Definition: "one past fourteene yeeres of age, beginning to bee moved with Venus delight" (Henry Cockeram, An English Dictionary, 1623)
For those of you who are unaccustomed to reading definitions written in the linguistic register of an early-17th century smarty-pants lexicographer, the meaning of the word above is, well, "horny teenager." This gives us a very fine example of how occasionally the words for common things are themselves quite uncommon, as hirquiticke is extremely rare. It is uncertain where Cockeram found the word, as we have no evidence of actual use prior to 1623, although he may have borrowed it from Thomas Eliot's Latin dictionary of 1538, which defined hirquitalus as "a chylde, whiche passeth the age of xiiii yeres, and begynneth to be styrred with lechery."
The Latin word for "he-goat" is hircus, from which we get hircine ("of, relating to, or suggestive of a goat; especially: resembling a goat in smell"). Occasional writers have used a variant of this root to make fanciful nonce-words based on the goat's reputed libidinousness.
To speak of her hirquitalliency at the elevation of the pole of his Microcosme, or of his luxuriousness to erect a gnomon on her horizontal dyal, will perhaps be held by some to be expressions full of obscœness, and offensive to the purity of chaste ears.
— Thomas Urquhart, Ekskybalauron, 1652