previous next

Click on a word to bring up parses, dictionary entries, and frequency statistics



ἐὰν δύο κύκλοι ἐφάπτωνται ἀλλήλων ἐκτός, ἐπὶ τὰ κέντρα αὐτῶν ἐπιζευγνυμένη διὰ τῆς ἐπαφῆς ἐλεύσεται.

δύο γὰρ κύκλοι οἱ ΑΒΓ, ΑΔΕ ἐφαπτέσθωσαν ἀλλήλων ἐκτὸς κατὰ τὸ Α σημεῖον, καὶ εἰλήφθω τοῦ μὲν ΑΒΓ
5κέντρον τὸ Ζ, τοῦ δὲ ΑΔΕ τὸ Η: λέγω, ὅτι ἀπὸ τοῦ Ζ ἐπὶ τὸ Η ἐπιζευγνυμένη εὐθεῖα διὰ τῆς κατὰ τὸ Α ἐπαφῆς ἐλεύσεται.

μὴ γάρ, ἀλλ᾽ εἰ δυνατόν, ἐρχέσθω ὡς ΖΓΔΗ, καὶ ἐπεζεύχθωσαν αἱ ΑΖ, ΑΗ.
10

ἐπεὶ οὖν τὸ Ζ σημεῖον κέντρον ἐστὶ τοῦ ΑΒΓ κύκλου, ἴση ἐστὶν ΖΑ τῇ ΖΓ. πάλιν, ἐπεὶ τὸ Η σημεῖον κέντρον ἐστὶ τοῦ ΑΔΕ κύκλου, ἴση ἐστὶν ΗΑ τῇ ΗΔ. ἐδείχθη δὲ καὶ ΖΑ τῇ ΖΓ ἴση: αἱ ἄρα ΖΑ, ΑΗ ταῖς ΖΓ, ΗΔ
15ἴσαι εἰσίν: ὥστε ὅλη ΖΗ τῶν ΖΑ, ΑΗ μείζων ἐστίν: ἀλλὰ καὶ ἐλάττων: ὅπερ ἐστὶν ἀδύνατον. οὐκ ἄρα ἀπὸ τοῦ Ζ ἐπὶ τὸ Η ἐπιζευγνυμένη εὐθεῖα διὰ τῆς κατὰ τὸ Α ἐπαφῆς οὐκ ἐλεύσεται:
20δι᾽ αὐτῆς ἄρα.

ἐὰν ἄρα δύο κύκλοι ἐφάπτωνται ἀλλήλων ἐκτός, ἐπὶ τὰ κέντρα αὐτῶν ἐπιζευγνυμένη εὐθεῖα διὰ τῆς ἐπαφῆς ἐλεύσεται: ὅπερ ἔδει δεῖξαι.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 United States License.

An XML version of this text is available for download, with the additional restriction that you offer Perseus any modifications you make. Perseus provides credit for all accepted changes, storing new additions in a versioning system.

load focus English (Thomas L. Heath, Sir Thomas Little Heath, 1956)
load Vocabulary Tool
hide Display Preferences
Greek Display:
Arabic Display:
View by Default:
Browse Bar: