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BONNYCASTLE'S

INTRODUCTION TO ALGEBRA;

CONTAINING THE

INDETERMINATE AND DIOPHANTINE

ANALYSIS,

AND THE

APPLICATION OF ALGEBRA TO GEOMETRY.

REVISED, CORRECTED AND ENLARGED

BY JAMES RYAN

AUTHOR OF "AN ELEMENTARY TREATISE ON ALGEBRA THEORETICAL
AND PRACTICAL," &C.

QA 154 .B716

1844 187408

Entered according to the Act of Congress, in the year 1831, by W E. Dean, if the Clerk's office of the District Court of the Southern District of New York.

ADVERTISEMENT

ΤΟ

THE SECOND NEW YORK EDITION.

It would be superfluous to advance any thing in commendation of "Bonnycastle's Introduction to Algebra," as the number of European editions, and the increase of demand for it since its publication in this country, are sufficient proofs of its great utility. But to make it universally useful both to the tutor and scholar, I have given, in this edition, the answers that were omitted by the author in the original.

In the course of the work, particularly in Addition, Subtraction, Multiplication, Division, Fractions, Simple Equations, and Quadratics, I have added a great variety of practical examples, as being essentially necessary to exercise young students in the elementary principles.

Several new rules are introduced, those of principal note are the following: Case 12. Surds, containing two rules for finding any root of a Binomial Surd, the Solution of Cubics by Converging Series, the Solution of Biquadratics by Simpson's and Euler's methods: all these rules are investigated in the plainest manner possible, with notes and remarks, interspersed throughout the work, containing some very useful matter.

There is also given all the Diophantine Analysis, contained in Bonnycastle's Algebra, Vol. I. Svo. 1820, being a methodical abstract of this part of the science, which comprehends most of the methods hitherto known for resolving problems of this kind, and will be found a ready compendium for such readers as may acquire some knowledge of the ANALYTIC ART. JAMES RYAN.

New York, January 1, 1822.