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ELEMENTS OF ALGEBRA,

BY

S. F. LACROIX.

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 PHILOSOPAY.

SECOND EDITION,

CAMBRIDGE, N. E.

PRINTED BY HILLIARD AND METCALF,

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

xo. 134 WASHINGTON STREET, BOSTON.

1825.

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viz:

DISTRICT OF MASSACHUSETTS, TO WIT.

District Clerk's Office. Be it remembered that on the twenty-fifth day of July, 1825, in the fiftieth 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 Algebra, by S. F. Lacroix. 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 Philosophy:'

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 supplementa. ry 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.

Lacroix'S ALGEBRA has been in use in the French schools for a considerable time. It has been approved by the best judges, and been generally preferred to the other elementary treatises, which abound in France. The following translation is from the eleventh edition, printed at Paris in 1815. No alteration has been made from the original, except to substitute English instead of French measures in the questions, where it was thought necessary. When there has been an occasion to add a note by way of illustration, the reference is made by a letter or an obelisk, the author's being always distinguished by an asterisk.

In a review of the two first parts of the Cambridge course of Mathematics, which appeared in the American Journal of Science and the Arts for 1822, after many favourable remarks, the writer, speaking of Lacroix's Algebra, observes, that “ there are instances of incorrect translation at pages 18, 23, 54.” It is regretted that the passages referred to were not more particularly pointed out. The places mentioned, however, have been carefully examined and compared with the original. · At page 18 the only passage to which the above remark can be supposed to apply, is the following; " and by arranging the letters in alphabetical order, they are more easily read;" of which the original reads thus : 6 et en intervertissant l'ordre des multiplications pour conserver l'ordre alphabétique, plus facile dans l'énonciation des lettres." Here, as in other parts, a little latitude is used for the sake of perspicuity, and of preserving the English idiom; but it is presumed that the sense is fully and exactly rendered. At page 23 there was clearly a mistake, the sense being the reverse of that of the original, and of that which the connexion obviously requires. At page 54, the only inaccuracy to be found is in printing “ multiplier” for “multiple.” “ At page 37" (97], says the

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