A.three-cornered, triangular, τὴν τ. ἐς χθόνα Νειλῶτιν, of the Delta, A.Pr.813; “τ. ῥυθμοί” Id.Fr.78; “βάσεις” Pl.Ti.55b; of the hearts of certain fish, Arist.Frr.314,330,333; of Sicily, Plb.1.42.3; of Britain, Str.4.5.1.
2. ἀριθμοὶ τρίγωνοι, triangular numbers, are those whose units can be disposed in a triangle, as 3 <*>, 6 <*>, etc., being represented by the formula n(n + 1)/2, Plu.2.1003f, cf. Nicom.Ar.2.8; these numbers are also called triangles (τρίγωνοι), Plu. 2.744b.
3. Astrol., in triangular or trine aspect, of planets when there are three signs of the zodiac between them, so that they are at the apices of an equilateral triangle, S.E.M.5.39, Plot.2.3.4; “τ. σχηματισμοί” Ptol.Tetr.35, cf. Man.3.344.
2. a musical instrument of triangular form, with strings of equal thickness but unequal lengths, Eup.77, Pl.Com.69.13, Pl.R.399c, Arist.Pol.1341a41, Diog.Ath.1.9; called τ. ψαλτήρια in Arist.Pr.919b12:—also as masc., “πολὺς δὲ Φρὺξ τρίγωνος” S.Fr.412, cf. Ath.4.183e.
3. one of the Athenian lawcourts, Din.Fr.89.35, Lycurg.Fr.10, Men.1076, Paus.1.28.8, Poll.8.121.
4. the constellation Triangulum, Eudox. ap. Hipparch.1.2.13.