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EUCLID'S FIRST BOOK.

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THE

TEXT OF EUCLID'S GEOMETRY.

BOOK I.

UNIFORMLY AND SYSTEMATICALLY ARRANGED.

WITH

A DISCUSSION OF EUCLID'S APPLICATION OF LOGICAL PRINCIPLES,

COPIOUS NOTES, EXERCISES, AND A FIGURE BOOK.

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PREFACE.

TAKING into consideration the number of Euclids which already exist, the author has feared it may savour of presumption to have published another. Having however been teaching Euclid almost daily for the last twenty years to pupils who, before coming under his tuition, had learnt something of Geométry from the different text books in use during that time, he ventures to think that this experience has made manifest to him the principal advantages and disadvantages of these numerous works, and thereby enabled him to present the propositions in the form most likely to be of educational value to those who are beginning either to learn or to teach the subject.

The principal features of this work are as follows:
(1) Uniform adherence to Euclid's Methods.

In the three propositions in which the author has deviated from this rule, translations from the Greek text have been given.

(2) Considerable alteration of the text.

The propositions are all treated in a uniform systematic way, the component parts of each, viz. the enunciation, construction, demonstration and conclusion being clearly displayed.

Every demonstration is separated into a series of links, in each of which cause precedes effect.

(3) The introduction of a list of facts supplementary to the definitions, postulates and axioms.

The author considers it of the utmost importance that young students of geometry should never be allowed to advance arguments without supporting each by direct reference to some

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