BY CHARLES DAVIES, LL.D., SHADOWS, AND PERSPECTIVE. 1 1 NEW YORK : CHICAGO: GEORGE SHERWOOD, 118 LAKE ST. 1864. ASTOR, LENOX AND 1902 Contit of Mathematics. Davies' Primary Arithmetic and Table-Book-Designed for Beginners ; containing the elementary tables of Addition, Subtraction, Vultiplication, Division, and Denominate Numbers ; with a large number oi easy and prac tical questions, both mental and written. Method of Teaching the Combinations of Figures by Sight. especial reference to Mental Training and Development. and the Science of Figures. their Applications according to the most Improved Methods of Analysis and Cancellation. Mensuration. the Mechanic Arts. Science, with graded examples. and practical examples. the course of Mathematical Instruction in the United States. Davies' Elements of Surveying and Navigation-Containing descriptions of the Instruments and necessary Tables.. Straight Line, the Conic Sections, and Surfaces.of the first and second order. try, Spherical Projections, and Warped Surfaces. struction Explained and Illustrated. Dabies' and Peck's Mathematical Dictionary and Cyclopedia of Mathes matical Scienie-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 eigbt 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. PRE FACE. Of 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 generality of the truths evolved. 20 MAY 02 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 |