t

AN

ELEMENTARY TREATISE

ON

ALGEBRA,

THEORETICAL AND PRACTICAL,

ADAPTED TO THE INSTRUCTION OF YOUTH IN SCHOOLS AND

COLLEGES.

BY JAMES RYAN,

AUTHOR OF THE DIFFERENTIAL AND INTEGRAL CALCULUS; THE NEW
AMERICAN GRAMMAR OF ASTRONOMY, &c.

TO WHICH IS ADDED,

AN APPENDIX,

CONTAINING AN ALGEBRAIC METHOD OF DEMONSTRATING THE PROPOSI-
TIONS IN THE FIFTH BOOK OF EUCLID'S ELEMENTS, ACCORDING
TO THE TEXT AND ARRANGEMENT IN SIMSON'S EDITION,

BY ROBERT ADRAIN, L.L.D. F.A.P.S. F.A.A.S., &c.
AND PROFESSOR OF MATHEMATICS AND NATURAL PHILOSOPHY, IN COLUM-
BIA COLLEGE, NEW-YORK.

THIRD EDITION,

REVISED, CORRECTED AND IMPROVED.

NEW YORK:

W. E. DEAN PRINTER & PUBLISHER, 32 ANN-ST.
COLLINS & HANNAY; N. & J. WHITE; J. B. COLLINS; JAMES RYAN;
LEAVITT, LORD & CO., AND ROE LOCKWOOD.

1835.

Entered according to the Act of Congress in the Year One Thousand Eight Hundred and Thirty-five, by W. E. Dean, in the Clerk's Office of the Southern District of New-York.

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AS UTILITY is the great object aimed at in this Publication, I have spared no pains to make a careful selection of materials, from the most approved sources, which may tend to elucidate, in a full and clear manner, the Elements of Algebra, both in theory and practice.

Those authors of whose labours I have principally availed myself, are Euler, Clairaut, Lacroix, Garnier, Bezout, Lagrange, Newton, Simpson, Emerson, Wood, Bonnycastle, Bridge and Bland.

To Bland's Algebraical Problems, (a work compiled for the use of Students in one of the first Universities in Europe), I am chiefly indebted for the problems in Simple, Pure and Quadratic Equations.

By permission of the learned Dr. Adrain, I have added, as an Appendix, his method of demonstrating algebraically the propositions in the fifth book of Euclid's Elements.

JAMES RYAN.

New-York, July 1, 1824.