Etymology
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cogitate (v.)

"to think earnestly or seriously," 1560s (transitive); 1630s (intransitive); from Latin cogitatus, past participle of cogitare "to think" (see cogitation). Related: Cogitated; cogitating.

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monitory (adj.)

"giving admonition, conveying a warning," late 15c., from Latin monitorius "admonishing," from monitus, past participle of monere "to admonish, warn, advise," from PIE *moneie- "to make think of, remind," suffixed (causative) form of root *men- (1) "to think."

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value (v.)
Origin and meaning of value
mid-15c., "estimate the value of," also "think highly of," probably from value (n.). Related: Valued, valuing.
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ideate (v.)
c. 1600, "imagine, form ideas," from idea + -ate (2). From 1862 as "to think." Related: Ideated; ideating.
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cogito ergo sum 

Latin phrase, literally "I think, therefore I am;" the starting point of Cartesian philosophy (see Cartesian), from cogito, first person singular present indicative active of cogitare "to think" (see cogitation) + ergo "therefore" (see ergo) + sum, first person singular present indicative of esse "to be" (from PIE root *es- "to be").

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meditate (v.)

1580s, "to ponder, think abstractly, engage in mental contemplation" (intransitive), probably a back-formation from meditation, or else from Latin meditatus, past participle of meditari "to meditate, think over, reflect, consider," frequentative form of PIE root *med- "take appropriate measures." From 1590s as "to plan in the mind," also "to employ the mind in thought or contemplation," especially in a religious way. Related: Meditated; meditating.

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monition (n.)

c. 1400, monicioun, "warning, instruction given by way of caution," from Old French monition (13c.) and directly from Latin monitionem (nominative monitio) "warning, admonition, reminding," noun of action from past-participle stem of monere "to admonish, warn, advise," from PIE *moneie- "to make think of, remind," suffixed (causative) form of root *men- (1) "to think." With specific meanings in civil and ecclesiastical law.

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premonition (n.)

mid-15c., premunicion, premunition, "preliminary warning, previous notification or admonishment," from Anglo-French premunition (late 14c.), Old French premonicion, from Medieval Latin praemonitionem (nominative praemonitio) "a forewarning," noun of action from past-participle stem of Latin praemonere "forewarn," from prae "before" (see pre-) + monere "to admonish, warn, advise," from PIE *moneie- "to make think of, remind," suffixed (causative) form of root *men- (1) "to think."

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ament (n.)
"person born an idiot," 1894, from Latin amentia "madness," from amentem "mad," from a for ab "away from" (see a- (2)) + mentem "mind," from PIE root *men- (1) "to think."
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memento (n.)

late 14c., "Psalm cxxxi in the Canon of the Mass" (which begins with the Latin word Memento and in which the dead are commemorated), from Latin memento "remember," second person singular imperative of meminisse "to remember, recollect, think of, bear in mind," a reduplicated form, related to mens "mind," from PIE root *men- (1) "to think." Meaning "a hint or suggestion to awaken memory, a reminder, an object serving as a warning" is from 1580s; sense of "keepsake" is recorded by 1768.

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