CORRESPONDING MEMBER OF THE ROYAL INSTITUTE OF FRANCE; FOURTH EDITION, IMPROVED AND EXPANDED. EDINBURGH: PRINTED FOR W. & C. TAIT, PRINCE'S STREET; AND LONGMAN, HURST, REES, ORME & BROWN, LONDON. PREFACE. THIS Volume, which, in spite of reluctant prejudice, has already obtained a large share of the public patronage, 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 persever ance. 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 |