Etymology
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tripartite (adj.)

"divided in three," early 15c., from Latin tripartitus "divided into three parts," from tri- "three" (see three) + partitus, past participle of partiri "to divide" (from pars "a part, piece, a share," from PIE root *pere- (2) "to grant, allot").

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terceroon (n.)
offspring of a white and a mulatto, 1760, from Spanish *terceron, from tercero "a third (person)," from tercio "third," from Latin tertius "a third," from root of tres "three" (see three). So called from being third in descent from a Negro.
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triumvir (n.)
"one of three men in the same office or of the same authority," mid-15c., from Latin triumvir, from Old Latin phrase trium virum, genitive plural of tres viri "three men," from tres "three" (see three) + viri, plural of vir "man" (from PIE root *wi-ro- "man"). The Latin plural was triumviri.
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tertiary (adj.)
1650s, "of the third order, rank, degree, etc.," from Latin tertiarius "of or pertaining to a third," from tertius "third, a third," from root of tres "three" (see three). The geological sense (with capital T-) of "era after the Mesozoic" (which formerly was called the Secondary) is attested from 1794, after Italian terziari, used in this sense 1760 by Italian geologist Giovanni Arduino (1714-1795).
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tercel (n.)
"male falcon," late 14c., from Old French tercel (c. 1200), from Medieval Latin tertiolus, from Latin tertius "third, a third," from root of tres "three" (see three). Various theories as to why it is called this; one says it's because the males are a third smaller than the females, another because a third egg in the nest (smaller than the other two) is believed always to produce a male bird.
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tertium quid (n.)
something indeterminate between two other things, 1724, Latin, literally "third something," from tertius "third, a third," from the root of tres "three" (see three). A loan-translation of Greek triton ti (Plato), used in alchemy for "unidentified element present in a combination of two known ones." The Latin word also figures in phrases tertium non datur "no third possibility exists," and tertius gaudens "a third party that benefits from conflict between the other two."
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trivium (n.)

by 1751, from Medieval Latin trivium (9c.) "grammar, rhetoric, and logic," the first three of the seven liberal arts, considered initiatory and foundational to the other four (arithmetic, geometry, astronomy, and music). From Latin trivium, in classical Latin "place where three roads meet; a frequented place; public street, highway," from tri- "three" (see three) + via "road" (see via). Compare trivia and also see quadrivium.

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travail (n.)
"labor, toil," mid-13c., from Old French travail "work, labor, toil, suffering or painful effort, trouble; arduous journey" (12c.), from travailler "to toil, labor," originally "to trouble, torture, torment," from Vulgar Latin *tripaliare "to torture," from *tripalium (in Late Latin trepalium) "instrument of torture," probably from Latin tripalis "having three stakes" (from tria "three;" see three + palus "stake" (from PIE *pakslo-, suffixed form of root *pag- "to fasten"), which sounds ominous, but the exact notion is obscure. The verb is recorded from late 13c. in English, from the verb in Old French.
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trinity (n.)

early 13c., "the Father, Son and Holy Spirit," constituting one God in prevailing Christian doctrine, from Old French trinite "Holy Trinity" (11c.), from Late Latin trinitatem (nominative trinitas) "Trinity, triad" (Tertullian), from Latin trinus "threefold, triple," from plural of trini "three at a time, threefold," related to tres (neuter tria) "three" (see three).

The Latin word was widely borrowed in European languages with the spread of Christianity (Irish trionnoid, Welsh trindod, German trinität). Old English used þrines as a loan-translation of Latin trinitas. Related: Trinitarian.

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tierce (n.)
old unit of liquid measure equal to one-third of a pipe (42 gallons), 1530s, from Anglo-French ters, Old French tierce (11c.). used in the sense "one-third" in various ways, from Latin tertia, fem. of tertius "a third," from PIE *tri-tyo-, from root *trei- (see three). Also used in Middle English for "a third part" (late 15c.), "the third hour of the canonical day" (ending at 9 a.m.), late 14c., and, in astronomy and geometry, "sixtieth part of a second of an arc."
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