THE

PRACTICAL ANALYST;

OR,

A TREATISE ON ALGEBRA,

CONTAINING THE MOST USEFUL PARTS OF THAT

SCIENCE,

Illustrated by a Copious Collection of Examples,

DESIGNED FOR THE USE OF SCHOOLS.

BY ENOCH LEWIS.

PHILADELPHIA:

PUBLISHED BY KIMBER AND SHARPLESS,

No. 93 MARKET STREET.

I. Ashmead & Co. Printers.

1826.

Eastern District of Pennsylvania, to wit:

SEAL.

BE IT REMEMBERED, that on the seventeenth day of August, in the fifty-first year of the independence of the United States of America, A. D. 1826, Kimber and Sharpless, of the said district, have deposited in this office the title of a book, the right whereof they. claim as proprietors, in the words following, to wit:

"The Practical Analyst; or, a Treatise on Algebra, containing the most useful parts of that Science, illustrated by a copious Collection of Examples, designed for the Use of Schools, by Enoch Lewis."

In conformity to the Act of the Congress of the United States, intituled, "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 times therein mentioned." And also to the Act, entitled, "An Act supplementary to an Act, entitled, 'An Act for the Encouragement of Learning, by securing the Copies of Maps, Charts, and Books, to the Authors and Proprietors rietors of such Copies during the times therein mentioned,' and extending the benefits thereof to the arts of designing, engraving, and etching Historical and other Prints."

D. CALDWELL,

Clerk of the Eastern District of Pennsylvania.

milelr 11-28-41 44358

PREFACE.

THE mathematical sciences, have been considered, since the early periods of their existence, among the noblest objects of human inquiry. Of these, next to arithmetic, geometry occupies the first place, in regard both to importance and to time. The Grecian philosophers cultivated this branch of knowledge, with an ardour and industry, which manifest their high opinion of its value. In the Ionian and Pythagorean schools, geometry was considered an indispensable preliminary to the study of philosophy. When a person, ignorant of geometry, applied for his instructions to the philosopher Xenocrates, he is said to have made this laconic reply: "thou hast not the handles of philosophy."

The perspicuity of geometrical reasoning, the accurate and inimitable dependence of its arguments, and the unfaltering certainty of its conclusions, are eminently calculated to form the mind to habits of attention, and to a regular and forcible concatenation of its ideas. No wonder then, that it was so highly prized by that acute and inquisitive people.

Two modes of procedure, according to the different objects in view, were adopted by the ancient geometers: synthesis and analysis.

Synthesis, or composition, consists in the direct solution of a problem; or, the demonstration of a proposition by a series of arguments, regularly deduced, from self-evident truths, or from other propositions previously established. This method is very proper for conveying,