Etymology
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imago (n.)

"final or adult stage of an insect," 1797, from Latin imago "an image, a likeness," from stem of imitari "to copy, imitate" (from PIE root *aim- "to copy"). "The name is due to the fact that such an insect, having passed through its larval stages, and having, as it were, cast off its mask or disguise, has become a true representation or image of its species." [Century Dictionary]

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imagine (v.)

mid-14c., "to form a mental image of," from Old French imaginer "sculpt, carve, paint; decorate, embellish" (13c.), from Latin imaginari "to form a mental picture, picture to oneself, imagine" (also, in Late Latin imaginare "to form an image of, represent"), from imago "an image, a likeness," from stem of imitari "to copy, imitate" (from PIE root *aim- "to copy"). Sense of "suppose, assume" is first recorded late 14c. Related: Imagined; imagining.

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emulation (n.)

"effort to equal or excel in qualities or actions that one admires in another or others; imitative rivalry," 1550s, from French émulation (13c.) and directly from Latin aemulationem (nominative aemulatio) "rivalry, emulation, competition," noun of action from past-participle stem of aemulari "to rival, strive to excel," from aemulus "striving, rivaling" (also as a noun, "a rival," fem. aemula), from Proto-Italic *aimo-, from PIE *aim-olo, suffixed form of root *aim- "copy" (from PIE root *aim- "to copy").

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image (n.)

c. 1200, "piece of statuary; artificial representation that looks like a person or thing," from Old French image "image, likeness; figure, drawing, portrait; reflection; statue," earlier imagene (11c.), from Latin imaginem (nominative imago) "copy, imitation, likeness; statue, picture," also "phantom, ghost, apparition," figuratively "idea, appearance," from stem of imitari "to copy, imitate" (from PIE root *aim- "to copy").

Meaning "reflection in a mirror" is early 14c. The mental sense was in Latin, and appears in English late 14c. Sense of "public impression" is attested in isolated cases from 1908 but not in common use until its rise in the jargon of advertising and public relations, c. 1958.

To þe ymage of god he made hym [Genesis i.27, Wycliffite Bible, early version, 1382]
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motiveless (adj.)

"having no motive or aim," 1798, from motive (n.) + -less.

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stochastic (adj.)
1660s, "pertaining to conjecture," from Greek stokhastikos "able to guess, conjecturing," from stokhazesthai "to guess, aim at, conjecture," from stokhos "a guess, aim, fixed target, erected pillar for archers to shoot at," perhaps from PIE *stogh-, variant of root *stegh- "to stick, prick, sting." The sense of "randomly determined" is from 1934, from German stochastik (1917).
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purposeful (adj.)

"characterized by definite aim; made or introduced on purpose," 1835, from purpose (n.) + -ful. Related: Purposefully; purposefulness.

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objective (n.)
1738, "something objective to the mind," from objective (adj.). Meaning "goal, aim" (1881) is from military term objective point (1852), reflecting a sense evolution in French.
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scopeless (adj.)

"having no purpose or aim,; affording no opportunity," 1660s, from scope (n.1) + -less. Related: Scopelessly; scopelessness.

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single-minded (adj.)
1570s, "sincere, honest" (a sense also in single-hearted); meaning "having a single aim or purpose" is from 1860. See single (adj.) + -minded. Related: Single-mindedly; single-mindedness.
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