ὑπερβολή

ὑπερβολή, ἡ, (ὑπερβάλλω) A. a throwing beyond others, δίσκων ὑπερβολαῖς Philostr. Im. 2.19: in intr. sense, altitude of a star, Arist. Mete. 342b32. 2. overshooting, superiority, χερῶν ὑπερβολαῖς E. Fr. 434; στρατιᾶς Th. 6.31. 3. 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 ὑ. ἔχει Men. Her. 62; so οὐδεμίαν or μηδεμίαν ὑ. λείπειν, Isoc. 4.5,110, cf. D. 3.25; οὐδεμίαν ὑ. καταλείπων φιλοτιμίας SIG 545.13 (Delph., iii B. C.); εἴ τις ὑ. τούτου if there is aught beyond (worse than) this, D. 19.66, cf. Isoc. 5.42; ταῦτʼ οὐχ ὑ.; is not this the extreme, the last degree? D. 27.38; ὑπερβολὴν ποιήσομαι I will put an extreme case, Id. 19.332; τοσαύτην ὑ. ποιεῖσθαι ὥστε . . to go so far that . . , Id. 18.190: folld. by a gen., ὑ. ποιεῖσθαι ἐκείνων τῆς αὑτοῦ βδελυρίας to carry his own rascality beyond theirs, Id. 22.52, cf. 23.201, And. 4.22, Lys. 14.38; ὑ. ποιεῖν τῆς τιμῆς to raise the price, Arist. Pol. 1259a26; εἰς ὑ. εὐδαιμονίας ἥκειν Isoc. 11.14; τοσαύτας ὑ. δωρειῶν παρές χηται D. 20.141; ὑ. ἀνοίας ἔχειν Polystr.p.27 W. 4. 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. ἐπαινεῖν extravagantly, Isoc. 5.11; οἱ καθʼ ὑ. ἐν ἐνδείᾳ ὄντες in extremity of need, Arist. Pol. 1295b18; αἱ καθʼ ὑ. ἡδοναί Id. EN 1151a12; τὸ καθʼ ὑ. τραχύ Phld. Po.Herc. 994.35; καθʼ ὑ. ἁμαρτωλός Ep.Rom. 7.13: c. gen., καθʼ ὑ. φιλοδοξίας OGI 472.9 (Didyma, i A. D.):—so in dat., εὐτελὴς ὑπερβολῇ Men. 615; παχεῖʼ ὑ. Philem. 41; ὑ. ἀγαθός Arist. HA 625a29, etc. 5. 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. 6. 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. 7. τὸ καθʼ ὑπερβολήν the superlative degree, in Adjectives, Arist. Top. 134b24; τιθέναι ὑπερβολῇ ib.139a9; καθʼ ὑ. εἰπεῖν Id. Cael. 281a16. 8. overbid at auction, PPetr. 2p.44 (iii B. C.). II. crossing over, passage of mountains, etc., X. An. 1.2.25, Plb. 3.34.6, etc. 2. 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. III. (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.). IV. 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.