in reference to writing in which the letters are joined and formed rapidly without lifting the pen or pencil, 1784, from French cursif (18c.), from Medieval Latin cursivus "running," from Latin cursus "a running," from past participle of currere "to run" (from PIE root *kers- "to run").
The notion is of "written with a running hand" (without raising the pen), originally as opposed to the older uncial hand. Greek cursive writing is attested from 160 B.C.E. An older name for it was joining-hand (1580s) because the successive letters of each word are joined. As a noun, "cursive letters or writing," by 1850. Related: Cursively.