The Elements of Euclid - Part 1 The eighth proposition of Book 1 of Euclid’s Elements is another theorem about triangles: GreekEnglish ᾿Εὰν δύο τρίγωνα τὰς δύο πλευρὰς [ταῖς] δύο πλευραῖς ἴσας ἔχῃ ἑκατέραν

The Elements of Euclid - Part 1 In Richard Fitzpatrick’s translation the seventh proposition of Book 1 of Euclid’s Elements reads: GreekEnglish ̓Επὶ τῆς αὐτῆς εὐθείας δύο ταῖς αὐταῖς εὐθείαις ἄλλαι δύο

The Elements of Euclid - Part 1 The sixth proposition of Book 1 of Euclid’s Elements is the converse of the first part of Proposition 1:5 (If a given triangle is an isosceles triangle, then the two angles

The Elements of Euclid - Part 1 The fifth proposition of Book 1 of Euclid’s Elements proves two things about isosceles triangles. The first of these is probably the best known property of this type of

The Elements of Euclid - Part 1 Book 1 of Euclid’s Elements opens with three constructions. The fourth proposition is the first true theorem. GreekEnglish ̓Εὰν δύο τρίγωνα τὰς δύο πλευρὰς [ταῖς] δυσὶ πλευραῖς

The Elements of Euclid - Part 1 Book 1 of Euclid’s Elements opens with three constructions. The third of these demonstrates how to cut off from the longer of two given line segments a segment equal in

The Elements of Euclid - Part 1 Book 1 of Euclid’s Elements opens with three constructions. The second of these demonstrates how to construct a line segment which is equal in length to a given line segment

The Elements of Euclid - Part 1 Book 1 of Euclid’s Elements opens with three constructions. The first of these, Proposition 1:1, demonstrates how to construct an equilateral triangle: GreekEnglish αʹ.

The Elements of Euclid - Part 1 Book 1 of Euclid’s Elements contains 48 propositions. These can be divided into two broad categories: Theorems Constructions A theorem is a proposition that proves some

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