Henry George Liddell, Robert Scott, A Greek-English Lexicon

A.Trito-born, a name of Athena, Il.4.515, 8.39, Od.3.378, Hes.Th.895,924, IG14.1389ii 1. (Variously expld. in antiquity, from the lake Τριτωνίς in Libya, from which an old legend represents the goddess to have been born, E.Ion872 (anap.), cf. Hdt.4.180; or from Triton, a torrent in Boeotia, Paus.9.33.7, cf. Apollod.1.3.6; or from a spring in Arcadia, Paus.8.26.6; or from τριτώ, Aeol. word for κεφαλή (Sch.Ar.Nu.985, Tz.ad Lyc.519; Athamanian acc. to Nic.（Fr.145) ap.Hsch.), i.e. head-born; or, born on the third day of the month, Ister 26 (the 23rd, τρίτῃ φθίνοντος, Sch.BT Il.8.39); or, the third child after Apollo and Artemis, Suid. s.v. τριτογενής; or, as representing Nature, born thrice in the year, D.S.1.12; or because she was author of the three main bonds of social life, Democr.1b,2.)

II. the Pythagoreans gave the name Ἀθηνᾶ τ. to the equilateral triangle, Plu.2.381e; cf. τρεῖς, τριάς.