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LONDON:

PRINTED BY WOODFALL AND KINDER,

ANGEL COURT, SKINNER STREET.

THE

ELEMENTS OF EUCLID,

WITH

MANY ADDITIONAL PROPOSITIONS,

AND

EXPLANATORY NOTES;

TO WHICH IS PREFIXED AN

INTRODUCTORY ESSAY ON LOGIC.

BY

HENRY LAW,

CIVIL ENGINEER.

PART I.

CONTAINING THE FIRST THREE BOOKS.

London:

JOHN WEALE, 59, HIGH HOLBORN.

1853.

Adr. Bili

PREFACE.

IN presenting to the public a new elementary work on the Principles of Geometry, it can hardly be necessary to defend the having made Euclid's Elements the basis of the work; for while it cannot be denied that many grave faults exist even in the best translations, and that, owing to the advances made in mathematical science since Euclid's day, the demonstrations of many important theorems are wanting in the Elements; it must, on the other hand, be acknowledged that, notwithstanding the numerous attempts which have been made by our best modern geometers to supersede it, the Elements has ever held the chief place in all our universities and colleges.

In the present edition the text of Dr. Simson has been principally followed, but occasionally preference has been given to that of Elrington; the whole has, however, been entirely rewritten, and it is hoped that, in the attempt to render it less verbose, it will not be found that the chain of proof has been in any case weakened. Considerable pains have been taken to distinguish the various parts of the propositions by the adoption of differences in the type; and the references have been grouped in tables under the diagrams, in order to show at sight upon which preceding theorems the truth of each depends.

In the explanatory notes which have been appended it will be found that many additional propositions have been added, and that in several instances other demonstrations have been given.

In the second book it has been endeavoured to point out the relative connection of Geometry and Algebra, and to illustrate by the former the theory of quadratic equations.

In order to remove one of the most practical objections which have been urged against the Elements, namely, its want of methodical arrangement, a classified index has been appended, by

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