euclid Tag Posts Index

Euclid’s Proposition 1:8

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

Euclid’s Proposition 1:7

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

Euclid’s Proposition 1:6

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

Euclid’s Proposition 1:5

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

Euclid’s Proposition 1:4

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

Euclid’s Proposition 1:3

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

Euclid’s Proposition 1:2

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

Euclid’s Proposition 1:1

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

The Propositions of Book 1

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

Other Common Notions

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

Euclid: Common Notion 5

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

Euclid: Common Notion 4

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

Euclid: Common Notion 3

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

Euclid: Common Notion 2

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,

Euclid’s Common Notion 1

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

Euclid’s Five Common Notions

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]

Euclid: Postulate 5

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

Euclid: Postulate 4

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.

Euclid : Postulate 3

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.

Euclid : Postulate 2

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