Τριτογένεια

A. Trito-born, a name of Athena, Il. 4.515, 8.39, Od. 3.378, Hes. Th. 895,924, IG 14.1389i i 1. (Variously expld. in antiquity, from the lake Τριτωνίς in Libya, from which an old legend represents the goddess to have been born, E. Ion 872 (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.