OF GEOMETRY AND TRIGONOMETRY; WITH PRACTICAL APPLICATIONS. BY BENJAMIN GREENLEAF, A. M., AUTHOR OF A MATHEMATICAL SERIES. IMPROVED ELECTROTYPE EDITION. BOSTON: PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: WILLIAM WOOD & CO., AND W. I. POOLEY. PHILADELPHIA: J. B. LIPPINCOTT & COMPANY. ST. LOUIS: KEITH AND WOODS. NEW ORLEANS: DUNCAN & CO. MATHEMATICAL SERIES. I. GREENLEAF'S NEW PRIMARY ARITHMETIC; an attractive book of easy lessons for beginners. 84 pp. II. GREENLEAF'S NEW INTELLECTUAL ARITHMETIC; a late work, with models of analysis. 180 pp. III. GREENLEAF'S COMMON SCHOOL ARITHMETIC; a complete system of Written Arithmetic for Common Schools. 324 pp. IV. GREENLEAF'S NATIONAL ARITHMETIC; a thorough course for High Schools, Academies, Normal Schools, and Commercial Colleges. 444 pp. V. GREENLEAF'S NEW ELEMENTARY ALGEBRA; or the First Principles of Analysis for Schools and Academies. 324 pp. VI. GREENLEAF'S NEW HIGHER ALGEBRA; an advanced Analytical Course, for High Schools and Colleges. 394 pp. VII. GREENLEAF'S ELEMENTS OF GEOMETRY; with applications to Mensuration. 320 pp. VIII. GREENLEAF'S ELEMENTS OF TRIGONOMETRY; with Practical Applications and Tables. 170 pp. IX. GREENLEAF'S GEOMETRY AND TRIGONOMETRY; or the last two works in one volume. 490 pp. X. GREENLEAF'S SURVEYING AND NAVIGATION, with Practical Applications and Tables. [In preparation.] Keys to the Arithmetics, Algebras, Geometry and Trigonometry. For Teachers only. 6 volumes. Entered according to Act of Congress, in the year 1858, by in the Clerk's Office of the District Court of the District of Massachusetts. Entered according to Act of Congress, in the year 1861, by in the Clerk's Office of the District Court of the District of Massachusetts. HARVARD PREFACE. THE preparation of this treatise was undertaken at the earnest solicitation of many teachers, who, having used the author's Arithmetics and Algebra with satisfaction, were desirous of seeing his series rendered more nearly complete by the addition of the Elements of Geometry and Trigonometry. That there are peculiar advantages in a graded series of textbooks on the same subject, few, if any, properly qualified to judge, will doubt. The author, therefore, feels justified in introducing this volume to the attention of the public. In the Elements of Geometry, he has followed, in the main, the simple and elegant order of arrangement adopted by Legendre; but in the methods of demonstration no particular authority has been closely followed, the aim having been to adapt the work fully to the latest and most approved modes of instruction. In this respect, there will be found incorporated a considerable number of important improvements. More attention than is usual in elementary works of this kind has been given to the converse of propositions. In almost all cases where it was possible, the converse of a proposition has been demonstrated. The demonstration of Proposition XX. of the first book is essentially the one given by M. da Cunha in the Principes Mathématiques, which has justly been pronounced by the highest mathematical authorities to be a very important improvement in elementary geometry. It has, however, never before been introduced into a text-book by an American author. |