"curved like an eagle's beak," 1640s, originally in English in reference to long, hooked noses, from Latin aquilinus "of or like an eagle," from aquila "eagle," a word of uncertain origin, usually explained as "the dark bird;" compare aquilus "blackish, swarthy, of the color of darkness," but some suggest the color word is from the bird.
De Vaan writes, "It is possible that 'eagle' was derived from aquilus 'dark' when this had received its colour meaning. It may not be the only dark bird, but it is certainly one of the biggest and most majestic of them." As for aquilus, "The Romans derived this colour from aqua 'water', which [Etymologicum Magnum] reject because they cannot imagine water being black. Still, this seems a more likely derivation to me than from aquila 'eagle' ...."
Meaning "pertaining to an eagle" is from 1650s; that of "eagle-like" is by 1742.