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PRIMER OF GEOMETRY

AN EASY INTRODUCTION

ΤΟ

THE PROPOSITIONS OF EUCLID

BY

FRANCIS CUTHBERTSON, M.A., LL.D.

LATE FELLOW OF CORPUS CHRISTI COLL., CAMBRIDGE

HEAD MATHEMATICAL MASTER OF THE

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PREFACE.

WHILST many of the Propositions of Euclid are very easy, there are others equally hard for the student to understand; moreover, they are not graduated according to their difficulty. Thus the Fifth Proposition of his First Book is invariably found to be a greater stumbling-block than most of those which follow. Now the earliest time at which the study of the Elements can be commenced is necessarily fixed by the difficult parts. Accordingly, inasmuch as those whose capacity is considerably below the limit thus indicated could master the easy portions, it follows that, by means of a course of Geometry embracing these, the subject might be introduced much sooner than it usually is.

As the beginner is always more interested in Problems than Theorems, one half of this work will be found to consist of Problems. The solu

tions to these are not only simple, but also practical. This is important, as the constructions generally given in theoretical works on Geometry are not employed in practice, whilst those in use are selected from treatises on Practical Geometry, and have no proofs attached to them. The Problems are mainly those of the first four Books of Euclid. The demonstrations of these, as also of the Theorems, assume no more than Euclid does in the corresponding Propositions, and may accordingly be substituted for them in examinations. This is therefore not merely a course preparatory to a more extended study of Geometry, but, in the event of its being followed by Euclid as a text-book, a great deal of the ground of his first four Books will then have been already covered by it, and in such a manner as to render the completion a matter of no great labour.

CITY OF LONDON SCHOOL,

October 1875.

PRELIMINARY NOTICES.

THE following axioms will be assumed :—

Things which are equal to the same thing are equal to one another.

The whole is equal to the sum of its parts.

If equals be added to equals the wholes are equal.

If equals be taken from equals the remainders are equal. Things which are double of equal things are equal to one

another.

Things which are halves of equal things are equal to one another.

After the first few Propositions the following symbols will be introduced :

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