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Late Professor of Mathematics in the Royal Military Academy.

THE THIRD AMERICAN EDITION:

From the Fifth, Sixth, and Seventh London Editions.

REVISED, CORRECTED, AND IMPROVED.

TO WHICH IS ADDED

An Elementary Essay on Descriptive Geometry.
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.

VOL. I.

NEWYORK:
PUBLISHED BY SAMUBL CAMPBELL & son, EVERT DUYCKINCK, T. & J. Swords,
A. M'DERMUT, T. A. RONALDS, COLLINS & HANNAY, AND GEORGE LONG.

George Long, Printer, No. 71, Pearl-Street.

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Southern District of Now-York, ss.

BE IT REMEMBERED, That on the twenty-seventh day of February, in the forty-sixth year of the Independence of the United States of America, George Long, of the said district, hath deposited in this office the title of a book, the right whereof be claims as proprietor, in the words following, to wit:

" A Course of Mathematics, for the Use of Academies, as well as Private Tuition. lo two Volumes. By Charles Hutton, LL.D. F. R.S. Late Professor of Mathematics in the Royal Military Academy. The Third American Edition, From the Fifth, Sixth, and Seventh London Editions. Revised, corrected, and improved. To which is added, An Elementary Essay on Descriptive Geometry, by Robert Adrain, LL.D. F. A.P.S. F.A.A.S. &c. and Professor of Mathematics and Natural Philosopby, 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, 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 times therein mentioned, and extending the benefits tbereof to the arts of designing, engraving, and etching historioal and other prints."

JAMES DILL, Clerk of the Southern District of New York.

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7-18 -42

PREFACE.

A SHORT and Easy Course of the Mathematical Sciences has long been considered as a desideratum for the use of Students in the different schools of education : one that should hold a middle rank between the more voluminous and bulky collections of this kind, and the mere abstract and brief common-place forms, of principles and memorandums.

For long experience, in all Seminaries of Learning, bas shown, that such a work was very much wanted, and would prove a great and general benefit; as, for want of it, recourse has always been obliged to be had to a number of other books by different authors; selecting a part from one and a part from another as seemed most suitable to the purpose in hand, and rejecting the other parts-a practice which occasioned much expense and trouble, in procuring and using such a number of odd volumes, of various forms and modes of composition ; besides wanting the benefit of uniformity and reference, which are found in a regular series of composition.

To remove these inconveniences, the Author of the present work has been induced from time to time, to compose various parts of this course of Mathematics; which the experience of many years' use in the Academy has enabled him to adapt and improve to the most useful form and quantity for the benefit of instruction there. And, to render that benefit more eminent and lasting, the Master General of the Ordnance bas been pleased to give it its present form, by ordering it to be enlarged and printed, for the use of the Royal Military Academy.

As this work has been composed expressly with the intention of adapting it to the purposes of academical education, it is not designed to hold out the expectation of an entire new mass of inventions and discoveries : but rather to collect and arrange the most useful known principles of mathematics, disposed in a convenient practical form, demonstrated in a plain and concise way, and illustrated with suitable examples, rejecting whatever seemed to be matters of mere curiosity, and retaining only such parts and branches, as have a direct tendency and application to some useful purpose in life or profession.

It is however expected that much that is new will be found in many parts of these volumes; as well in the matter, as in the arrangement and manner of demonstration, throughout the whole work, especially in the geometry, which is rendered much more easy and simple than heretofore ; and in the conic

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