1520s, "not precise, vague," from Latin indefinitus "indefinite," from in- "not, opposite of, without" (see in- (1)) + definitus, past participle of definire (see define). In reference to number, "The term was introduced by Pascal. Descartes distinguished between the indefinite, which has no particular limit, and the infinite which is incomparably greater than anything having a limit. The distinction is considered as highly important by many metaphysicians." [Century Dictionary]
1580s, the tense of Greek verbs that most closely corresponds to the simple past in English, from Greek aoristos (khronos) "indefinite (tense)," from aoristos "without boundaries, undefined, indefinite," from assimilated form of a- "not" (see a- (3)) + horistos "limited, defined," verbal adjective from horizein "to limit, define," from horos "boundary, limit, border" (see horizon). Related: Aoristic.
"simple, uninflected form of a verb, expressing its general sense," 1510s, from earlier use as an adjective (mid-15c.), from Late Latin infinitivus "unlimited, indefinite," from Latin infinitus "not limited" (see infinite). "Indefinite" because not restricted by person or number. Related: Infinitival; infinitively.
1905, "of an indefinite number," originally Morse code slang for "dash," influenced by association with numerals such as twenty, thirty, etc.
by 1717, in algebra textbooks, in phrase to the nth, a mathematical term indicating an indefinite number, in which n is an abbreviation for (whole) number (n.). Figurative (non-mathematical) use is by 1852.
indefinite article before words beginning with vowels, 12c., from Old English an (with a long vowel) "one; lone," also used as a prefix meaning "single, lone" (as in anboren "only-begotten," anhorn "unicorn," anspræce "speaking as one"). See one for the divergence of that word from this. Also see a, of which this is the older, fuller form.
In other European languages, identity between the indefinite article and the word for "one" remains explicit (French un, German ein, etc.). Old English got by without indefinite articles: He was a good man in Old English was he wæs god man.
In texts of Shakespeare, etc., an as a word introducing a clause stating a condition or comparison conjunction is a reduced form of and in this now-archaic sense "if" (a usage first attested late 12c.), especially before it.
"quality or state of endless duration, continued uninterrupted existence for an indefinite period of time," late 14c., perpetuite, from Old French perpetuité "permanence, duration" (13c., Modern French perpétuité) and directly from Latin perpetuitatem (nominative perpetuitas) "uninterrupted duration, continuity, continuous succession," from perpetuus (see perpetual).