PLANE AND SOLID GEOMETRY. TO WHICH IS ADDED PLANE AND SPHERICAL TRIGONOMETRY AND MENSURATION. ACCOMPANIED WITH ALL THE NECESSARY LOGARITHMIC AND TRIGONOMETRIC TABLES. BY GEORGE R. PERKINS, LL. D. NEW YORK: D. APPLETON & CO., 443 & 445 BROADWAY, AND 16 LITTLE BRITAIN, LONDON. M DCCC LX. NEW YOR PUBLIC LIBRARY 478728 ABTOR, LENOX AND 1909 Entered according to Act of Congress, in the year 1854, BY GEORGE R. PERKINS, In the Clerk's Office of the District Court for the Northern District of New York. PREFACE. THIS work is not designed to take the place of the "ELEMENTS OF GEOMETRY," but rather to give a more extended and com prehensive course, better adapted to the use of Advanced Schools and Colleges. In the First Part of the work, which is confined to the theoretical principles of Geometry, great care has been taken to classify and arrange the various Theorems, by bringing together such as correspond to analogous subjects. We have also arranged the Problems by themselves, and have in no case mixed them up with the Theorems. In the preparation of the Geometrical portion of this work, we have made free use of the admirable work of VINCENT. The edition used is the fifth, revised by its author, with the assistance of the distinguished BOURDON. This is a most excellent and valuable French work, but it is not in all respects well adapted to the wants of our Higher Institutions; we have, therefore, preferred to make selections from it, rather than to give a translation of the whole. We have endeavored to arrange and present the different Propositions in the manner which to us appeared best calculated to impart a thorough knowledge of the most important principles of the science of Geometry. As a general thing, we have adhered to the ordinary method of conducting our demonstrations; still we have Lot hesitated to introduce the algebraic notation, when by so |