Etymology
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finite (adj.)
early 15c., "limited in space or time, finite," from Latin finitum, past participle of finire "to limit, set bounds; come to an end" (see finish (v.)). Related: Finitely; finiteness.
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finity (n.)
1670s, "an instance of finiteness," from French finité, from fini, past participle of finir "to bound," from Latin finire (see finite).
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non-renewable (adj.)

also nonrenewable, "not able to be renewed," by 1896 of licenses, library book loans, etc., from non- + renewable. Of natural resources or sources of energy, "existing in finite quantity; not capable of being replenished," by 1935. 

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rational (adj.)

late 14c., racional, "pertaining to or springing from reason;" mid-15c., of persons, "endowed with reason, having the power of reasoning," from Old French racionel and directly from Latin rationalis "of or belonging to reason, reasonable," from ratio (genitive rationis) "reckoning, calculation, reason" (see ratio).

In arithmetic, "expressible in finite terms," 1560s. Meaning "conformable to the precepts of practical reason" is from 1630s. Related: Rationally. It is from the same source as ratio and ration; the sense in rational is aligned with that in related reason (n.), which got deformed in French.

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contingent (adj.)

late 14c., "depending upon circumstances, not predictable with certainty, provisionally liable to exist," from Old French contingent or directly from Latin contingentem (nominative contingens) "happening; touching," in Medieval Latin "possible, contingent," present participle of contingere "to happen to one, befall, come to pass," originally "to touch" (see contact (v.)).

Meaning "not existing or occurring through necessity, happening by chance, accidental" is from 1610s. The noun is from 1540s, "thing happening by chance or by the will of a finite free agent;" as "a group forming part of a larger group" from 1727, originally especially "share of troops to be furnished by a power in a treaty or alliance," on the notion of "that which falls to one in a division or apportionment among a number."

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