1. Let the following be postulated: To draw a straight line from any point to any point.
1. Ἠιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν.
2. To produce a finite straight line continuously in a straight line.
2. καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπʼ εὐθείας ἐκβαλεῖν.
3. To describe a circle with any centre and distance.
3. καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι.
4. That all right angles are equal to one another.
4. καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι.
5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
5. καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν ἐλάσσονας ποιῇ, ἐκβαλλομένας τὰς δύο εὐθείας ἐπʼ ἄπειρον συμπίπτειν, ἐφʼ ἃ μέρη εἰσὶν αἱ τῶν δύο ὀρθῶν ἐλάσσονες.