Origin and history of -ae

1620s, "place of combat," from Latin harena "place of combat, enclosed space in the middle of Roman amphitheaters," originally "sand, sandy place" (source also of Spanish arena, Italian rena, French arène "sand"), a word of uncertain origin, perhaps from Etruscan. The central stages of Roman amphitheaters were strewn with sand to soak up the blood. Figuratively, "scene of contest of any kind" by 1814.

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.