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 ; ταῦτ’ 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., κτήσαιτ’ 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 :—καθ’ ὑπερβολὰν τοξεύσας with surpassing aim, S. OT 1196 (lyr.); καθ’ ὑ. ἐπαινεῖν extravagantly, Isoc. 5.11 ; οἱ καθ’ ὑ. ἐν ἐνδείᾳ ὄντες in extremity of need, Arist. Pol. 1295b18 ; αἱ καθ’ ὑ. ἡδοναί Id. EN 1151a12 ; τὸ καθ’ ὑ. τραχύ Phld. Po.Herc. 994.35 ; καθ’ ὑ. ἁμαρτωλός Ep.Rom. 7.13 : c. gen., καθ’ ὑ. φιλοδοξίας OGI 472.9 (Didyma, i A. D.):—so in dat., εὐτελὴς ὑπερβολῇ Men. 615 ; παχεῖ’ ὑ. Philem. 41 ; ὑ. ἀγαθός Arist. HA 625a29 , etc.

5). preeminence, perfection, without any notion of excess, δῑ 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 καθ’ ὑ. φιλία, = ἡ καθ’ 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 καθ’ ὑπερβολήν the superlative degree, in Adjectives, Arist. Top. 134b24 ; τιθέναι ὑπερβολῇ ib. 139a9 ; καθ’ 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.