1. Things which are equal to the same thing are also equal to one another.
1. τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα.
2. If equals be added to equals, the wholes are equal.
2. καὶ ἐὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα.
3. If equals be subtracted from equals, the remainders are equal. [7] Things which coincide with one another are equal to one another.
3. καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ, τὰ καταλειπόμενά ἐστιν ἴσα. [καὶ ἐὰν ἀνίσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἄνισα.] [καὶ τὰ τοῦ αὐτοῦ διπλάσια ἴσα ἀλλήλοις ἐστίν.] [καὶ τὰ τοῦ αὐτοῦ ἡμίση ἴσα ἀλλήλοις ἐστίν.] καὶ τὰ ἐφαρμόζοντα ἐπʼ ἄλληλα ἴσα ἀλλήλοις ἐστίν.
8. [8] The whole is greater than the part.
8. καὶ τὸ ὅλον τοῦ μέρους μεῖζον [ἐστιν]. καὶ δύο εὐθεῖαι χωρίον οὐ περιέχουσιν.