"endlessly," Latin, literally "to infinity" from ad "to, unto" (see ad-) + infinitum "infinity," neuter accusative of adjective infinitus "endless" (see infinite). The English version to infinity is attested from 1630s.
Entries linking to ad infinitum
ad-
word-forming element expressing direction toward or in addition to, from Latin ad "to, toward" in space or time; "with regard to, in relation to," as a prefix, sometimes merely emphatic, from PIE root *ad- "to, near, at."
Simplified to a- before sc-, sp- and st-; modified to ac- before many consonants and then re-spelled af-, ag-, al-, etc., in conformity with the following consonant (as in affection, aggression). Also compare ap- (1).
In Old French, reduced to a- in all cases (an evolution already underway in Merovingian Latin), but French refashioned its written forms on the Latin model in 14c., and English did likewise 15c. in words it had picked up from Old French. In many cases pronunciation followed the shift.
Over-correction at the end of the Middle Ages in French and then English "restored" the -d- or a doubled consonant to some words that never had it (accursed, afford). The process went further in England than in France (where the vernacular sometimes resisted the pedantic), resulting in English adjourn, advance, address, advertisement (Modern French ajourner, avancer, adresser, avertissement). In modern word-formation sometimes ad- and ab- are regarded as opposites, but this was not in classical Latin.
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.