OF GEOMETRY AND TRIGONOMETRY, FROM THE WORKS OF A. M. LEGENDRE. ADAPTED TO THE COURSE OF MATHEMATICAL INSTRUCTION IN BY CHARLES DAVIES, LL.D., AUTHOR OF ARITHMETIC, ALGEBRA, PRACTICAL MATHEMATICS FOR PRACTICAL MEN, OF DIFFERENTIAL AND INTEGRAL CALCULUS, AND SHADES, SHADOWS, AND PERSPECTIVE. NEW YORK: BARNES & BURR, PUBLISHERS, 51 & 53 JOHN ST. CHICAGO: GEORGE SHERWOOD, 118 LAKE ST. ST. LOUIS: KEITH AND WOODS. 1863. Course of Mathematics. Davies' Primary Arithmetic AND Cable-Book-Designed for Beginners; containing the elementary tables of Addition, Subtraction, Multiplication, Division, and Denominate Numbers; with a large number of easy and practical questions, both mental and written. Davies' First Lessons in Arithmetic-Combining the Oral Method with the Method of Teaching the Combinations of Figures by Sight. Babies' Entellectual Arithmetic-An Analysis of the Science of Numbers, with especial reference to Mental Training and Development. Davies' New School Arithmetic-Analytical and Practical. Bey to Davies' New School Arithmetic. Davies' Erammar of Arithmetic-An Analysis of the Language of Numbers and the Science of Figures. Davies' New University Arithmetic--Embracing the Science of Numbers, and their Applications according to the most Improved Methods of Analysis aud Cancellation. Bey to Davies' New University Arithmetic. Davies' Elementary Algebra-Embracing the First Principles of the Science. Bey to Davies' Elementary Algebra. Davies' Elementary Geometry AND Trigonometry-With Applications in Mensuration. Babies' Practical Mathematics--With Drawing and Mensuration applied to the Mechanic Arts. Davies' University Algebra-Embracing a Logical Development of the Science, with graded examples. Babies' Bourdon's Algebra-Including Sturm's and Horner's Theorems, and practical examples. Babies' Legendre's Geometry and Trigonometry-Revised and adapted to the course of Mathematical Instruction in the United States. Babies' Elements of Surveying AND Navigation-Containing descriptions of the Instruments and necessary Tables. Badies' Analytical Geometry-Embracing the Equations of the Point, the Straight Line, the Conic Sections, and Surfaces. of the first and second order. Davies' Differential and Integral Calculus. Davies' Descriptive Geometry-With its application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces. Davies' Shades, Shadows, and Perspective. Babies' Logic and Utility of Mathematics-With the best methods of In3ruction Explained and Illustrated. Babies' and Peck's Mathematical Dictionary and Cyclopedia of Mathematical Science-Comprising Definitions of all the terms employed in Mathematics-an Analysis of each Branch, and of the whole, as forming a single Science. ENTERED, according to Act of Congress, in the year one thousand eight hundred and sixty-two, by CHARLES DAVIES, in the Clerk's Office of the District Court of the United States for the Southern District of New York. WILLIAM DENYSE, STEREOTYPER AND ELECTROTYPER, 183 William Street, New York. PREFACE. Or the various Treatises on Elementary Geometry which have appeared during the present century, that of M. LEGENDRE stands preëminent. Its peculiar merits have won for it not only a European reputation, but have also caused it to be selected as the basis of many of the best works on the subject that have been published in this country. In the original Treatise of LEGENDRE, the propositions are not enunciated in general terms, but by means of the diagrams employed in their demonstration. This departure from the method of EUCLID is much to be regretted. The propositions of Geometry are general truths, and ought to be stated in general terms, without reference to particular diagrams. In the following work, each proposition is first enunciated in general terms, and afterwards, with reference to a particular figure, that figure being taken to represent any one of the class to which it belongs. By this arrangement, the difficulty experienced by beginners in comprehending abstract truths, is lessened, without in any manner impairing the gener ality of the truths evolved. The term solid, used not only by LEGENDRE, but by many other authors, to denote a limited portion of space, seems calculated to introduce the foreign idea of matter |