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ELEMENTS

OF

GEOMETRY,

AND

PLANE TRIGONOMETRY.

WITH AN

APPENDIX,

AND COPIOUS NOTES AND ILLUSTRATIONS.

BY

Sir JOHN LESLIE, F.R.S.E.

PROFESSOR OF MATHEMATICS IN THE UNIVERSITY

OF EDINBURGH.

THIRD EDITION,

IMPROVED AND ENLARGED.

EDINBURGH:
PRINTED FOR ARCHIBALD CONSTABLE & co.
AND FOR LONGMAN, HURST, REES, ORME, & BROWN,

LONDON.

1817.

Library
QA
529
L635e
1 &17

EDINBURGH ;

Printed by Abernethy & Walker.

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The volume now laid before the public, is the first of a projected Course of Mathematical Science. Many compendiums or elementary treatises have appeared-at different times, and of various merit ; but there seemed still wanting, in our language, a work that should embrace the subject in its full extent,--that should unite theory with practice, and connect the ancient with the modern discoveries. The magnitude and difficulty of such a task might deter an individual from the attempt, if he were not deeply impressed with the importance of the undertaking, and felt his exertions to accomplish it animated by zeal, and supported by active perseverance.

The study of Mathematics holds forth two capital objects :- While it traces the beautiful relations of figure and quantity, it likewise accustoms the mind to the invaluable exercise of patient attention and accurate reasoning. Of these distinct objects, the last is perhaps the most important in a course of liberal education. For this purpose,

the Geometry of the Greeks is the most powerfully recommended, as bearing the stamp of that acute people, and displaying the finest specimens of logical deduction. Some of its conclusions, indeed, might be reached by a sort of calculation; but such an artificial mode of procedure gives merely an apparent facility, and leaves no clear or permanent impression on the mind.

We should form a wrong estimate, however, did we consider the Elements of Euclid, with all its merits, as a finished production. That admirable work was composed at the period when Geometry was making its most rapid advances, and new prospects were opening on every side. No wonder that its structure should now appear loose and defective. In adapting it to the actual state of the science, I have therefore endeavoured care. fully to retain the spirit of the original, but have sought to enlarge the basis, and to dispose the accumulated materials into a regular and more compact system. By simplifying the order of arrangement, I presume to have materially a. bridged the labour of the student. The numerous additions that are incorporated in the text, so far from retarding, will rather facilitate his progress, by rendering more continuous the chain of demonstration,

The view which I have given of the nature of Proportion, in the Fifth Book, will contribute, I

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