Democritus, Mathematical Works

LCL 335: 228-229

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Greek Mathematics

VII. Democritus

Plut. De Comm. Notit. 39. 3, 1079 e

Ἔτι τοίνυν ὅρα τίνα τρόπον ἀπήντησε Δημοκρίτῳ, διαποροῦντι φυσικῶς καὶ ἐπιτυχῶς, εἰ κῶνος τέμνοιτο παρὰ τὴν βάσιν ἐπιπέδῳ, τί χρὴ διανοεῖσθαι τὰς τῶν τμημάτων ἐπιφανείας, ἴσας ἢ ἀνίσους γινομένας; ἄνισοι μὲν γὰρ οὖσαι τὸν κῶνον ἀνώμαλον παρέξουσι, πολλὰς ἀποχαράξεις λαμβάνοντα βαθμοειδεῖς καὶ τραχύτητας· ἴσων δ᾿ οὐσῶν, ἴσα τμήματα ἔσται, καὶ φανεῖται τὸ τοῦ κυλίνδρου πεπονθὼς ὁ κῶνος, ἐξ ἴσων συγκείμενος καὶ οὐκ ἀνίσων κύκλων, ὅπερ ἐστὶν ἀτοπώτατον.

Archim. Meth., Archim. ed. Heiberg ii. 430. 1–9

Διόπερ καὶ τῶν θεωρημάτων τούτων, ὧν Εὔδοξος ἐξηύρηκεν πρῶτος τὴν ἀπόδειξιν, περὶ τοῦ κώνου καὶ τῆς πυραμίδος, ὅτι τρίτον μέρος ὁ μὲν κῶνος


Greek Mathematics

VII. Democritus

Plutarch, On the Common Notions 39. 3, 1079 e

Consider further in what manner it occurred to Democritus,a in his happy inquiries in natural science, to ask if a cone were cut by a plane parallel to the base,b what must we think of the surfaces forming the sections, whether they are equal or unequal? For, if they are unequal, they will make the cone irregular, as having many indentations, like steps, and unevennesses; but if they are equal, the sections will be equal, and the cone will appear to have the property of the cylinder, and to be made up of equal, not unequal, circles, which is very absurd.c

Archimedes, Method, Archim. ed. Heiberg ii. 430. 1–9

This is a reason why, in the case of those theorems concerning the cone and pyramid of which Eudoxus first discovered the proof, the theorems that the cone

DOI: 10.4159/DLCL.democritus_philosopher-mathematical_works.1939