ELEMENTS

OF

G E O METRY,

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.

CAMBRIDGE, N. E.

PRINTED BY HILLIARD AND METCALF,

At the University Press.
SOLD BY W. HILLIARD, CAMBRIDGE, AND BY CUMMINGS AND UILLTARD,

NO. 1 CORXHILL, BOSTON.

DISTRICT OF MASSACHUSETTS, TO WIT:

District Clerk's Office. BE IT REMEMBERED, That on the fifth day of April, A. D. 1819, and in the forty. third year of the Independence of the United States of America, Cummings & Hilliard 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, viz.

** 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."

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, 4 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,
Clerk of the District of Massachusetts.

ADVERTISEMENT.

souhlenburg Braun

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 bas 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, corollaries, &c., in one continued series. Moreover the work is considered as divided into two parts, one treating of plane figures and the other of solids ; and the subdivisions of each part are denominated sections.

The translator has omitted a number of propositions on spherical isoperimetrical figures terminating the third section of the second part, an appendix to the second and third sections of this part on regular polyedrons, and most of the notes. These are printed in a smaller character in the original to denote that they are less useful, or that they require more attention t'ian other parts of the work. Also the articles numbered in the translation from 229 to 235 inclusive, and from 295 to 312 inclusive, and article 348, are distinguished by the author in the

a

same manner; and may be passed over or not in the first reading at the discretion of the teacher.

As the reader is supposed to be acquainted with algebraical signs and the theory of proportions, a brief explanation of these, taken chiefly from Lacroix's geometry, and forming properly a supplement to his arithmetic, is prefixed to the work under the title of an introduction.

The translation is from the 11th edition, printed at Paris in 1817.

Cambridge, April, 1819.