Euclid, Elements, 1.postulates
Janey Capers Newland / Euclid
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- Modified on 2018-03-20 14:03:11
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Euclid, Elements, book 1, definitions
Ἑλληνική Transliterate
English
Ἠιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν .
καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖν .
καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι .
καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι .
καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν ἐλάσσονας ποιῇ , ἐκβαλλομένας τὰς δύο εὐθείας ἐπ᾽ ἄπειρον συμπίπτειν , ἐφ᾽ ἃ μέρη εἰσὶν αἱ τῶν δύο ὀρθῶν ἐλάσσονες .
καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ᾽ εὐθείας ἐκβαλεῖν .
καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι .
καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι .
καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν ἐλάσσονας ποιῇ , ἐκβαλλομένας τὰς δύο εὐθείας ἐπ᾽ ἄπειρον συμπίπτειν , ἐφ᾽ ἃ μέρη εἰσὶν αἱ τῶν δύο ὀρθῶν ἐλάσσονες .
Let the following be postulated : To draw a straight line from any point to any point .
To produce a finite straight line continuously in a straight line .
To describe a circle with any centre and distance .
That all right angles are equal to one another .
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 .