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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.

New-York:

PUBLISHED BY COLLINS AND HANNAY,

NO. 230 PEARL-STREET.

13 EW YORK PUBLIC LIBRARY 343221B

AER, DIX AND MPEN FOUNDAMONS 1946

L

Southern District of New York, ss.

BK IT REMEMBERED, That on the first day of July in the forty. eighth year of the Independence of the United States of America, JAMES RYAN, of the said District, bas depositell in this office the title of a Book, the right whereof be claims as Author, in the words following, lo wit:

"An Elementary Treatise on Algebra, theoretical and practical, adapted to the Instruction of Youth in Schools and Colleges. By James Ryan, Author of a Key to Bunnycastle's Algebra. To which is added, an Appendix, containing an Algebraic Method of demonstrating the Propositions in the fifth book of Euclid's Elements, according to the text and arrangement in Simson's edition, by Robert Adrain, LL.D. F.A.P.8. F.A.AS. &r, and Professor of Mathematics and Natural Philosophy, in Columbia College, New-York."

In conformity to the Act of Congress of the United States, entitled “ An Act for the encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during the time therein mentioned ;” and also to an Act, entitled “ An Act, supplementary to an Act, entitied an Act for the encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies, during ihe tinies therein mentioned, and extending the benefits thereof to the arts of designing, engraving, and etching historical, and other prints."

JAMES DILL,
Clerk 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 author's 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.

1

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 Ele ments.

JAMES RYAN.

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