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MEMBER OF THE INSTITUTE AND THE LEGION OF HONOUR, OF THE ROYAL.
SOCIETY OF LONDON, &c.
TRANSLATED FROM THE FRENCH
THE USE OF THE STUDENTS OF THE UNIVERSITY
CAMBRIDGE, NEW ENGLAND,
BY JOHN FARRAR,
CORRECTED AND ENLARGED.
CAMBRIDGE, N. E.
PRINTED BY HILLIARD AND METCALF,
At the University Press.
No. 134 WASHINGTON STREET, BOSTON.
DISTRICT OF MASSACHUSETTS, TO WIT.
District Clerk's Office. Be it remembered, that on the thirtieth day of May 1825, in the fortyninth year of the independence of the United States of America, Cummings, Hilliard & Co. 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,
“Elements of Geometry, by A. M. Legendre, member of the Institute, and the Legion of Honour, of the Royal Society of London, &c. Translated from the French, for the use of the students of the University at Cambridge, New England. By John Farrar, Professor of Mathematics and Natural Fhilosophy. Second edition, corrected and enlarged."
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 an 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.”
JNO. W. DAVIS,
The work of M. LEGENDRE, of which the following is a translation, is thought to unite the advantages of modern discoveries and improvements with the strictness of the ancient method. It has now been in use for a considerable number of years, and its character is sufficiently established. It is generally considered as the most complete and extensive treatise on the elements of geometry which has yet appeared. It has been adopted as the basis of the article on geometry in the fourth edition of the Encyclopædia Brittanica, lately published, and in the Edinburgh Encyclopædia, edited by Dr. Brewster.
In the original the several parts are called books, and the propositions of each book are numbered after the manner:of.. Euclid. It was thought more convenient for:purposes.of reference to number definitions, propositions, corollarjes; &č., .in one continued series. Moreover the work is divided into two parts, one treating of plane figures and the other of solids; and the subdivisions of each part are denominated sections.
As a knowledge of algebraical signs and the theory of proportions is necessary to the understanding of this treatise, a brief explanation of these, taken chiefly from Lacroix's geometry, and forming properly a supplement to this arithmetic, is prefixed to the work under the title of an Introduction.
The parts omitted in the former edition of this translation on spherical isoperimetrical polygons, and on the regular polyedrons, are inserted in this at the end of the fourth section of the