ideate (v.)

late 14c., "archetype, concept of a thing in the mind of God," from Latin idea "Platonic idea, archetype," a word in philosophy, the word (Cicero writes it in Greek) and the idea taken from Greek idea "form; the look of a thing; a kind, sort, nature; mode, fashion," in logic, "a class, kind, sort, species," from idein "to see," from PIE *wid-es-ya-, suffixed form of root *weid- "to see."

In Platonic philosophy, "an archetype, or pure immaterial pattern, of which the individual objects in any one natural class are but the imperfect copies, and by participation in which they have their being" [Century Dictionary].

Meaning "mental image or picture" is from 1610s (the Greek word for it was ennoia, originally "act of thinking"), as is the sense "concept of something to be done; concept of what ought to be, differing from what is observed." Sense of "result of thinking" first recorded 1640s.

Idée fixe (1836) is from French, literally "fixed idea." Through Latin the word passed into Dutch, German, Danish as idee, which also is found in English dialects. The philosophical sense has been somewhat further elaborated since 17c. by Descartes, Locke, Berkeley, Hume, Kant. Colloquial big idea (as in what's the ...) is from 1908.

verbal suffix for Latin verbs in -are, identical with -ate (1). Old English commonly made verbs from adjectives by adding a verbal ending to the word (such as gnornian "be sad, mourn," gnorn "sad, depressed"), but as the inflections wore off English words in late Old and early Middle English, there came to be no difference between the adjective and the verb in dry, empty, warm, etc. Thus accustomed to the identity of adjectival and verbal forms of a word, the English, when they began to expand their Latin-based vocabulary after c. 1500, simply made verbs from Latin past-participial adjectives without changing their form (such as aggravate, substantiate) and it became the custom that Latin verbs were Englished from their past participle stems.