District Clerk's Office. BE IT REMEMBERED, That on the thirtieth day of September, A. D. 1818, 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 Algebra, by S. F. Lacroix, 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, " 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, 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 of illustration, the reference is made by a letter or an obelisk, the author's being always distinguished by an asterisk. Cambridge, June, 1818. CONTENTS. The nature and object of algebra Explanation and use of algebraic signs Examples of the solution of problems by means of algebraic signs To solve questions by the assistance of algebra Explanation of the words, equation, members, and terms Resolution of equations of the first degree, having but one un- Rule for transposing any term from one member of an equation To disengage au unknown quantity from multipliers Of equations, the terms of which have divisors Rule for making the denominators in an equation to disappear Methods for performing, as far as is possible, the operations in- dicated upon quantities, that are represented by letters Explanation of the terms, simple quantities, binomials, trinomials, Subtraction of algebraic quantities Rule for performing subtraction Multiplication of algebraic quantities Manner of indicating multiplication Value of a quantity whose exponent is zero How an expression employing division may be simplified when the operation cannot be performed Division of compound quantities The greatest common divisor of two algebraic quantities - divisor, contains several terms having the letter, with refer- ence to which the arrangement is made, of the same degree To obtain the divisor independent of this letter, Recapitulation of the rules for the calculus of fractions Resolution of a literal equation of the first degree |