OF GEOMETRY AND TRIGONOMETRY. TRANSLATED FROM THE FRENCH OF A. M. LEGENDRE, aut MEMBER OF THE INSTITUTE AND OF THE LEGION OF HONOUR, AND OF THE ROTAG SOCIETIES OF LONDON AND EDINBURGH, &C. BY DAVID BREWSTER, LL. D. EDINBURGH, &c. &c. REVISED AND ADAPTED TO THE COURSE OF MATHEMATICAL INSTRUCTION IN THE UNITED STATES. AND AUTHOR OF THE COMMON SCHOOL ARITHMETIC, ELEMENTS OF DESCRIPTIVE AND PERSPECTIVE. PUBLISHED BY WILEY & LONG; COLLINS, KEESE & co., New York,-DESILVER, THOMAS & Co., PHILADELPHIA,-RUSSELL, SHATTUCK & CO., Boston,-. F. -S. BABCOCK & CO., CHARLESTON, S. C.- TRUMAN & SMITH, CINCINNATI. 1836. DAVIES' ARITHMETIC-Designed for the use of Aca demies and Schools. It is the purpose of this work to explain, in a brief and clear manner, the properties of num bers, and the best rules for their various applications. DAVIES' BOURDON'S ALGEBRA-Being an abridg ment of the work of M. Bourdon, with the additions of practical examples, DAVIES' LEGENDRE'S GEOMETRY AND TRIGO NOMETRY–Being an abridgment of the work of Legendre, with the addition of a treatise on Mensuration of Planes and Solids, and a Table of Logarithms and Logarithmic Sines. DAVIES' SURVEYING-With a description and plates of, the Theodolite, Compass, Plane-Table and Level,--also, Maps of the Topographical Signs adopted by the Engineer Department, and an explanation of the method of surveying the Public Lands, DAVIES' ANALYTICAL GEOMETRY-Embracing the Equations of the Point and Straight Line—of the Conic Sections-of the Line and Plane in Space-also, the discussion of the General Equation of the second degree, and of surfaces of the second order. DAVIES' DESCRIPTIVE GEOMETRY-With its ap plication to Spherical Projections. DAVIES' SHADOWS AND LINEAR PERSPECTIVE. DAVIES' DIFFERENTIAL AND INTEGRAL CAL CULUS. Entered according to the Act of Congress, in the year one thousand eight bundred and thirty-four, by CHARLES Davies, in the Clerk's Office of the Distriet Court of the United States, for the Southern District of New-York. 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. 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. It is believed that this departure from the method of Euclid has been generally regretted. The propositions of Geometry are general truths, and as such, should be stated in general terms, and without reference to particular figures. The method of enunciating them by the aid of particular diagrams seems to have been adopted to avoid the difficulty which beginners experience in comprehending abstract propositions. But in avoiding this difficulty, and thus lessening, at first, the intellectual labour, the faculty of abstraction, which it is one of the primary objects of the study of Geometry to strengthen, remains, to a certain extent, unimproved. |