELL>12</CELL>
<CELL>0</CELL>
<CELL>de.</CELL>
<CELL>m.</CELL>
<CELL>de.</CELL>
<CELL>m.</CELL>
<CELL>&s;e.</CELL>
</ROW>
<ROW>
<CELL>11</CELL>
<CELL>1</CELL>
<CELL>14</CELL>
<CELL>45</CELL>
<CELL>11</CELL>
<CELL>38</CELL>
<CELL>51</CELL>
</ROW>
<ROW>
<CELL>10</CELL>
<CELL>2</CELL>
<CELL>29</CELL>
<CELL>45</CELL>
<CELL>24</CELL>
<CELL>6</CELL>
<CELL>31</CELL>
</ROW>
<ROW>
<CELL>9</CELL>
<CELL>3</CELL>
<CELL>44</CELL>
<CELL>45</CELL>
<CELL>37</CELL>
<CELL>4</CELL>
<CELL>2</CELL>
</ROW>
<ROW>
<CELL>8</CELL>
<CELL>4</CELL>
<CELL>59</CELL>
<CELL>45</CELL>
<CELL>53</CELL>
<CELL>19</CELL>
<CELL>12</CELL>
</ROW>
<ROW>
<CELL>7</CELL>
<CELL>5</CELL>
<CELL>74</CELL>
<CELL>45</CELL>
<CELL>70</CELL>
<CELL>48</CELL>
<CELL>6</CELL>
</ROW>
<ROW>
<CELL>6</CELL>
<CELL>6</CELL>
<CELL>89</CELL>
<CELL>45</CELL>
<CELL>89</CELL>
<CELL>40</CELL>
<CELL>51</CELL>
</ROW>
</TABLE></P>
<P>For the Sun being 46 deg, 13 min. of Altitude makes a &s;hadow of 95. parts of &s;uch as the gno|mon is 100, &s;o then mul|tiply the length of the gnomon 100 by the Radius, and di|vide by 95, and it yeelds 105263 the natural Tangent of that Ark.</P>
<P><PB N="124" REF="71"><HI>Prop. 5.</HI> By &s;hadow we may take the height of any Building, by the Rule of Proportion; if a gnomon of 6 foot high give a &s;hadow of 10 foot: how high is that hou&s;e who&s;e &s;hadow is <HI>25</HI> foot? re&s;olved by the Rule of Three.</P>
<P><HI>Prop. 6.</HI> By &s;hadow al&s;o we learn the magnitude of the Earth, according to <HI>Erato&s;thenes</HI> his propo&s;ition.</P>
<P><HI>Prop. 7.</HI> By &s;hadow we learne the true Equinoctial line, running from Ea&s;t to We&s;t, which cro&s;&s;ed at right Angles is a true Meridian, where note, that in the times of the Equinoctiall that the &s;hadows of one gnomon is all in one right line.</P>
<P><HI>Prop. 8.</HI> By &s;hadow we know the Earth to be but as a point, as may appear by the &s;hadow of the Earth on the body of the Moon.</P>
<P><HI>Prop. 9.</HI> By &s;hadow we may learn the di&s;tance of pla|ces, by the quantity of the ob&s;curity of an Eclip&s;e.</P>
<P><HI>Prop. 10.</HI> By gnomonicals we make di&s;tinctions of Climates and People, &s;ome <HI>Hetorezii,</HI> &s;ome <HI>Perezii,</HI> &s;ome <HI>Amphitii.</HI></P>
<P><HI>Prop. 11.</HI> By &s;hadow the Climates are known, in the cold intemperate Zones the &s;hadow goes round. In the hot intemperate Zones the &s;hadow is toward the We&s;t at the ri&s;ing Sun, and toward the Ea&s;t at the &s;etting Sun, and no &s;hadow at Noones to them as dwel under the Parallels. And to them in the temperate Zones always one way, to|ward the North, or toward the South.</P>
<P><HI>Prop. 12.</HI> By &s;hadow we are taught the Rule of de|lineating painting, according to the per&s;pective way, how much is to be light or dark, accordingly drawn as the center is di&s;po&s;ed to the eye: &s;o the Office of &s;hadow is mani|fold, as in the Optical conclu&s;ions are more amply decla|red;
<PB N="125" REF="71">
therefore I referre you to other more learned works, and de&s;i&s;t to &s;peak.</P>
<P>But for matter of Information, I will here in&s;ert cer|tain definitions taken out of <HI>Optica Agulion ii lib.</HI> 5.</P>
<P>Fir&s;t, &s;aith he, we call that a light body from whence light doth proceed; truly &s;aith he, the definition is plain, and wants not an Expo&s;itor, &s;o &s;ay I, it matters not whe|ther you under&s;tand the luminous body: only that which doth gli&s;ter by proper brightne&s;s as doth the Sun, or that which doth not &s;hine but by an external overflow|ing light, as doth the Moon.</P>
<P>2. That we call a <HI>diaphon</HI> body, through which light may pa&s;s, and is the &s;ame that <HI>Ari&s;totle</HI> cals per&s;picuous.</P>
<P>3. It is called <HI>Adiopton,</HI> or <HI>Opacous;</HI> through which the light cannot pa&s;s, &s;o &s;aith he, you may ea&s;ily collect from a <HI>diaphon</HI> body the definition of &s;hadow: for as that is tran&s;|parent through which the light may pa&s;s: &s;o al&s;o is that <HI>opacous,</HI> or of a <HI>den&s;e</HI> nature wherein the light cannot pa&s;s.</P>
<P>4. That is generated from a &s;hining body, is called the fir&s;t light, that hath his immediate beginning from the luminous body, it is called the &s;econd light, which hath his beginning from the fir&s;t, the third which hath his be|ginning from the &s;econd, and &s;o the re&s;t in the &s;ame order.</P>
<P>Whence we make this di&s;tinction of day and light, day is but the &s;econd light, receiving from the Sun the fir&s;t, &s;o that day is light, but the Sun is the light.</P>
<P>5. Splendor is light repercu&s;&s;ed from a pure poli&s;hed body; and as light is called &s;o from the luminous body: &s;o this is called &s;plendent from the &s;plendor.</P>
<P><HI>Theor.</HI> Light doth not onely proceed from the Cen|ter, but from every part of the &s;uperficies.</P>
<P><HI>Theor.</HI> Light al&s;o is di&s;per&s;ed in right lines.</P>
<P><PB N="126" REF="72"><HI>Theor&punc;</HI> Light di&s;per&s;ed about every where, doth col|lect into a Spherical body.</P>
<P>6. The beames of light, &s;ome are equi di&s;tant parallels, &s;ome inter&s;ect each other, and &s;ome diver&s;ly &s;haped. Let A be the Light, a beam from A to B, and another from C to D are parallel, A D and C B inter&s;ect; and the other two doe diver&s;ly happen, one a&s;cending, the other de&s;cending: its plaine.</P>
<P><FIGURE>
</FIGURE></P>
<P>7. That is called a full and perfect &s;hadow, to which no beam of light doth come.</P>
<P>8. That is called a full and perfect light; which doth proceed from all parts of that which gives light; but that which giveth light but in part, is imperfect: this he exem|plified by an Eclip&s;e, the Moon interpo&s;ing her &s;elf be|tween the Sun and Earth, doth eclip&s;e the perfect light of the Sun: whereby there appeares but a certaine ob&s;cure, dim, glimmering light, and is &s;o made imperfect.</P>
<P>Hence we may learn to di&s;tingui&s;h day from night; for day is but the pre&s;ence of the Sun by a perfect light re|ceived, which we count from Sun ri&s;ing to Sun &s;etting.</P>
<P>Twy-light is but an imperfect light from the partial &s;hining or neighbourhood with Sun: whereas Night is a total deprivation or perfect &s;hadow, to which no beam of light doth appettain.</P>
<P>Yet from the over-flowing light of the Sun, the Starres are illuminated; yet becau&s;e &s;hadow is always in the op|po&s;ite, tho&s;e Stars that are in direct oppo&s;ition to the Sun, are ob&s;cure for that &s;ea&s;on, and hence proceeds the Eclip&s;e of the Moon.</P>
<P><PB N="127" REF="72">Hence it is with the <HI>Sciothericalls</HI> as it is with the Dutch <HI>Emblami&s;t,</HI> comparing Love to a Diall, and the Sun with the Motto, <HI>Nil &s;ine te,</HI> and his compari&s;on to</P>
<LG>
<L>Coele&s;tis cum me Sol a&s;picit ore &s;ereno,</L>
<L>Protin&ugrave;s ad numeros mens reddit apta &s;uos.</L>
</LG>
<P>Implying that as &s;oone as the Sun &s;hines it returnes to the number, &s;o a Lover &s;eeing his Love on a high Tower, and a Sea between, yet (<HI>protin&ugrave;s ad numeros</HI>) he will &s;wim the Sea and &s;cale tbe Ca&s;tle to return to her: So here lyes the gradation, fir&s;t, from the Suns light, from the light by the opoacus body, interpo&s;ition, &s;hadow, and from the &s;hadow of the Axis is demon&s;trated the houre. Adde al&s;o, the beam and &s;hadow of a gnomon, have one and the &s;ame termination or ending, toward which I now draw my pen; de&s;iring you to take notice that the whole Me|thod of Dialling, as may appear by the former di&s;cour&s;e, doth &s;eem to be foure-fold, <HI>viz.</HI> Geometrical, Arith|metical, or by Tables mechanically, or by Ob&s;ervation. So that the Art of &s;hadowes is no other then a certain and demon&s;trative motion of the Heavens in any Plaine or Su|perficies, and a Gnomonical Houre is no other then a direct projecting of the hour-lines of any Plain; &s;o as that it &s;hal li|mit a Style &s;o to ca&s;t its &s;hadow from one line to another, as that it &s;hall be ju&s;t the twenty-fourth part of the natural day, which con&s;i&s;teth of 24 houres; and this I have laid down after a mo&s;t plain manner following: A gnomo|nical day is the &s;ame that the Artificial day is; which the &s;hadow of a gnomon maketh from the ri&s;ing of the Sun, till the &s;etting of the &s;ame in a concave &s;uperficies: which length of the day is al&s;o projected from the motion of the &s;hadow of the Style, a gnomonical Moneth is al&s;o de&s;cri|bed on Planes, which is the &s;pace that the &s;hadow of a
<PB N="128" REF="73">
Gnomon maketh from one Parallel of the &s;igne, to an other &s;ucceeding Parallel of a &s;igne, again, a gnomonical year is limited by the &s;hadow of a Gnomon, from a point in the Meridian of the Tropick of <HI>Cancer,</HI> till it &s;hall revolve to the &s;ame Meridian Altitude and point of the Tropick, and is the &s;ame as is a tropical year: wherefore, above all things we ought fir&s;t tobe acquainted with the knowledge of the Circles of the Sphaere&punc; Secondly, to have a judici|ous and exact di&s;cerning of tho&s;e Planes in which we ought to project Dials. Thirdly, to con&s;ider the Style, Quality, and Po&s;ition of the axis or Style, with con&s;ide|ration of the cau&s;e, nature and effects in &s;uch or &s;uch Planes as al&s;o an artificial projecting of the &s;ame, either on a Superficies by a Geometricall Knowledge, and reducing them to Tables by Arithmetick, which we have afore demon&s;trated, and come now to the conclu&s;ion: So that as I began with the Diall of Life, So we &s;hall <HI>Dye-all,</HI> For,</P>
<TRAILER>Mors ultima linea.</TRAILER>
</DIV3>
</DIV2>
</DIV1>
<DIV1 TYPE="letter">
<PB N="129" REF="73">
<HEAD>TO ABRAHAM CHAMBRELAN E&s;q. <HI>S M.</HI> con&s;ecrateth his <HI>Court of Arts.</HI></HEAD>
<OPENER><SALUTE>SIR.</SALUTE></OPENER>
<P>_IF the Originall Light be manife&s;tatiu, by it I have made a double di&s;covery, your <HI>genius</HI> did &s;o di&s;cover it &s;elf according to the quality of the <HI>Sun,</HI> that I am umbrated and pa&s;&s;ive like the eclip&s;ed <HI>Moon,</HI> yet cannot but reflect a beame which I have received from the fountain of <HI>Light;</HI> 'tis you which I make the Patron to my fancy (which perhaps you may wonder at the Idlene&s;s of my head, to tell you a dream, or a prae|ludium of the &s;everal <HI>Arts:</HI> how&s;oever knowing you are a Lover of them, I did ea&s;ily believe you could not but delight in the Scaene; though in mo&s;t I have written, I have in &s;ome &s;ort imitated Nature it &s;elf, which di&s;pen&s;eth not her <HI>Light</HI> without <HI>Shadows,</HI> which will truly follow them from whom they proceed, and &s;hall <HI>Sir,</HI> in time to come render me like Pentheus who&s;e curio&s;ity in prying into Secrets makes me un|certain. <HI>Et Solem Geminum duplices &s;e o&s;tendere The|bas,</HI> &amp; while I know neither <HI>Copernicus,</HI> nor <HI>Ptolomies Sy|&s;teme</HI> of the <HI>World,</HI> dare affirmatively reject neither, but run after both; and &s;ubmitting my wi&s;dome to the wi&s;e&s;t of men, mu&s;t conclude, that <HI>Cuncta fecit tempe&s;tatibus &s;uis pulchra,</HI> and hath al&s;o &s;et the <HI>World</HI> in their meditation: Yet can not Man find out the Work that God hath wrought. <HI>Sir,</HI> pardon my boldne&s;s, in fa&s;tning this on your Patronage, who indeed are called to this <HI>Court</HI> of <HI>Arts,</HI> as being Nobly de&s;cended, whom only it concernes; and only who&s;e Vertue hath arrived them to the Temple of <HI>Honour,</HI> who are all invited as appeareth in the conclu&s;ion of this imaginary de&s;cription, wherein, whil&s;t I &s;eem to be in a dream; yet <HI>Sir,</HI> I am certain, I know my &s;elfe to be</P>
<CLOSER><SIGNED>Yours in all that I am able to &s;erve you, S. M.</SIGNED></CLOSER>
</DIV1>
<DIV1 TYPE="text">
<PB N="130" REF="74">
<HEAD>TOPOTHESIA. <HI>OR</HI> An IMAGINARY DESCRIPTION of the <HI>CO&V;RT of ART.</HI></HEAD>
<P>_COmming into a <HI>Librarie</HI> of Learning, where there was more <HI>Languages</HI> then I had <HI>Tongues,</HI> that if I had been asked to bring <HI>brick</HI> I &s;hould have brought <HI>morter,</HI> and going gradually a|long, as then but <HI>pa&s;&s;us Geometricus,</HI> there I met <HI>Minerva,</HI> which &s;aid unto me (<HI>Vade mecum</HI>) &amp; had not the expre&s;&s;ion of her ge&s;ture be-&s;poke my company, I &s;hould have &s;hunned her; &s;he then taking me by the hand, led me to the end, where &s;at one which was called as I did inquire, <HI>Clemency,</HI> the name indeed I under&s;tood, but the Office I did not, who&s;e In&s;cription was <HI>Cu&s;tos Artis,</HI> I being touched now with a de&s;ire to under&s;tand this In|&s;cription; began with De&s;ire, &amp; craving leave, u&s;ed dili|gence to peru&s;e the <HI>Library,</HI> and found then a Booke inti|tuled the <HI>Gate of Languages,</HI> by that I had peru&s;ed it, I under&s;tood the fore-named In&s;cription, and craving leave of <HI>Clemency</HI> in what re&s;pect &s;he might be called the <HI>Keeper of Arts,</HI> who an&s;wered with <HI>Claudanus</HI> thus;</P>
<LG>
<L>Principio magni Cu&s;tos Clementia Mundi,</L>
<L>Quae Jovis incoluit Zonam quae temper at Aethrum,</L>
<L>Frigoris &amp; flammae mediam quae maxima natu,</L>
<L>Coelicolum: nam prima Chaos Clementia &s;olvit,</L>
<L>Congeriem mi&s;erata rudem, vultu&abque; &s;ereno,</L>
<L>Di&s;cu&s;&s;us tenebris in lucem &s;aecula fundit.</L>
</LG>
<P><PB N="131" REF="74">And ari&s;ing from a Globe which was then her &s;eat, &s;he began to di&s;cour&s;e of the Nature and Magnitude of the Terre&s;tiall body, and propounded to me que&s;tions: as fir&s;t,</P>
<P>If one degree an&s;werable to a Coele&s;tiall degree yield 60 miles, what &s;hall 360 degrees yield, the proportion was &s;o plainly propounded, that I re&s;olved it by the ordinary rule of Proportion, &s;he &s;eeing the re&s;olution, propounded a|gain, and &s;aid, if this &s;olid Body were cut from the center how many &s;olid obtu&s;e angles might be cut from thence, at this I &s;tumbled, and de&s;ired, con&s;idering my &s;mall pra|cti&s;e, that &s;he would reduce this <HI>Chaos</HI> al&s;o, and turne dark|ne&s;&s;e into light: &s;eeing then my de&s;ire and diligence bid me make ob&s;ervation for tho&s;e three were the wayes to bring me to peace, and re&s;olved, that as from the center of a Circle but three obtu&s;e angles could be &s;truck, &s;o from the center of a Globe, but three &s;uch angles could be &s;truck and from thence fell to another que&s;tion, &amp; asked what I thought of the motion of that body: I an&s;wered, Motion I thought it had none, &s;eeing I had &s;uch Secretaries of Nature on my &s;ide, and was loth to joyn my forces with the <HI>Copernicans.</HI></P>
<P>She an&s;wered, it was part of folly to condemn without knowing the rea&s;ons, I &s;aid it &s;hould &s;til remain a Hypothe|&s;is to me, but not a firme Axiome: for the re&s;olution of which I wil onely &s;ing as &s;ometimes other Poets &s;ang con|cerning the beginning of the world, and invert the &s;en&s;e onely, as that in another ca&s;e, &s;o this for our purpp&s;e.</P>
<LG>
<L>If <HI>Tellus</HI> winged bee</L>
<L>The Earth a motion round,</L>
<L>Then much deceiv'd are they</L>
<L>That it before nere found.</L>
<L><PB N="132" REF="75"><HI>Solomon</HI> was the wi&s;e&s;t,</L>
<L>His wit ner'e this attain'd;</L>
<L>Cea&s;e then <HI>Copernicus,</HI></L>
<L>Thy Hypothe&s;is vain.</L>
</LG>
<P>And he &s;aith, man cannot finde out the work that is done under the &s;unne, and if it be &s;o, how comes it that a cloud, which is but the motion of the ayr; if it move we&s;terly, that the earth doth not leave it behind, &s;eeing that is of a more &s;wift motion; but clemency told me, it was not for man to inquire of the things unrevealed, lea&s;t he wade from his own, till he come beyond his own depth, and come &s;hort of his expected &s;hoare; the truth is the &s;ame, if we &s;uppo&s;e the earth to move, and the ri&s;ing of the Sun, Moon, and Starres &s;hall keep the &s;ame corre&s;pondence that now. Be&s;ide, if the great Body of the Heavens &s;hould move, it mu&s;t move 42 398437 and a half, a motion incre|dible, whereas if the earth move about, it doth not move a thou&s;and miles in an houre: if you allow the earth 24 thou&s;and miles in compa&s;&s;e, which is more then your A|&s;tronomers allow. Then in re&s;pect of yet an unre&s;olved novelty, I propounded another que&s;tion to her, whether it were probable to be a habitable world in the Moon, to which Clemency made an&s;wer, if that were mainteined, &s;he would ask them but one que&s;tion, and leave them in a dilemma for their &s;alvation, <HI>viz.</HI> Did Chri&s;t &s;uffer in the <HI>Jeru&s;alem</HI> above, or here below? now there is no <HI>Jeru|&s;alem</HI> above but the glorified <HI>Jeru&s;alem;</HI> but if there be a <HI>Jeru&s;alem</HI> al&s;o in that planet, then take which you will: if Chri&s;t dyed there, there the old <HI>Adam</HI> was made alive, and his death <HI>quid proficit te?</HI> if he dyed here? either they are no &s;inners, or he came not to &s;ave &s;inners: I thank|ed
<PB N="133" REF="75">
her, and turning &s;pake to <HI>Minerva,</HI> de&s;ired &s;he would now &s;hew me part of her Diety; &s;he asked me what I would learn, I told her Dyalling; &s;he then after many Definitions of &s;uch Circles as were on the Globe, turning it about, &s;et it to the Elevation, and &s;aid; this done, put the Equinoctiall colure under the meridian, which is the circle de&s;cribed between <HI>Aries</HI> and <HI>Libra,</HI> pa&s;&s;ing by the two poles, then number 15 degrees on the Aequator, and where the circle pa&s;&s;ing through that point doth cro&s;&s;e the horizon, that is the di&s;tance of the fir&s;t hour, which mea|&s;ure on the degree of the horizon, for the &s;econd hour, num|ber that colure 30 degrees, for the third 45, for the fourth-60 degrees, &amp;c. on the horizon; &s;o having the hour di|&s;tances on the horizon, it is ae|&s;ie to protract them down with a chord or part of a Circle; but the more to exerci&s;e you, I wil leave the others to you to con|ceive, and mu&s;t apply my &s;elf el&s;ewhere: in the mean, I will commit you into the hands of two of my attendants, and &s;o bid me take my leave of Cle|mency, and follow her, for in the paths of vertue, there was to be no &s;tay, and &s;o brought me into a yard, where &s;tood a pillar, con&s;ecrated to Art, where on the South &s;ide &s;tood <HI>A&s;tro|nomia,</HI> re&s;pecting the Sun, and on the North &s;ide <HI>Geographia,</HI> re&s;pecting the Pole: but their
<FIGURE>
</FIGURE>
<PB N="134" REF="76">
In&s;truments only remains, as it fell out happened to come while I was there. So that <HI>Clarentieux</HI> his &s;hare fell to <HI>A&s;tronomia,</HI> and <HI>Norroy</HI> to <HI>Geographia,</HI> to &s;hew that Art as well as Antiquity. &s;hall have po&s;&s;e&s;&s;ion of the North and South, and &s;o <HI>Minerva</HI> took her leave. Then I fell in the protection of <HI>Geographia,</HI> who had a marine compa&s;&s;e in her hand, he and it alwayes re&s;pecting one &s;tarre.</P>
<P>And began to di&s;cour&s;e of the longitude of the earth, and then I demanded what benefit might incurre from thence to a young Dialli&s;t, &s;he an&s;wered above all one mo&s;t nece&s;&s;ary Probleme, which we may finde in <HI>Peti&s;cus</HI> his ex|ample, and propounded it thus; The difference of meridi|ans given, to finde the difference of hours.</P>
<P>If the place be ea&s;terly, adde the difference of longitude converted into time to the hours given: if it be we&s;terly, &s;ub&s;tract the ea&s;terly places, who&s;e longitude is greater &amp; <HI>contra,</HI> as in <HI>Peti&s;cus</HI> his example, the meridian of <HI>Craco|via</HI> is 45 deg. 30 min. the longitude of the meridian of <HI>Heidelberge</HI> is 30 degrees, 45 minutes, therefore <HI>Heidleberg</HI> is the more we&s;terly.</P>
<LIST>
<HEAD>One &s;ub&s;tracted from</HEAD>
<ITEM>45</ITEM>
<ITEM>30</ITEM>
<ITEM>30</ITEM>
<ITEM>45</ITEM>
</LIST>
<P>the other &s;heweth the difference of longitude, to which degrees and minutes doth an&s;wer o <HI>ho. 59 m.</HI> for as</P>
<GAP DESC="math">
<P>Therefore when it is 2 hours <HI>po&s;t merid.</HI> at <HI>Cracovia;</HI> at <HI>Neidelberg,</HI> it is but 1 hour, 1 minute pa&s;t noon. For,</P>
<P><PB N="135" REF="76">
<GAP DESC="math"></P>
<P>There is left 1 houre 1 minute.</P>
<P>Thus out of the difference of meridians, the divers &s;i|tuation of the heavens is known, and from the line of ap|pearances of the heavens, the divers hours of divers places is known, and this is the foundation of ob&s;erving the longi|tude: if it be ob&s;erved what houre an Eclip&s;e appears in one place, and what in another, the difference of time would &s;hew the longitude, and hereby you may make a dyall that together with the proper place of elevation, &s;hall &s;hew for any other country; for this Propo&s;ition I did hartily grati|fie <HI>Geographia,</HI> and turning, &s;aid <HI>A&s;tronomy,</HI> why &s;tand you &s;o &s;ad? &s;he an&s;wered, Art is grown contemptible, and e|very one was ready to &s;ay (<HI>A&s;trologus e&s;t Ga&s;trologus</HI>) then I &s;aid, what though vertue was de&s;pi&s;ed, yet let them take this an&s;wer:</P>
<LG>
<L>Thou that contemne&s;t Art</L>
<L>And makes it not regarded,</L>
<L>In Court of Art &s;hal have no part</L>
<L>None there but Arts rewarded.</L>
<L>Gna&s;hing the teeth as if ye &s;trive to blame it,</L>
<L>Yet know I'le &s;pare no co&s;t for to obtein it.</L>
</LG>
<P>Perceiving your willingne&s;&s;e &s;aid <HI>A&s;tronomy,</HI> I will yet extend my charity and lay down the numbers, &s;o that if you add the &s;econd and third and &s;ub&s;tract the fir&s;t, it &s;hall give the fourth; the que&s;tion demanded, and then I being careful of the tuition of what &s;he &s;hould &s;ay, took a Table|book and writ them as follows.</P>
<LIST>
<ITEM>1 The &s;ine comp. elevation pole 38&frac12;, &s;ine 90; &s;ine of the decl. of the &s;un yields the &s;ine of the amplitude ortive:
<PB N="136" REF="77">
which is the di&s;tance of the &s;uns ri&s;ing from due Ea&s;t.</ITEM>
<ITEM>2 The &s;ine 90, the &s;ine ele. pole 51d&frac12;; the &s;ine of decli. yields the &s;ine of the &s;uns height at &s;ix a clock.</ITEM>
<ITEM>3 Sine comp. of altitude of the &s;un, &s;ine comp. declina. &s;ine 90; the &s;ine of the angle of the vertical circle, and the meridian for the Azimuth of the &s;un at the hour of 6: The Azimuth is that point of the compa&s;&s;e the &s;un is on.</ITEM>
<ITEM>4 Sine comp. decli. of the &s;un: &s;ine compl. eleva. pole 38d&frac12;, &s;ine Altitude of the &s;un; the houre di&s;tance from &s;ix.</ITEM>
<ITEM>5 Sine compl. of decli. &s;ine 90; compl, of &s;ine &s;uns am|plitude to &s;ine compl. of the A&s;&s;entional difference.</ITEM>
<ITEM>6 The &s;ine of the difference of a&s;&s;ention, Tang. decli. &s;un; &s;ine 90: Tangent complement of the elivation.</ITEM>
<ITEM>7 Sine altitude of the &s;un, &s;ine declina. of the &s;un; &s;ine 90: Elevation of the pole.</ITEM>
<ITEM>8 Sine 90, &s;ine com. of di&s;tance from 6; &s;ine com. de|clination of the &s;un: &s;ine comp. of the altitude &s;un.</ITEM>
<ITEM>9 Sine 90, &s;ine eleva. pole; &s;ine alti. of a &s;tar: &s;ine decli. of that &s;tar.</ITEM>
<ITEM>10 The &s;ine of a &s;tars altitude in an ea&s;t Azimuth, &s;ine amplitude <HI>ortive;</HI> &s;ine 90: &s;ine of the elevation.</ITEM>
<ITEM>11 The greate&s;t meridian altitude, the le&s;&s;e &s;ub&s;tracted &s;ines; the di&s;tance of the Tropicks, who&s;e halfe di&s;tance is the greate&s;t declination of the &s;un; which added to the lea&s;t meridian altitude, or &s;ub&s;tracted from the greater, leavs the altitude of the <HI>Equator:</HI> the complement whereof, is the elevation of the pole.</ITEM>
<ITEM>12 Tang. eleva. pole, &s;ine 90; Tang. decli. of the &s;un, to the co-&s;ine of the hour from the meridian, when the &s;un will be due ea&s;t or we&s;t.</ITEM>
</LIST>
<P>By the&s;e Propo&s;itions &s;aid <HI>A&s;tronomy,</HI> you may much benifit your &s;elfe; but let us now go &s;ee the <HI>Court</HI> of <HI>Art:</HI>
<PB N="137" REF="77">
I liked the motion, and we went and behold the &s;ight had like to made me a Delinquent, for I &s;aw nought but a poor Anatomy &s;itting on the earth naked expo&s;ed to the open Ayre, which made me think on the hardne&s;&s;e of a Child of Art, that it had neither hou&s;e nor bed, and now being at a pitch high enough re&s;olve never to fol|low it: this Anatomy al&s;o it &s;eems was ruled by many, both Rams, and Buls and Lions, for he was de&s;canted thus on.</P>
<LG>
<L>Anatomy why do'&s;t not make thy moane,<NOTE PLACE="marg">&rindx;</NOTE></L>
<L>So many limbes, and yet can'&s;t govern none;</L>
<L>Thy head although it have a manly &s;igne,</L>
<L>Yet art thou placed on watry feminine.</L>
<L>'Tis true, yet &s;trong, but prethee let me tell yee,</L>
<L>Let not the Virgin always rule your belly:</L>
<L>For what, although the Lion rule your heart;</L>
<L>The weake&s;t ve&s;&s;ell will get the &s;tronge&s;t part.</L>
<L>Then be content &s;et not your foot upon</L>
<L>A &s;lippery fi&s;h, that's in an in&s;tant gone;</L>
<L>A &s;lippery woman, who at <HI>Cupids</HI> call</L>
<L>Will &s;lip away, and &s;o give you a fall:</L>
<L>And if Rams horns &s;he do on your head place;</L>
<L>It is a dangerous &s;lip, may &s;poil your face.</L>
</LG>
<P>Here at I &s;miled, then &s;aid A&s;tronomy, what is your thought? then &s;aid I, do men or Arti&s;ts &s;o depend on women, as that their &s;trength con&s;i&s;ts in them? &s;he &s;aid, I mi&s;under&s;tand him, for the Ram that rules the head is a &s;igne ma&s;culine, becau&s;e it is hot and dry, the Fi&s;h that rules the feet is cold and moi&s;t is therefore called fe|minine.</P>
<LG>
<L><HI>Pi&s;ces</HI> the Fi&s;h you know's a watery creature,<NOTE PLACE="marg">&rindx;</NOTE></L>
<L>'Tis &s;lippery, and &s;hews a womans nature;</L>
<L><PB N="138" REF="78">So women in their be&s;t performance fail,</L>
<L>There's no more hold then in a Fi&s;hes tail.</L>
</LG>
<P>But the more to affect the beholder, I will typigraphe this Court of Art.</P>
<P><FIGURE>
</FIGURE></P>
<P>Under was written the&s;e lines, to &s;hew mans mi&s;ery by the fall, which I will deliver you, as followes:</P>
<LG>
<L>When <HI>Chaos</HI> became <HI>Co&s;mos,</HI> oh Lord! than</L>
<L>How excellent was <HI>Microco&s;mus,</HI> Man</L>
<L>When he was &s;ubject to the Makers will,</L>
<L>Stars influence could no way worke him ill:</L>
<L>But &s;ince his fall his &s;tage did open lye,</L>
<L>And Con&s;tellations work his de&s;tiny.</L>
<L>Thus man no &s;ooner in the World did enter,</L>
<L>But of the Circumference is the Center.</L>
</LG>
<P>And then came in Vertue, making a &s;peech, and &s;aid;</P>
<LG>
<L>Honour to him, that honour doth belong:</L>
<L>You &s;tripling Arti&s;t, coming through this throng,</L>
<L>Have found out Vertue that doth &s;tand to take</L>
<L>You by the hand, and Gentleman you make.</L>
<L>For Geometry, I care not who doth hear it,</L>
<L>May bear in &s;hield Coat Armor by his merit:</L>
<L><PB N="139" REF="78">We re&s;pect merit, our love is not &s;o cold,</L>
<L>We love mens worth (not in love with mens gold)</L>
<L>Not Herald-like to &s;el, an Armes we give;</L>
<L>Honour to them that honourably live.</L>
</LG>
<P>And then &s;he told me, &s;he would leave me, and withall &s;aid there was an Armes for my reward, and I loth to leave her made Apologies for her &s;tay, which I could not obtein, then I prayed A&s;tronomy to be my A&s;&s;ociate, but he &s;aid, &s;he could go no further then Vertue would give her leave: this done, my dream vani&s;hed, and I a|waked, but I found my &s;elf in a maze, and began to think my &s;elfe to be a Child of Art, finding my &s;elfe without a hou&s;e, though tho&s;e Planets which have their names from Errour wandring had two hou&s;es, onely the Sun and Moon were in Conjunction, and had but one hou&s;e a piece, while I was in this mu&s;e, and this maze, which my memory hath here depicted, there appeared unto me one in a long robe, named <HI>Caliope,</HI> which was
<FIGURE>
</FIGURE>
the fir&s;t &amp; highe&s;t of the 9 Mu&s;es, who &s;aid unto me, why
<PB N="140" REF="79">
art thou &s;o di&s;tracted? to whom I told; the progre&s;&s;ion I had made in the Court of Art, and how I was bereft of all her lovers, and had onely the appearance of a re|ward, being a Coat of Arms; which while I looked after a painted &s;hew, I find I had but a &s;eeming amends, then &s;aid <HI>Caliope,</HI> thou ha&s;t obtained a favour beyond thy ex|pectation, for thou art brought to the Temple of honour by the hand of Vertue, and whereas before thou &s;awe&s;t the outward Court, I &s;hall now &s;hew thee the inward Garden, wherein thou maye&s;t take notice fir&s;t of this maze &s;o ordered, that if thou &s;ette&s;t thy foot in <HI>Aries,</HI> and continues thy cour&s;e, thou &s;halt find it to be one of the hou&s;es of <HI>Mars,</HI> and continuing this cour&s;e by the &s;ame line it &s;hall bring thee to <HI>Scorpio,</HI> the other hou&s;e of the &s;ame Planet: &s;o that thou &s;ee&s;t here a way where|by thou maie&s;t pre&s;ently know the &s;everall hou&s;es of the Planets, for the &s;igns thou &s;ee&s;t beginning with <HI>Aquarius</HI> are &s;ucce&s;&s;ive, as al&s;o the Planets in their order, and if the one &s;ign be the day hou&s;e of one Planet, the next is the night hou&s;e of the next Planet, and if thou account this fir&s;t &s;igne for <HI>January,</HI> and &s;o the moneths &s;ucce&s;&s;ive|ly, thou knowe&s;t in what &s;igne the Sun is in. I being plea&s;ed at the&s;e &s;peculations, I was led to an Arbor Roy|all, where I &s;aw that that gave me yet more content, for there methought I &s;aw over the entrance thereof a fair Coat of Armes, which being my profe&s;&s;ion, I was in|qui&s;itive at that time to blazon it, but being then in the pre&s;ence of <HI>Caliope,</HI> the Godde&s;&s;e of <HI>Heralds,</HI> I de&s;ired her to blazon that Coat (which &s;he &s;aid was that Armes as was given to me and Arti&s;ts) &s;he then &s;aid unto me, that becau&s;e I profe&s;&s;ed a love to the Mathematicks, it was mo&s;t proper to be blazoned by Planets, and began thus.</P>
<P><PB N="141" REF="79">The noble Profe&s;&s;ours of the Sciences, may bear as is here blazoned, (<HI>viz.</HI>) the field is <HI>Jupiter,</HI> Sun and Moon in conjunction proper, in a chief of the &s;econd, <HI>Saturn, Venus, Mercury</HI> in trine or perfect amity; and <HI>Mars</HI> in the center of them; Mantled of the Light, doubled of the night, and on a wreath of its colours a <HI>Helitropian</HI> or Marigold of the colour of <HI>Helion</HI> with this Motto, <HI>Quod est &s;uperius, e&s;t &s;icut inferius;</HI> then did I de&s;ire to know, what did each Planet &s;ignifie in colour, &s;he then told me as followeth.</P>
<P><TABLE>
<ROW>
<CELL>&Sun;</CELL>
<CELL><HI>Or</HI></CELL>
<CELL>Gold</CELL>
</ROW>
<ROW>
<CELL>&Moon;</CELL>
<CELL><HI>Argent</HI></CELL>
<CELL>Silver</CELL>
</ROW>
<ROW>
<CELL>&Mars;</CELL>
<CELL><HI>Gules</HI></CELL>
<CELL>Red</CELL>
</ROW>
<ROW>
<CELL>&Jupit;</CELL>
<CELL><HI>Azure</HI></CELL>
<CELL>Blew</CELL>
</ROW>
<ROW>
<CELL>&Saturn;</CELL>
<CELL><HI>Sable</HI></CELL>
<CELL>Black</CELL>
</ROW>
<ROW>
<CELL>&Venus;</CELL>
<CELL><HI>Vert</HI></CELL>
<CELL>Green</CELL>
</ROW>
<ROW>
<CELL>&Merc;</CELL>
<CELL><HI>Purpre</HI></CELL>
<CELL>Purple</CELL>
</ROW>
</TABLE></P>
<P>And by mantled of Light, &s;he meant <HI>Argent</HI> and of the night &s;he meant an <HI>Azure</HI> mantle, powdered with <HI>E&s;toiles,</HI> or Stars Silver. I indeed liked the Blazon, and went in, where al&s;o I found a fair Genealogie of the Arts proceeding from the Conjunction of Arithmetick and Geometry collected by the famous <HI>Beda Dee</HI> in his Ma|thematicall Praeface. Both number and magnitude &s;aith he have a certain originall &s;eed of an incredible proper|ty; of number a unit, of magnitude a point.</P>
<DIV2 TYPE="genealogy">
<PB N="142" REF="80">
<LIST>
<ITEM><HI>Number,</HI> is the union and unity of Unites, and is called <HI>Arithme|tick.</HI></ITEM>
<ITEM>&Moon; <HI>Magnitude</HI> is a thing Mathematicall&punc; and is di|vi&s;ible for ever, and is called <HI>Geometry.</HI></ITEM>
<ITEM><HI>Geode&s;ie,</HI> or Land mea&s;uring</ITEM>
<ITEM><HI>Geographia,</HI> &s;hewing wayes either in &s;pherick, plane, or other the &s;ci|tuation of Cities, Towns, Villages, &amp;c</ITEM>
<ITEM><HI>Chorographia,</HI> teach|ing how to de&s;cribe a &s;mall proportion of ground, not regarding what it hath to the whole &amp;c.</ITEM>
<ITEM><HI>Hydrographia,</HI> &s;hew|ing on a Globe or Plane the analogicall de&s;crip|tion of the Ocean, Sea-Coa&s;ts, through the world, &amp;c.</ITEM>
<ITEM><HI>N<GAP DESC="illegible" EXTENT="1 letter">vigation,</HI> demon|&s;trating how by the &s;horte&s;t way, and in the &s;horte&s;t time a &s;ufficient Ship, betweene any two places in pa&s;&s;ages navi|gable a&s;&s;igned, may be conducted, &amp;c.</ITEM>
<ITEM><HI>Per&s;pective,</HI> is an art Mathematicall which demon&s;trateth the pro|perties of Radiations, di|rect, broken, &amp; reflected</ITEM>
<ITEM><HI>A&s;tronomie</HI> demon|&s;trates the di&s;tance of magnitudes and naturall motions, apparances and pa&s;&s;ions proper to the Planets and fixed &s;tars.</ITEM>
<ITEM><HI>Co&s;mographie;</HI> the whole &amp; perfect de&s;crip|tion of the heavenly, &amp; al&s;o elementall part of the world &amp; their homo|logall &amp; mutuall collati|on nece&s;&s;ary.</ITEM>
<ITEM><HI>Stratarithmetrie.</HI> is the ki<GAP DESC="illegible" EXTENT="2 letters"> appertaining to the War<GAP DESC="illegible" EXTENT="2 letters">, to &s;et in fi|gure any number of men appointed: differing from <HI>Tacticie</HI> which is the wi&s;dome &amp; fore&s;ight.</ITEM>
<ITEM><HI>Mu&s;ick,</HI> &s;aith <HI>Plato,</HI> is &s;i&s;ter to <HI>A&s;tronomie,</HI> &amp; is a Science Mathemati|call, which teacheth by &s;ence &amp; rea&s;on perfectly, to judge &amp; order the di|ver&s;ity of &s;ounds high &amp; low.</ITEM>
<ITEM><HI>A&s;trologie,</HI> &s;everall from, but an off-&s;pring of <HI>A&s;tronomie,</HI> which de|mon&s;trated rea&s;onably the operation and effects of the naturall beams of light, and &s;ecret influ|ence of the Stars.</ITEM>
</LIST>
<P><HI>Statick;</HI> is an Art Mathematicall, demon&s;trating the cau&s;es of heavine&s;&s;e and lightne&s;&s;e of things. <HI><GAP DESC="illegible" EXTENT="2 letters">thropographie,</HI> being the de&s;cription of the number, weight, figure, &s;<GAP DESC="illegible" EXTENT="2 letters">uation and colour of every diver&s;e thing conteined in the body of man. <HI>Trochilike,</HI> de&s;cended of number and mea&s;ure, de|mon&s;trating the properties of wheel or circular motions, whether &s;imple or com|pound, neer Si&s;ter to whom is <HI>Holico&s;ophie,</HI> which is &s;een in the de&s;cribing of the &s;everall conicall Sections and Hyperbolicalline in plants of Dyals or other by Spirall lines, Cylinder, Cone, &amp;c. <HI>Pneumatithmie,</HI> demon&s;trating by clo&s;e hollow figures Geometricall, the &s;trange properties of motion, or &s;tay of water, ayr, &s;moak, fire in their continuity. <HI>Menadrie,</HI> which demon|&s;trateth
<PB N="143" REF="80">
how above natures vertue and force, power may be multiplyed&punc; <HI>Hypogeodie,</HI> being al&s;o a child of Mathematicall Arts, &s;hewing how under the &s;phaericall &s;uperficies of the earth at any depth to any perpendicular a&s;|&s;igned, to know both the di&s;tance and Azimuth from the entrance. <HI>Hydra|gogie,</HI> demon&s;trating the po&s;&s;ible leading of water by Natures law, and by artificiall help. <HI>H<GAP DESC="illegible" EXTENT="1 letter">rometrie,</HI> or this pre&s;ent work of <HI>Horologiographia,</HI> of which it is &s;aid, the commodity thereof no man would want that could know how to be&s;tow his time. <HI><GAP DESC="illegible" EXTENT="1 letter">ographie,</HI> demon&s;trating how the inter&s;ection of all vi&s;uall Pyramids made by any plane a&s;&s;igned, the center, di&s;tance and lights, may be by lines and proper colours repre&s;ented. Then followed <HI>Architecture,</HI> as chief Ma&s;ter, with whom remained the demon&s;trative rea|&s;on and cau&s;e of the Mechanick work in line, plane and &s;olid, by the help of all the forementioned Sciences. <HI>Thaumaturgike,</HI> giving certain order to make &s;trange works, of the &s;ence to be perceived, and greatly to be wondred at. <HI>Arthemea&s;tire,</HI> teaching to bring to actuall experience, all worthy conclu&s;ions by the Arts Mathematicall.</P>
</DIV2>
<DIV2 TYPE="section">
<P>While I was bu&s;ied in this imployment which indeed is my calling, I que&s;tioned <HI>Caliopie,</HI> why &s;he put the note of Illegitima|cy upon <HI>A&s;trologie;</HI> &s;he &s;aid, it indeed made <HI>A&s;tronomy</HI> her father, but it was never owned to participate of the inheritance of the Arts, and therefore the Pedegree doth very fitly &s;ay, doth rea&s;onably not, <HI>qua&s;i Intellectiv&egrave;&punc;</HI> but <HI>Imperfectiv&egrave;;</HI> then did I ask again, why <HI>Arithmetick</HI> had the di&s;tinction of an elder bro|ther the <HI>Labell,</HI> &s;he told me, becau&s;e it was the unity of units, and hath three files united in one <HI>Lambeaux,</HI> and did therefore &s;ig|nifie a my&s;tery, then &s;aid I, why do you repre&s;ent magnitude by the di&s;tinction of a &s;econd Brother, to which &s;he &s;aid, becau&s;e as the Moon, &s;o magnitude in increa&s;ing or decrea&s;ing is the &s;ame in rea&s;on, then did &s;he being the principall of the nine Mu&s;es, and Godde&s;&s;e of <HI>Heralds</HI> &s;ummon to <HI>Urania,</HI> and &s;o to all the o|ther to be &s;ilent, at which &s;ilence was heard <HI>Harmonicon Coele&s;te</HI> by the various Motions of the Heavens, and Fame her Trumpe|ter &s;ounded forth the prai&s;e of men, famous in their generation; and concluded with the Dedication and Con&s;ecration of the Court of Arts in the&s;e words of the learned <HI>Vencelaus Clemens.</HI></P>
<LG>
<L>Templum hoc &s;acrum e&s;t, Pietati, Virtuti,</L>
<L>Honori, Amori, Fidei, &s;emi De&ucirc;m erg&ograve;, &amp;</L>
<L>Coelo Ductum genus, vos magni minore&s;que Dei,</L>
<L>Vos turba mini&s;tra Deorum vos inquam.</L>
<L><PB N="144" REF="81">Sancti <HI>Davides,</HI> magnanimi <HI>Hercules,</HI> genero&s;i <HI>Megi&s;tanes</HI></L>
<L>Bellico&s;i <HI>Alexandri,</HI> glorio&s;i <HI>Augu&s;ti,</HI> docti <HI>Platones,</HI></L>
<L>Facundi <HI>Ne&s;tores,</HI> imici <HI>Jonathanes,</HI> fidi <HI>Achatae.</HI></L>
<L>Uno verbo boni</L>
<L>Huc ade&s;te, praei&s;te, prode&s;te</L>
<L>Vos ver&ograve; orbis propudia</L>
</LG>
<LG>
<L>Impii <HI>Holophernes,</HI> dolo&s;i <HI>Achitopheles,</HI> &s;uperbi <HI>Amanes,</HI></L>
<L>Truculenti <HI>Herodes,</HI> proditorus Judae, impuri <HI>Nerones,</HI></L>
<L>Fal&s;i <HI>Sinones,</HI> &s;editio&s;i <HI>Catilinae,</HI> apo&s;tatae <HI>Juliani.</HI></L>
<L>Adeoque, quicunque, quacunque, quodcunque es</L>
<L>Malus, mala, malum, exe&s;te</L>
<L>Procul hinc procul ite prophani.</L>
<L>Templi hujus Pietas excubat antefores,</L>
<L>Virtute &amp; Honore vigilantibus</L>
<L>Amore &amp; fide a&s;&s;i&s;tentibus</L>
<L>Reliqua providente aedituo Memoria,</L>
<L>Apud quam nomin<GAP DESC="illegible" EXTENT="1 letter"> profiteri</L>
<L>Fas &amp; Jura &s;in<GAP DESC="illegible" EXTENT="1 letter">nt.</L>
<L>Quantum hoc e&s;t? tantum</L>
<L>Vos caetera, quos demi&s;&s;e compellamus, prae&s;tabitis,</L>
<L>Vivite, vincite, valete, Favete.</L>
</LG>
<P><HI>Et vos &ocirc; viri omnium ordinum, Dignitatum, Honorum, &s;pectati&s;|&s;imi ampli&s;&s;imi, chri&s;tiani&s;&s;imi, &amp;c.</HI></P>
<P>Which being done, the Mu&s;es left me, and I found my &s;elf like <HI>Memnon,</HI> or a youth too forward, who being as the learned <HI>Sir Francis Bacon</HI> &s;aith, animated with popular applau&s;e, did in a ra&s;h boldne&s;&s;e come to incounter in &s;ingle combate with <HI>Achil|les</HI> the valiante&s;t of the Grecians, which if like him I am over|come by greater Arti&s;ts, yet I doubt not but this work &s;hall have the &s;ame ob&s;equies of pitty &s;hed upon it, as upon the &s;onne of <HI>Aurora's</HI> Bright Armour, upon who&s;e &s;tatue the &s;un reflecting with its morning beames, did u&s;ually &s;end forth a mourning &s;ound. And if you &s;ay, I had better have followed my Heral|dry (being it is my calling) henceforth you &s;hall find me in my own &s;phear.</P>
<TRAILER>FINIS.</TRAILER>
</DIV2>
</DIV1>
</BODY>
</TEXT>
</EEBO>
</ETS>
