ELEMENTS OF TRIGONOMETRY, SURVEYING, AND NAVIGATION. 194 pp., $1 50. The Trigonometry and Tables, bound in one volume. 360 pp., 82 00. ELEMENTS OF ANALYTICAL GEOMETRY. Revised Edition. 261 pp., $1 50. PRACTICAL ASTRONOMY. 499 pp., $2 00. Entered according to Act of Congress, in the year 1876, by In the Office of the Librarian of Congress, at Washington. PREFACE. THE stereotype plates of my Elements of Geometry and Conic · Sections having become so much worn by long-continued use that it was found necessary to recast them, the opportunity has been improved to give the entire book a thorough revision. As the general plan of the original work has met with very extensive approval, it has not been thought best to modify it materially; nevertheless, the minor changes which have been made are numerous and of considerable importance. The volume commences with a brief sketch of the history of Elementary Geometry, which, it is hoped, may increase the student's interest in a subject which has occupied the attention of so many gifted minds. The definitions of Book I. have been somewhat amplified, for the purpose of giving clearer ideas of the philosophy of the subject; and several notes have been added to the first pages of the book which, it is hoped, may be found useful and suggestive, although they are generally such as any competent teacher might easily have supplied. In Book II. the subject of Ratio has been expanded, especially for the purpose of meeting the difficulty of incommensurable quantities; and in this I have followed substantially the method of Vincent in his Cours de Géométrie. A few new propositions have been added to Books III., IV., and V.; and at the close of Book VI. is given a considerable collection of new theorems and problems, with some numerical exercises on the preceding books. These theorems and problems are so simple that it is hoped many students may be encouraged to labor upon them; for no one can be considered as master of the subject of Geometry who has not acquired the ability to discover the demonstration of new theorems and the solution of new problems. Those who find these exercises too difficult may be benefited by practice upon the numerical examples here given, and such similar ones as any competent teacher can readily furnish. Occasional alterations of some importance will be noticed in Books VII., VIII., and IX., and at the close of Book X. will be found more numerical exercises, designed to impress the preceding principles upon the mind of the student. In the Treatise on the Conic Sections the alterations will be found more numerous. Several new propositions have been added, and the mode of demonstration has in several instances been materially changed. At the close of each chapter is given a small collection of new theorems and several numerical exercises. If the former should be found too difficult, the latter will not be beyond the power of any student who thoroughly understands the preceding principles; and the teacher can easily supply a greater number of similar exercises if it should be thought expe dient. As the demand has frequently been made for a brief treatise on Trigonometry to accompany the volume on Geometry, a concise outline of Plane Trigonometry has been added to this volume, together with a Table of Logarithms, and of Sines and Tangents sufficiently extensive for the solution of all the problems contained in this Treatise. Throughout the entire volume I have aimed to remove difficulties to such an extent as not to discourage any faithful student, and yet have designed to leave sufficient difficulty to call out his best exertions; since that does not deserve the name of education which does not summon the student to grapple with difficulties; and each one is conscious that every difficulty which is overcome by his own efforts imparts increased power to surmount fresh difficulties. I have again to acknowledge my obligations to Professor H.A Newton, who has carefully read all the proofs of that part of this volume embracing Conic Sections and Plane Trigonometry. N.B.-When reference is made to a Proposition in the same Book, only the number of the Proposition is usually given; but when the Proposition is found in |