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 not hesitated to introduce the algebraic notation, when by so doing we could present the subject in a clearer and more satisfactory manner. Throughout the Second Part, which is of a more mixed or practical nature, we have studied to present the whole in a distinct and clear manner, giving in all cases the full and complete work of all examples necessary to illustrate each principle. We would direct the attention in particular to the chapters on Spherical Trigonometry. This subject is generally regarded as intricate and difficult. It is believed the student will find the arrangement and full development of the different cases as here given, nearly as simple and of as easy comprehension as those of Plane Trigonometry. We might particularize other portions of the work, but will content ourselves by remarking that we have spared no pains to make the whole acceptable to the mathematical student of the present age. How well we have succeeded remains to be shown. UTICA, September, 1854. GEO. R. PERKINS. Of chords, secants, and tangents Of inscribed and circumscribed polygons. Of secant and tangent circles. Explanation of Table III. of natural sines and tangents. |