SERIES OF MATHEMATICS. By WILLIAM CHAUVENET, Late Professor of Mathematics and Astronomy in Washington CHAUVENET'S GEOMETRY. A Treatise on Elementary Geometry, with Appendices containing a Copious Collection of Exercises for the Student and an Introduction to Modern Geometry. Crown 8vo. Cloth. $1.40. CHAUVENET'S PLANE AND SPHERICAL TRIGONOMETRY. New and Revised Edition. 8vo. Cloth. $1.28. CHAUVENET'S METHOD OF LEAST SQUARES. 8vo. Cloth. $1.28. CHAUVENET'S SPHERICAL AND PRACTICAL ASTRONOMY. 2 vols. 8vo. Cloth. $2.50 per vol. Chauvenet's Series of Mathematics need no commendations further than a brief mention of their success. They have been the standard in the leading colleges of the country since their publication. Chauvenet's Geometry is used at Harvard, Yale, West Point, and Annapolis. It has been copied by nearly every author who has written a geometry since its appearance, RECOMMENDATIONS, "I am glad to see at last an American text-book on this subject which is not from seventy-five to two thousand years behind the time, and which, without casting away what is good in the old, does not totally exclude the brilliant geometrical discoveries of the present century. I shall recommend its adoption as a text-book in this university.”—PROF. J. W. SAFFORD, Director of the Dearborn Observatory, Chicago, Ill. "I regard Chauvenet's works on 'Geometry' and 'Trigonometry' as far above all others in merit. Their simplicity and scientific precision are everywhere praised. They are written from the stand-point of the higher analysis, but are made so clear that the most elementary minds may master them."-Wм. T. HARRIS, Esq., Superintendent of Public Schools, St. Louis, Mo. TREATISE ON ELEMENTARY GEOMETRY REVISED AND ABRIDGED BY W. E. BYERLY PROFESSOR OF MATHEMATICS IN HARVARD UNIVERSITY ROIT STAVAN PHILADELPHIA J. B. LIPPINCOTT COMPANY Mathematics Copyright, 1887, by J. B. LIPPINCOTT COMPANY. J.B.LIPPINCOTT STEREOTYPERSANDPRINTERS COMPANY PREFACE. IN preparing this edition of Chauvenet's Geometry I have endeavored to compel the student to think and to reason for himself, and I have tried to emphasize the fact that he should not merely learn to understand and demonstrate a few set propositions, but that he should acquire the power of grasping and proving any simple geometrical truth that may be set before him; and this power, it must be remembered, can never be gained by memorizing demonstrations. Systematic practice in devising proofs of new propositions is indispensable. On this account the demonstrations of the main propositions, which at first are full and complete, are gradually more and more condensed, until at last they are sometimes reduced to mere hints, by the aid of which the full proof is to be developed; and numerous additional theorems and problems are constantly given as exercises for practice in original work. A syllabus, containing the axioms, the postulates, and the captions of the main theorems and corollaries, has been added to aid student and teacher in reviews and examinations, and to make the preparation of new proofs more easy and definite. In the order of the propositions I have departed considerably from the larger Chauvenet's Geometry, with the double object of simplifying the demonstrations and of giving the student, as soon as possible, the few theorems which are the tools with which he must most. frequently work in geometrical investigation. Teachers are strongly advised to require as full and formal proofs of the corollaries and exercises as of the main propositions, and to lay much stress upon written demonstrations, which should be arranged as in the illustrations given at the end of Book I. In preparing a written exercise, or in passing a written examination, the student should have the syllabus before him, and may then conveniently refer to the propositions by number. In oral recitation, however, he should quote the full captions of the theorems on which he bases his proof. CAMBRIDGE, MASS., 1887. W. E. BYERLY. |