MEMBER OF THE INSTITUTE, AND OF THE LEGION OF HONOUR AND BY DAVID BREWSTER, LL.D. FELLOW OF THE ROYAL SOCIETY OF LONDON, AND SECRETARY REVISED AND ALTERED FOR THE USE OF THE MILITARY ACADEMY NEW-YORK: PUBLISHED BY JAMES RYAN, 322 BROADWAY. 1828. Southern District of New-York, ss. E IT REMEMBERED, That on the eighteenth day of August, A. D. 1828, in the fifty B third year of the Independence of the United States of America, James Ryan, 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: "Elements of Geometry and Trigonometry, with notes. Translated from the French of A. M. Legendre, member of the institute and of the legion of honour, and of the Royal Societies of London and Edinburgh, &c. By David Brewster, LL.D. Fellow of the Royal Society of London, and Secretary to the Royal Society of Edinburgh, &c. &c. Revised and altered for the use of the Military Academy at West Point." 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 thereof to the arts of designing, engraving, and etching historical and other prints." FREDERICK J. BETTS, Clerk of the Southern District of New-York. © 5-9-46 AKH Cey 5-6-46 PREFACE TO THE AMERICAN EDITION. THE Editor, in offering to the public Dr. Brewster's translation of Legendre's Geometry under its present form, is fully impressed with the responsibility he assumes in making alterations in a work of such deserved celebrity. The alterations made, are chiefly in the texts of the propositions. In the original work, as well as in the translations of Dr. Brewster and Professor Farrar, the propositions are not enunciated in general terms, but with reference to, and by the aid of, the particular diagrams used for the demonstrations. The fact to be demonstrated is stated as belonging to particular lines, or to particular figures, and after the proof is made, the mind'is left to infer that it is a general truth, and exists independently of the diagram used to demonstrate it. |