ἄκρα

A. highest or farthest point:

1. headland, cape, Il. 4.425, 14.36, Od. 9.285, S. Tr. 788, Pl. Criti. 111a: metaph., ἄκρην πενίης οὐχ ὑπερεδράμομεν Thgn. 619, cf. A. Eu. 562; κάμπτειν Men. 4.

2. hill-top, height, Od. 8.508, Hymn.Is. 72 (pl.).

3. of a wave, crest, οὐ γὰρ ὑπερθεῖν κύματος ἄκραν δυνάμεσθα E. Fr. 230.

4. Hom. only in phrase κατ’ ἄκρης, νῦν ὤλετο πᾶσα κατ’ ἄκρης Ἴλιος αἰπεινή from top to bottom, i.e. utterly, Il. 13.772; κατ’ ἄ. Ἴλιον ἑλέειν 15.557, cf. 24.728, Hdt. 6.18, Th. 4.112; κατ’ ἄ. ἐξαιρεῖν Pl. Lg. 909b; γῆν πατρῴαν . . πρῆσαι κατ’ ἄ. utterly, S. Ant. 201: metaph., κατ’ ἄ. ὡς πορθούμεθα how utterly . .! A. Ch. 691, cf. S. OC 1242, E. IA 778; but ἔλασεν μέγα κῦμα κατ’ ἄ. from above, Od. 5.313.

5. citadel built on a steep rock overhanging a town (usu. ἀκρόπολις), X. An. 7.1.20, Hyp. Lyc.Fr. 3, Luc. Bis Acc. 13.

6. end, extremity, Arist. HA 512a6, 518a9: Math., of lines, Papp. 682.14; of the extremes in a proportion, Id. 70.6, Euc. 6.16, etc.