---
title: "Elements · Στοιχεῖα"
author: "Euclid"
translator: "Thomas Little Heath"
languages: [grc, en]
shelf: "Classical Greek"
section: 3 of 49
url: https://scriptura.si/works/euclid-elements/3/
cite: "Euclid, tr. Thomas Little Heath, Elements · Στοιχεῖα, section 3. Scriptura (scriptura.si), https://scriptura.si/works/euclid-elements/3/"
---

# Elements · Στοιχεῖα

*Euclid, tr. Thomas Little Heath*

The thirteen books of geometry and number theory that taught mathematics for two thousand years, from the definition of a point to the five regular solids.

> Greek: ed. Johan Ludvig Heiberg, from the Perseus Digital Library (canonical-greekLit, tlg1799.tlg001, CC BY-SA 4.0).

> English: Thomas Little Heath, from the Perseus Digital Library (tlg1799.tlg001.perseus-eng2). Notes are not included.

> Rows follow the references the two texts share (books, chapters and sections), cut where both reach the end of a sentence.

## 3. Book I · Common Notions

Source: https://scriptura.si/works/euclid-elements/3/ · cite a paragraph as https://scriptura.si/works/euclid-elements/3/#p-N

[¶0] 1. Things which are equal to the same thing are also equal to one another.

> Greek: 1. τὰ τῷ αὐτῷ ἴσα καὶ ἀλλήλοις ἐστὶν ἴσα.

[¶1] 2. If equals be added to equals, the wholes are equal.

> Greek: 2. καὶ ἐὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα.

[¶2] 3. If equals be subtracted from equals, the remainders are equal. [7] Things which coincide with one another are equal to one another.

> Greek: 3. καὶ ἐὰν ἀπὸ ἴσων ἴσα ἀφαιρεθῇ, τὰ καταλειπόμενά ἐστιν ἴσα. [καὶ ἐὰν ἀνίσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἄνισα.] [καὶ τὰ τοῦ αὐτοῦ διπλάσια ἴσα ἀλλήλοις ἐστίν.] [καὶ τὰ τοῦ αὐτοῦ ἡμίση ἴσα ἀλλήλοις ἐστίν.] καὶ τὰ ἐφαρμόζοντα ἐπʼ ἄλληλα ἴσα ἀλλήλοις ἐστίν.

[¶3] 8. [8] The whole is greater than the part.

> Greek: 8. καὶ τὸ ὅλον τοῦ μέρους μεῖζον [ἐστιν]. καὶ δύο εὐθεῖαι χωρίον οὐ περιέχουσιν.