JOHN LESLIE, F. R.S. E.

PROFESSOR OF MATHEMATICS IN THE UNIVERSITY

OF EDINBURGH.

SECOND EDITION,

IMPROVED AND ENLARGED.

EDINBURGH:

PRINTED FOR JOHN BALLANTYNE AND COMPANY;

AND FOR

LONGMAN, HURST, REES, ORME AND BROWN,

LONDON.

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