1640s, from Medieval Latin *infinitudo, from Latin infinitus (see infinite) on model of multitudo, magnitudo. Or the English word is perhaps from or modeled on French infinitude (1610s).
Entries linking to infinitude
infinite adj.
late 14c., "eternal, limitless," also "extremely great in number," from Old French infinit "endless, boundless" and directly from Latin infinitus "unbounded, unlimited, countless, numberless," from in- "not, opposite of" (see in- (1)) + finitus "defining, definite," from finis "end" (see finish (v.)). The noun meaning "that which is infinite" is from 1580s.