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TRANSLATED FROM THE FRENCH WITH SUCH ALTERATIONS AND
ADDITIONS AS WERE FOUND NECESSARY IN ORDER TO ADAPT

IT TO THE USE OF AMERICAN STUDENTS.

BY JOHN FARRAR,

Professor of Mathematics and Natural Philosophy in the University at Cambridge.

THIRD EDITION,

CORRECTED AND SOMEWHAT ENLARGED.

CAMBRIDGE, N. E.

PRINTED BY HILLIARD AND METCALF, AT THE UNIVERSITY PRESS.
Soled by W. Hilliard, Cambridge, and by Cummings, Hilliard, & Co.

No. 134 Washington Street, Boston.

1825.

DISTRICT OF MASSACHUSETTS, TO WIT:

District Clerk's Office. BE IT REMEMBERED, that on the twenty-first day of June, A. D. 1825, in the forty-ninth 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, to wit:

"An elementary treatise on Arithmetic, taken principally from the Arithmetic of S. F. Lacroix, and translated from the French, with such Alterations and Additions as were found necessary in order to adapt it to the Use of American Students. By John Farrar, Professor of Mathematics and Natural Philosophy in the University at Cambridge. Third edition, corrected and somewhat 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 bistorical and other prints."

JNO. W. DAVIS,
Clerk of the District of Massachusetts.

Exch. Wil Clements like 7-24 -36

ADVERTISEMENT.

The first principles, as well as the more difficult parts of Mathematics, have, it is thought, been more fully and clearly explained by the French elementary writers, than by the English ; and among these, Lacroix has held a very distinguished place. His treatises have been considered as the most complete, and the best suited to those who are destined for a public education. They have received the sanction of the government, and have been adopted in the principal schools, of France. The following translation is from the thirteenth Paris edition. The original being written with reference to the new system of weights and measures, in which the different denominations proceed in a decimal ratio, it was found necessary to make considerable alterations and additions, to adapt it to the measures in use in the United States. The several articles relating to the reduction, addition, subtraction, multiplication, and division of compound numbers, have been written anew; a change has been made in many of the examples and questions, and new ones have been introduced after most of the rules, as an cise for the learner.

Cambridge, Aug. 1818.

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