OF MATHEMATICAL SCIENCE 101637 FOR THE SCHOOL-ROOM. BY CHARLES DAVIES, LL.D., AUTHOR OF A FULL COURSE OF MATHEMATICS. NEW YORK: PUBLISHED BY A. S. BARNES & CO., 1867. ADVERTISEMENT. THE attention of Teachers is respectfully invited to the REVISED EDITIONS of Dabies' Arithmetical Series FOR SCHOOLS AND ACADEMIES. 1. DAVIES' PRIMARY ARITHMETIC. 4. DAVIES' UNIVERSITY ARITHMETIC. The above Works, by CHARLES DAVIES, LL.D., Author of a Complete Course of Mathematics, are designed as a full Course of Arithmetical Instruction necessary for the practical duties of business life; and also to prepare the Student for the more advanced Series of Mathematics by the same Author. The following New Editions of Algebra, by Professor DAVIES, are commended to the attention of Teachers: 1. DAVIES' NEW ELEMENTARY ALGEBRA AND KEY. 2. DAVIES' UNIVERSITY ALGEBRA AND KEY. 3. DAVIES' BOURDON'S ALGEBRA AND KEY. Entered according to Act of Congress, in the year one thousand eight hundred and sixty-seven, BY CHARLES DAVIES, In the Clerk's Office of the District Court of the United States for the Southern District of New York. PREFACE AND PLAN. THE object of this work is to furnish to the teacher, in the school-room, an aid and guide in his daily labors of giving Mathematical Instruction. The work is but an analysis, in an abridged form, of that system of mathematical instruction which has been steadily pursued at the Military Academy over a third of a century, and which has given to that institution its celebrity as a school of mathematical science. It is the essence of this system that a principle be taught before it is applied to practice-that Science should precede Art—and that general laws and general principles are the only true foundations of knowledge. Where, then, for the instruction of the young, can we find these laws and principles ? The first impressions which the child receives of Number and Space are the foundations of his mathematical knowledge. They form, as it were, a part of his intellectual being. The laws of mathematical science are generalized truths derived from the con |