A.head, top: hence,
1. crown, top of the head, of a horse, Il.8.83, X.Eq.1.11; of a man or god, h.Ap.309, Pi.O.7.36, Hdt.4.187, Sammelb.6003.8 (iv A. D.): between βρέγμα and ἰνίον, Arist.HA491a34; “τὸ ὀστέον τῆς κ.” Hp.VC2.
2. top, peak of a mountain (so mostly Hom.), “οὔρεος ἐν κορυφῇς” Il.2.456; “ὄρεος κορυφῇσι” 3.10, cf. Alcm.60.1; “κορυφαὶ γαίας” B.5.24; “κ. Οὐλύμποιο” Il.1.499, cf. Ar.Nu.270; “Αἴτνας μελάμφυλλοι κορυφαί” Pi.P.1.27; “τηλαυγέ᾽ ἀγ κορυφάν” Id.Pae.7.12; “κ. πόληος” Alc.Supp.17.6; “ἀστρογείτονας κ.” A.Pr.722, cf. Hdt.4.49, 181, 9.99.
3. generally, summit, top, κατὰ κορυφὴν ἐσβαλεῖν ἐς τὴν κάτω Μακεδονίαν straight over the summit, ridge, Th.2.99, cf. IG42(1).71.11 (Epid., iv B. C.), OGI383.125 (Nemrud Dagh, i B. C.); κατὰ κ. [τῆς στήλης] ἔσφαττον (sc. ταύρους) Pl.Criti.119e; ἵσταται κατὰ κ. ὁ ἥλιος in the zenith, Plu.2.938a; τὸ κατὰ κ., with or without σημεῖον, the zenith, Gem.5.64, etc., cf. Plu.Mar.11, Procl.Hyp.4.59; ταῖς τῶν κατὰ κ. λίθων ἐμβολαῖς by the stones falling vertically, Plb.8.7.3.
4. apex, vertex of a triangle, Id.2.14.8; of the Delta, Pl.Ti.21e; point of an angle, “τὸ ἐπὶ τὴν κ. μέρος” Plb.1.26.16, etc.; apex of a cone, Arist.Mete.362b3; κατὰ κορυφήν vertically opposite, of angles, Euc.1.15; of halves of double cone, Apollon. Perg.1 Def.
5. extremity, tip, κορυφαὶ [κλημάτων], τῶν συγκυπτῶν, Thphr.CP3.14.8, Ath.Mech.22.8; in Anatomy, the os coccygis, Poll. 2.183: in pl., finger-tips, Ruf.Onom.85, cf. Poll.2.146: Medic., of an abscess, ἐς κορυφὴν ἀνισταμένης ἀποστάσιος coming to a head, Aret. SA1.7.
II. metaph., λόγων κορυφαί the sum of all his words, Pi.O.7.69, cf. Pae.8.23; “ἔρχομαι ἐπὶ τὴν κ. ὧν εἴρηκα” Pl.Cra.415a; but λόγων κ. ὀρθάν true sense of legends, Pi.P.3.80; κορυφὰς ἑτέρας ἑτέρῃσι προσάπτων μύθων springing from peak to peak, i.e. treating a subject disconnectedly, Emp.24; κ. ὁ λόγος ἐπιθεὶς ἑαυτῷ having reached its conclusion, put the finishing touch to itself, Plu.2.975a; κ. τοῦ κακοῦ height, full development of . . , Aret.SD1.6; τοῦ πάθεος κ. ἴσχοντος ib.1.16.
2. height, excellence of . . , i.e. the choicest, best, “κορυφαὶ πολίων” Pi.N.1.15; κ. ἀρετᾶν ib.34, cf. O.1.13; κ. ἀέθλων, of the Olympic games, Id.O.2.13, cf. N.9.9; “φιάλαν . . πάγχρυσον κ. κτεάνων” Id.O.7.4; ὁ καιρὸς παντὸς ἔχει κορυφάν is the best of all, Id.P.9.79.
4. ἡ τῆς οἰκουμένης κ., of Rome, Lib.Or.59.19.