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, A. S. BARNES & COMPANY, NEW YORK AND CHICAGO. 1871. THE NEW YORK PUBLIC LIBRARY 561924DAVIES' MATHEMATICS. ASTOR, LENOX AND OUNDATIONS. THE WEST POINT COURSE, And Only Thorough and Complete Mathematical Series. IN THREE PARTS. I. COMMON SCHOOL COURSE Davies' Primary Arithmetic.-The fundamental principles displayed in Davies' Intellectual Arithmetic.-Referring all operations to the unit 1 as Davies' Elements of Written Arithmetic.-A practical introduction to the whole subject. Theory subordinated to Practice. Davies' Practical Arithmetic.*-The most successful combination of Theory and Practice, clear, exact, brief, and comprehensive. 11. ACADEMIC COURSE. w Davies' University Arithmetic.*-Treating the subject exhaustively as a science, in a logical series of connected propositions. Davies' Elementary Algebra.*-A connecting link, conducting the pupil easily from arithmetical processes to abstract analysis. Davies University Algebra.*For institutions desiring a more complete but not the fullest course in pure Algebra. Davies' Practical Mathematics.-The science practically applied to the useful arts, as Drawing, Architecture, Surveying, Mechanics, etc. Davies' Elementary Geometry.-The important principles in simple form, Davies' Elements of Surveying.-Re-written in 1870. The simplest and III. COLLEGIATE COURSE. Davies' Bourdon's Algebra.*-Embracing Sturm's Theorem, and a most exhaustive and scholarly course. Davies' University Algebra.*-A shorter course than Bourdon, for Institutions have less time to give the subject. Davies' Legendre's Geometry.-Acknowledged the only satisfactory treatise Davies' Analytical Geometry and Calculus.-The shorter treatises, Davies' Shades, Shadows, and Perspective.-A succinct exposition of Davies' Science of Mathematics.-For teachers, embracing I. GRAMMAR OF ARITHMETIC, II. OUTLINES OF MATHEMATICS, III. LOGIC AND UTILITY OF MATHEMATICS, IV. MATHEMATICAL DICTIONARY. * Keys may be obtained from the Publishers by Teachers only. Entered, according to Act of Congress, in the year 1862, by In the Clerk's Office of the District Court of the United States for the Southern District of L. New York. PREFACE. Or the various Treatises on Elementary Geometry which have appeared during the present century, that of M. LEGENDRE stands preeminent. 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. 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 |