Ideal
late Middle English (as a term in Platonic philosophy, in the sense ‘existing as an archetype’): from late Latin idealis, from Latin idea (see idea).
wiktionary
From French idéal, from Late Latin ideālis(“existing in idea”), from Latin idea(“idea”); see idea. In mathematics, the noun ring theory sense was first introduced by German mathematician Richard Dedekind in his 1871 edition of a text on number theory. The concept was quickly expanded to ring theory and later generalised to order theory. The set theory and Lie theory senses can be regarded as applications of the order theory sense.
etymonline
ideal (adj.)
early 15c., "pertaining to an archetype or model," from Late Latin idealis "existing in idea," from Latin idea in the Platonic sense (see idea). Senses "conceived as perfect; existing only in idea," are from 1610s.
ideal (n.)
"(hypothetical) perfect person, thing, or state," 1796, in a translation of Kant, from ideal (adj.). Hence "standard or model of perfection" (1849).
