ὑπερβολ-ή · hyperbol-ē — LSJ
a throwing beyond others, δίσκων ὑπερβολαῖς Philostr. Im. 2.19: in intr. sense, altitude of a star, Arist. Mete. 342b32.
overshooting, superiority, χερῶν ὑπερβολαῖς E. Fr. 434; στρατιᾶς Th. 6.31.
excess, τοῦ μεγέθεος Archyt. 1; opp. ἔλλειψις or ἔνδεια, Pl. Prt. 356a, 357a, 357b; θερμασίης Hp. Vict. 2.65; ὑ. δισσὴ . . , τῷ ποσῷ καὶ τῷ ποιῷ Arist. PA 668b14; ὑπερβολὴν τῆς ἐπιθυμίας ἔχειν c. acc. et inf., And. 3.33, etc.: hence in various phrases, χρημάτων ὑπερβολῇ . . πρίασθαι at an extravagant price, E. Med. 232; ἐπέφερον τὴν ὑ. τοῦ καινοῦσθαι pushed on their extravagance in revolutionizing, Th. 3.82; οὐκ ἔχον ἐστὶν ὑπερβολήν it can go no further, D. 21.119, cf. 25.54; ἃ μηδὲ πιθανὰς τὰς
with Prep. in Adverbial phrases, = ὑπερβαλλόντως, εἰς ὑπερβολήν in excess, exceedingly; εἰς ὑ. ἄμεινον E. Fr. 494; ἀγαθὸς εἰς ὑ. Antiph. 80.11; ἐς ὑ. ἐκθερμαίνεσθαι Hp. Vict. 2.65: c. gen., κτήσαιτʼ ἂν ὄλβον εἰς ὑ. πατρός E. Fr. 282.6 (v.l. εἰς ὑπεκτροφὴν πάτρας); far beyond, τοῦ πρόσθεν εἰς ὑ. πανοῦργος, i.e. far more wicked, Id. Hipp. 939, cf. D. 61.33; ἀναλίσκειν πάντα εἰς ὑπερβολάς Pl. Ep. 326d:—ἐξ ὑπερβολῆς Plb. 8.15.8:—καθʼ ὑπερβολὰν τοξεύσας with surpassing aim, S. OT 1196 (lyr.); καθʼ ὑ.
preeminence, perfection, without any notion of excess, διʼ ἀρετῆς ὑπερβολήν Id. EN 1145a24, cf. Rh. 1367b1, Pol. 1284a4; ἡ ὑ. τῆς φιλίας the best and noblest kind of friendship, Id. EN 1166b1; but ἡ καθʼ ὑ. φιλία, = ἡ καθʼ ὑπεροχήν, Id. EE 1238b18.
overstrained phrase, hyperbole, ὑπερβολὰς εἰπεῖν Isoc. 4.88; οἱ πρὸς ὑπερβολὴν πεπονημένοι λόγοι ib. 11; ὑπερβολὰς εἰπεῖν make strong statements, Id. 3.35, D. 27.64; as a figure of speech, Arist. Rh. 1413a29, Demetr. Eloc. 52, Str. 3.2.9; πρὸς -ὴν εἰρημένος Id. 1.2.33.
τὸ καθʼ ὑπερβολήν the superlative degree, in Adjectives, Arist. Top. 134b24; τιθέναι ὑπερβολῇ ib. 139a9; καθʼ ὑ. εἰπεῖν Id. Cael. 281a16.
overbid at auction, PPetr. 2p.44 (iii B. C.).
crossing over, passage of mountains, etc., X. An. 1.2.25, Plb. 3.34.6, etc.
in sg. or pl., place of passage, mountain-pass, with or without τοῦ ὄρους, τῶν ὀρέων, X. An. 3.5.18, 4.1.21, 4.4.18; ὑ. τοῦ Ταύρου Wilcken Chr. 1 ii 14 (iii B. C.); αἱ τῶν Ἄλπεων ὑ. Plb. 3.39.10; αἱ Ἄλπιαι ὑ. Str. 7.1.5; ἡ κατὰ τὸν Αἷμον ὑ. D.S. 19.73.
(from Med.) delay, τοῦ κακοῦ Hdt. 8.112, cf. Decr. ap. D. 18.29, Plb. 14.9.8; [τῆς κρίσεως] ὑ. λαβούσης PEnteux. 65.3 (iii B. C.).
the conic section called hyperbola, because the square of the ordinate is equal to a rectangle with height equal to the abscissa applied to the parameter (as base) but exceeding (ὑπερβάλλον), i. e. overlapping, that base, Apollon.Perg. Con. 1.12, Procl. in Euc. p.419F.