PROFESSOR OF MATHEMATICS. IN TIE MLITARY ACADEMS AT WEST POINT. NEW-YORK : PRINTED AND PUBLISHED BY J.'& J. HARPEK, AND SOLD BY W. C. LITTLE AND CO., ALBANY ; A. AND E. PICKET, WHEELING, VA.; N. AND G. GUILFORD, CINCINNATI ; F. LUCAS, JR., BALTIMORE; MORTON AND CO., LOUISVILLE, 68.; 562080 ASTOR, LENOX AND TILDEN FOUNDATIONS, R 1912 L SOUTHERN DISTRICT. GÉ NEW-YORK, 8s. BE IT REMEMBERED, That on the first day of March, A. D. 1830, in the fifty-fourtit year of the Independence of the United States of America, J. & J. HARPER, of the said District, have deposited in this office the title of a Book, the right whereof they claim as proprietors, in the words following, to wits “Elements of Surveying. With the necessary Tables. By CHARLES Davies, Professor of Mathematics in the Military Academy at West Point.” In conformity to the act of the Congress of the United States, entitled " An act for the encouragement of learning, by securing the copies of maps, charts, and books to the authors and proprietors of such copies, during the times therein mentioned.” And also to the act, entitled, * An act supplementary to an act, entitled an act for the encouragement of learning, by securing the copies of maps, charts, and books to the authors and proprietors of such copies, during the times therein mentioned, and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints." FREDERICK I. BETTS, PREFACE. These Elements have been compiled for the use of the Cadets of the Military Academy. In submitting them to the public, the author does not intend to express the opinion that the work is superior to those, on the same subject, which are now in general use. A course of academic instruction is not only limited to a few branches of knowledge, but is also restricted to very partial examinations of those subjects which engage the attention of the student. A complete treatise should, therefore, be a very different work from a mere text-book: the former discussing all that belongs to the subject treated of; the latter presenting general views in a condensed and concentrated form. а If this work do not, on the whole, receive the approbation of the intelligent reader, it will be but fair to bear in mind, that it has been prepared for a particular purpose ; that it is not put forth as a full treatise on the subject of Surveying; and |