Etymology
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Words related to *trep-

apotropaic (adj.)

"having the power of averting evil influence," 1883, with -ic + Greek apotropaios "averting evil," from apotrepein "to turn away, avert," from apo "off, away" (see apo-) + trepein "to turn" (from PIE root *trep- "to turn"). Related: Apotropaion "amulet, etc., reputed to avert evil;" apotropaism.

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atropine (n.)
also atropin, "poisonous crystalline alkaloid obtained from nightshade," 1831, from Latin atropa "deadly nightshade" (from which the alkaloid poison is extracted), from Greek atropos "inflexible, unchangeable," also the name of one of the Fates (see Atropos) + chemical suffix -ine (2). By 1821 in French and German.
Atropos 
one of the Fates (the one who holds the shears and determines the manner of a person's death and cuts the thread), from Greek, "inflexible, unchangeable," literally "not to be turned away," from a- "not" (see a- (3)) + stem of trepein "to turn" (from PIE root *trep- "to turn"). Related form atropa was the Greek name for deadly nightshade.
contrive (v.)

early 14c., controve, contreve, "to invent, devise, plan;" late 14c., "to manage by a plan or scheme," from Old French controver (Modern French controuver) "to find out, contrive, imagine," from Late Latin contropare "to compare" (via a figure of speech), from an assimilated form of Latin com "with, together" (see con-) + tropus "song, musical mode," from Greek tropos "figure of speech" (from PIE root *trep- "to turn").

Sense evolution (in French) was from "invent with ingenuity" to "invent falsely." Spelling in English was altered by the same unexplained 15c. sound change that also affected briar, friar, choir. Related: Contrived; contriving.

entropy (n.)

1868, from German Entropie "measure of the disorder of a system," coined 1865 (on analogy of Energie) by German physicist Rudolph Clausius (1822-1888), in his work on the laws of thermodynamics, from Greek entropia "a turning toward," from en "in" (see en- (2)) + trope "a turning, a transformation" (from PIE root *trep- "to turn"). The notion is supposed to be "transformation contents." Related: Entropic.

It was not until 1865 that Clausius invented the word entropy as a suitable name for what he had been calling "the transformational content of the body." The new word made it possible to state the second law in the brief but portentous form: "The entropy of the universe tends toward a maximum," but Clausius did not view entropy as the basic concept for understanding that law. He preferred to express the physical meaning of the second law in terms of the concept of disgregation, another word that he coined, a concept that never became part of the accepted structure of thermodynamics. [Martin J. Klein, "The Scientific Style of Josiah Willard Gibbs," in "A Century of Mathematics in America," 1989]
heliotrope (n.)

"plant which turns its flowers and leaves to the sun," 1620s, from French héliotrope (14c., Old French eliotrope) and directly from Latin heliotropium, from Greek hēliotropion "sundial; heliotropic plant," from hēlios "sun" (from PIE root *sawel- "the sun") + tropos "a turn, change" (from PIE root *trep- "to turn"). In English the word in Latin form was applied c. 1000-1600 to heliotropic plants. Related: Heliotropic.

isotropic (adj.)
"having the same properties in all directions," 1856, from iso- + -tropic, from Greek tropikos "belonging to a turning," from tropos "a turning, way, manner," from trepein "to turn" (from PIE root *trep- "to turn"). Isotropous is from 1859.
psychotropic (adj.)

"affecting a person's mental state," especially "of or pertaining to drugs that affect mental states," 1956, from psycho- + -tropic, from Greek tropos "a turning," from trepein "to turn" (from PIE root *trep- "to turn"). Hence, what "turns" the mind.

retrieve (v.)

early 15c., retreven, "find or discover again," originally in reference to dogs finding lost game, from retruev-, stem of Old French retreuver (Modern French retrouver) "find again, recover, meet again, recognize," from re- "again" (see re-) + trouver "to find," probably from Vulgar Latin *tropare "to compose," from Greek tropos "a turn, way, manner" (from PIE root *trep- "to turn").

Altered 16c. to retrive; modern form is from mid-17c. Specifically, of a dog, "to find and bring to hand game wounded or killed by a sportsman" is by 1856. The mental sense of "recall, recover by effort of memory" is from 1640s; computer sense of "obtain (stored information) again" is by 1962.

trope (n.)
1530s, from Latin tropus "a figure of speech," from Greek tropos "a turn, direction, course, way; manner, fashion," in rhetoric, "turn or figure of speech," related to trope "a turning" and trepein "to turn," from PIE root *trep- "to turn." Technically, in rhetoric, "a figure of speech which consists in the use of a word or phrase in a sense other than that which is proper to it" [OED], "as when we call a stupid fellow an ass, or a shrewd man a fox" [Century Dictionary].