Euclid Book 1

Proposition 28

Theorem

Statement A

Statement B

Original statement

ἐὰν ϵἰς δύο ϵὐθϵίας ϵὐθϵῖα ἐμπίπτουσα τὴν ἐκτὸς γωνίαν τῇ ἐντὸς καὶ ἀπϵναντίον καὶ ἐπὶ τὰ αὐτὰ μέρη ἴσην ποιῇ ἢ τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη δυσὶν ὀρθαῖς ἴσας, παράλληλοι ἔσονται ἀλλήλαις αἱ ϵὐθϵῖαι.

English translation

If a straight line falling on two straight lines make the exterior angle equal to the interior and opposite angle on the same side, or the interior angles on the same side equal to two right angles, the straight lines will be parallel to one another.

Computable version A

Computable version B

Additional instances

Proof outline

Dependency graphs

Classes