A COURSE OF MATHEMATICS. IN TWO VOLUMES. FOR THE USE OF ACADEMIES, AS WELL AS PRIVATE TUITION. BY CHARLES HUTTON, L. L. D. F.R.S. LATE PROFESSOR OF MATHEMATICS IN THE ROYAL MILITARY ACADEMY. FROM THE FIFTH AND SIXTH LONDON EDITIONS? REVISED AND CORRECTED BY ROBERT ADRAIN, A. M. FELLOW OF THE AMERICAN PHILOSOPHICAL SOCIETY, AND PROFESSOR OF MATHEMATICS IN QUEEN'S COLLEGE NEW JERSEY. VOL. I. NEW-YORK: PUBLISHED BY SAMUEL CAMPBELL, EVERT DUYCKINCE, 1818. RVARD COLLEGE LIBRARY JANUARY 26, 1824 ADVERTISEMENT. THE HE publishers of this third American edition of Dr. Hutton's Course of Mathematics, were induced to engage in the work from a conviction of its utility to private Students, as well as to Colleges and other Seminaries, in which Mathematical Science constitutes a branch of education. They also had in view the furnishing of the Military School of their country with a Text Book of high standing, and long in use in the British Military Academy And in order that this edition might derive advantage from the progress of the Science, and thereby become more worthy of the public patronage, they engaged a gentleman of acknowledged eminence to revise its pages and superintend the printing; and they confidently trust this duty has been performed with some profit to the work generally. To gentlemen, therefore, who study this delightful science in private, and to the literary and military institutions of their country, the publishers and proprietors look for remuneration-and they feel as though they should not look in vain. An increasing taste for Mathematical Studies will produce a correspondent increase of purchasers; white the preference which an honourable patriotism gives to American editions when well executed, will receive additional activity from the super-eminence of the work itself. Orders for this publication will be thankfully received by any of the proprietors; all whose names are printed at the foot of the title-page. New-York, 1818. District of New-York, ss. BE IT REMEMBERED, that on the eleventh day of August, in the thirty-seventh year of the Independence of the United States of America, Samuel Campbell, of the said district, hath deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit: A Course of Mathematics. In two volumes. For the use of Academies as well as Private Tuition. By Charles Hutton. L. L. D. F. R. S. late Professor of Mathematics in the Royal Military Academy by Robert Adrain. A. M. Fellow of the American Philosophical Society, and Professor of From the fifth and sixth London editions, revised and corrected Mathematics in Queen's College, New-Jersey." In conformity to the Act of the 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 times 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 thereof to the arts of designing, engraving, and etching historical and other prints." CHARLES CLINTON, George Long, Printer. 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, has 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 has 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 sections, |