#postulates

The Elements of Euclid - Part 1 As we have seen, Book 1 of Euclid’s Elements lists five Common Notions: axioms that are shared by geometry and several other branches of logic and mathematics. Over the

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the fifth of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish εʹ. Καὶ τὸ ὅλον τοῦ μέρους μεῖζόν [ἐστιν].5. And the whole [is]

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the fourth of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish δʹ. Καὶ τὰ ἐφαρμόζοντα ἐπ ̓ ἀλλήλα ἴσα ἀλλήλοις ἐστίν.4. And things

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the third of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish γʹ. Καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ, τὰ καταλειπόμενά ἐστιν ἴσα.3.

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the second of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish βʹ. Καὶ ἐὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα.2. And if equal

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, the first of the Five Common Notions reads (Fitzpatrick 7): GreekEnglish αʹ. Τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα.1. Things equal to the

The Elements of Euclid - Part 1 In Book 1 of the Elements, following the Five Postulates, Euclid states five Common Notions, or Κοιναὶ ἔννοιαι [Koinai ennoiai] (Fitzpatrick 7): GreekEnglish αʹ. Τὰ τῷ αὐτῷ

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 5 reads (Fitzpatrick 7): GreekEnglish εʹ. Καὶ ἐὰν εἰς δύο εὐθείας εὐθεῖα ἐμπίπτουσα τὰς ἐντὸς καὶ ἐπὶ τὰ αὐτὰ μέρη γωνίας δύο ὀρθῶν

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 4 reads (Fitzpatrick 7): GreekEnglish δʹ. Καὶ πάσας τὰς ὀρθὰς γωνίας ἴσας ἀλλήλαις εἶναι.4. And that all right-angles are equal

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 3 reads (Fitzpatrick 7): GreekEnglish γʹ. Καὶ παντὶ κέντρῳ καὶ διαστήματι κύκλον γράφεσθαι.3. And to draw a circle with any center

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 2 reads (Fitzpatrick 7): GreekEnglish βʹ. Καὶ πεπερασμένην εὐθεῖαν κατὰ τὸ συνεχὲς ἐπ εὐθείας ἐκβαλεῖν.2. And to produce a finite

The Elements of Euclid - Part 1 In Book 1 of Euclid’s Elements, Postulate 1 reads (Fitzpatrick 7): GreekEnglish αʹ. ̓Ηιτήσθω ἀπὸ παντὸς σημείου ἐπὶ πᾶν σημεῖον εὐθεῖαν γραμμὴν ἀγαγεῖν.1. Let it have been

The Elements of Euclid - Part 1 In the last article in this series we studied the twenty-third and final definition in Book 1 of Euclid’s Elements. We turn now to the Five Postulates—Αἰτήματα [Aitēmata]—which

In my last post I mentioned the two postulates Einstein formulated in 1905: The Principle of Relativity: The laws in nature are the same in all inertial reference frames. The Constance of Light: In all