关于欧几里得《几何原本》电子版的英译文阅读说明

坦率地说，由于时间过于久远，翻译希腊文原著绝非容易的事情。为准确翻译，译者把希腊语原文插入英语句子中间，以便相互对照，增加了阅读困难。

历史上，直到2007年，欧几里得《几何原本》电子版（英文PDF版本）才上网，

注意：欧几里得《几何原本》电子版的英文原文是：EULID’S ELEMENTS OF GEOMETRY，其PDF版本有示意图。

希尔伯特《几何基础》与欧几里得《几何原本》的对比研究正在进行中。

袁萌  陈启清   3月15日

附件：

EULID’S ELEMENTS OF GEOMETRY

The Greek text of J.L. Heiberg (1883–1885)

from Euclidis Elementa, edidit et Latine interpretatus est I.L. Heiberg, in aedibus B.G. Teubneri, 1883–1885

edited, and provided with a modern English translation, by

Richard Fitzpatrick

First edition - 2007 Revised and corrected - 2008

ISBN 978-0-6151-7984-1

Contents

Introduction 4

Book 1 5

Book 2 49

Book 3 69

Book 4 109

Book 5 129

Book 6 155

Book 7 193

Book 8 227

Book 9 253

Book 10 281

Book 11 423

Book 12 471

Book 13 505

Greek-English Lexicon 539

Introduction

Euclid’s Elements is by far the most famous mathematical work of classical antiquity, and also has the distinction of being the world’s oldest continuously used mathematical textbook. Little is known about the author, beyond the fact that he lived in Alexandria around 300 BCE. The main subjects of the work are geometry, proportion, and number theory.

Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematicians such as Pythagoras (and his school), Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos. However, Euclid is generally credited with arranging these theorems in a logical manner, so as to demonstrate (admittedly, not always with the rigour demanded by modern mathematics) that they necessarily follow from ve simple axioms. Euclid is also credited with devising a number of particularly ingenious proofs of previously discovered theorems: e.g., Theorem 48 in Book 1.

The geometrical constructions employed in the Elements are restricted to those which can be achieved using a straight-rule and a compass. Furthermore, empirical proofs by means of measurement are strictly forbidden: i.e., any comparison of two magnitudes is restricted to saying that the magnitudes are either equal, or that one is greater than the other………