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OF

THE FIFTH BOOK OF EUCLID

PROVED ALGEBRAICALLY:

WITH AN

INTRODUCTION, NOTES, AND QUESTIONS.

BY

GEORGE STURTON WARD, M.A.,

MATHEMATICAL LECTURER IN MAGDALEN HALL, AND PUBLIC EXAMINER

IN THE UNIVERSITY OF OXFORD.

Orford and London:

JOHN HENRY AND JAMES PARKER.

1862.

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PREFACE.

THE primary object of the following pages is to pro

vide a text-book for the use of Candidates in the Mathematical Final School of this University, who have the option allowed them of applying Algebra in the demonstration of the propositions of the Fifth Book of Euclid.

An Introduction is prefixed, in which will be found a brief exposition of the principles on which geometrical magnitudes are represented by algebraical symbols, explanations of the terms" ratio” and “compound ratio,” and a comparison of the geometrical and algebraical definitions of “proportion.'

It is hoped that the explanations here offered may help to remove some of the difficulties usually experienced by learners in the algebraical treatment of propositions relating to geometrical magnitudes, ratios, and proportion; and in particular that the third part of the Introduction will satisfactorily exhibit the agreement of Euclid's Fifth Definition with the assumption of the equality of algebraical fractions as a test of the sameness of ratios.

Definitions of "equimultiples” and “continual proportionals” are inserted.

A few brief Notes on the Propositions are appended.

And Questions are added, the answers to which are contained in the Introduction and Notes.

OXFORD, Nov. 1, 1862.

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