Scaife ATLAS

CTS Library / Commentarii in libros de sphaera et cylindro

Commentarii in libros de sphaera et cylindro (16)

urn:cts:greekLit:tlg4072.tlg001.1st1K-grc1:16
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37
Εἰς τὸ λζ.

Ἀλλὰ τὸ ὑπὸ ΕΘ καὶ τῶν ΕΖ, Γ, ΚΑ δέδεικται ἴσον τῷ ὑπὸ τῶν ΕΛ, ΚΘ Ἐν γὰρ τῷ δευτέρῳ καὶ εἰκοστῷ θεωρήματι δέδεικται ὅτι αἱ ΕΖ, Γ, ΚΑ πρὸς τὴν ΘΚ
τὸν αὐτὸν ἔχουσι λόγον, ὃν ΛΕ πρὸς ΕΘ· ὥστε τὸ ὑπὸ τῶν ἄκρων ἴσον ἐστὶ τῷ ὑπὸ τῶν μέσων.

Τὸ δὲ ὑπὸ ΕΛ, ΚΘ ἔλασσόν ἐστι τοῦ ἀπὸ ΘΑ Καὶ γὰρ τοῦ ὑπὸ ΛΘ, ΘΚ ἴσου ὄντος τοῦ ἀπὸ ΘA, ὥς ἐστι δῆλον ἐπιζευγνυμένης τῆς ΑΛ καὶ διὰ τοῦτο ὁμοίου
γινομένου τοῦ ΘΑΚ τριγώνου τῷ ΘΑΛ· ἔσται γὰρ ὡς ΛΘ πρὸς ΘΑ, ΑΘ πρὸς ΟΚ, καὶ τὸ ὑπὸ τῶν ἄκρων ἴσον τῷ ἀπὸ τῆς μέσης.

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