An Etymological Dictionary of Astronomy and Astrophysics

1. (n.) A standard of perfection, beauty, or excellence.
   Math.: A subset of a ring that is closed under addition and multiplication by any element of the ring.
   
2. (adj.) Existing only in the imagination; not real or actual.
   Conforming exactly to an ideal, law, or standard; perfect. → ideal gas.

Etymology (EN): M.E. ydeall, from L.L. idealis “existing in idea,” from L. → idea.

Etymology (PE): Ârmân “ideal” in Mod.Pers., traditionally “desire; hope; grief,” variants armân, urmân, prefixed from mân, “thought, mind,” → idea. The first element may be related to Av. armaē- “in peace, still; quietly;” PIE base *er[ə]- “to be still” (cf. Skt. īrmā (adv.) “quiet, still, being in the same place;” Gk. erôé “calm, peace;” O.H.G. rouwa “rest”), as in Av. armaē.šad- “sitting quietly,” armaē.štā- “standing still, stagnant.” Therefore, Pers. ârmân may be related to Av. *armaē.manah- (PIE *ermen-) “thought in peace, quiet mind.”
Mineyi, minevâr, adj. from miné, → idea.