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CONTAINING AN ALGEBRAIC METHOD OF DEMONSTRATING THE
PROPOSITIONS IN THE FIFTH BOOK OF EUCLID'S ELE-

MENTS, ACCORDING TO THE TEXT AND AR-

RANGEMENT IN SIMSON'S EDITION,

BY ROBERT ADRAIN, LL.D. F.A.P.S. F.A.A.S., &c.
And Professor of Mathematics and Natural Philosophy, in Columbia

College, New-York.

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PUBLISHED BY COLLINS AND HANNAY,

NO. 230 PEARL-STREET.

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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.

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Those author's of whose labours I have principally availed myself, are Euler, Clairaut, Lacroix, Garnier, Bezout, Lagrange, Newlon, 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. Adrai. I have added, as an Appendix, his metho of demonstrating algebraically the prope sitions in the fifth book of Euclid's El ments.

JAMES RYAN.

New-York, July 1, 1824.

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