I.)

ELEMENTS

OF

GEOMETRY,

GEOMETRICAL ANALYSIS,

AND

PLANE TRIGONOMETRY.

WITH AN

APPENDIX,

NOTES AND ILLUSTRATIONS.

BY

JOHN LESLIE,

PROFESSOR OF MATHEMATICS IN THE UNIVERSITY CF EDINBURGH,

EDINBURGH:

Printed by James Ballantyne and elor
FOR BROWN AND CROMBIE, AND JOHN BALLANTYNE
AND CO. EDINBURGH; AND LONGMAN, HURST, REES, AND ORME,

J. MURRAY, R. SCHOLEY, AND J. MAWMAN, LON-

DON; AND J. DEIGHTON, CAMBRIDGE.

1809.

PRE FACE.

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 was 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 modere discoveries. The magnitude and difficulty of such a jask. 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 rela