Sextus Empiricus, Against the Professors

LCL 382: 244-245

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Sextus Empiricus

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ΠΡΟΣ ΓΕΩΜΕΤΡΑΣ

1

Ἐπεὶ οἱ γεωμέτραι συνορῶντες τὸ πλῆθος τῶν ἐπακολουθούντων αὐτοῖς ἀπόρων1 εἰς ἀκίνδυνον εἶναι δοκοῦν καὶ ἀσφαλὲς πρᾶγμα καταφεύγουσι, τὸ ἐξ ὑποθέσεως αἰτεῖσθαι τὰς τῆς γεωμετρίας ἀρχάς, καλῶς ἂν ἔχοι καὶ ἡμᾶς τῆς πρὸς αὐτοὺς ἀντιρρήσεως ἀρχὴν τίθεσθαι τὸν περὶ τῆς ὑποθέσεως 2λόγον. καὶ γὰρ ὁ Τίμων ἐν τοῖς πρὸς τοὺς φυσικοὺς τοῦτο ὑπέλαβε δεῖν ἐν πρώτοις ζητεῖν, φημὶ δὲ τὸ εἰ ἐξ ὑποθέσεώς τι ληπτέον. διόπερ καὶ ἡμᾶς οἰκεῖόν ἐστιν ἐκείνῳ στοιχοῦντας τὸ παραπλήσιον ποιεῖν ἐν τῇ πρὸς τοὺς ἀπὸ τῶν 3μαθημάτων διεξόδῳ. τάξεως δὲ ἕνεκα προληπτέον ὅτι πολλαχῶς μὲν καὶ ἄλλως ὑπόθεσις προσαγορεύεται, τὰ νῦν δὲ ἀπαρκέσει τριχῶς λέγεσθαι, καθ᾿ ἕνα μὲν τρόπον ἡ δραματικὴ περιπέτεια, καθὸ καὶ τραγικὴν καὶ κωμικὴν ὑπόθεσιν εἶναι λέγομεν καὶ Δικαιάρχου τινὰς ὑποθέσεις τῶν Εὐριπίδου καὶ Σοφοκλέους μύθων, οὐκ ἄλλο τι καλοῦντες 4ὑπόθεσιν ἢ τὴν τοῦ δράματος περιπέτειαν. καθ᾿ ἕτερον δὲ σημαινόμενον ὑπόθεσις προσαγορεύεται ἐν ῥητορικῇ ἡ τῶν ἐπὶ μέρους ζήτησις, καθὸ καὶ

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Against The Geometers

Book III

Against the Geometers

Since the Geometers, perceiving the multitude of1 difficulties which beset them, take refuge in a method which seems to be free from danger and safe, namely, to beg by “hypothesis” the principles of geometry, it will be well for us, too, to begin our attack against them with the argument about “hypothesis.” For2 Timon, in his book Against the Physicists, assumed that one ought to raise this question first of all,—I mean, whether anything should be accepted from “hypothesis.” Hence it is proper for us, in conformity with him, to do likewise in our treatise against these Mathematicians. And, for the sake of3 due order, one must premise that the word “hypotheses” is used in a number of different senses; but it will be enough now to mention three: in one sense it means the peripeteia (or “argument” or “plot”) of a drama, as we say that there is a tragic or a comic “hypothesis,” and certain “hypotheses” of Dicaearchusa of the stories of Euripides and Sophocles, meaning by “hypothesis” nothing else than the peripeteia of the drama. And “hypothesis” is used4 with another signification in rhetoric, as investigation of particulars, in which sense the sophists are wont

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DOI: 10.4159/DLCL.sextus_empiricus-against_professors.1949