## An Introduction to Algebra, with Notes and Observations: Designed for the Use of Schools and Places of Public Education. To which is Added an Appendix, on the Application of Algebra to Geometry |

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according added addition Algebra angled answer applied arise arithmetical assumed base become binomial called changed coefficients common consequently consisting contained continued cube root denominator denoted determined difference division divisor equal equation evident EXAMPLES expression extracting factors figure find the sum find the value former formula four fourth fraction geometrical give Given greater greatest Hence infinite integral involving kind known last term latter least less logarithms manner means method multiplied negative Note observed obtained operation person placed positive PROBLEM progression proper proportion proposed quadratic question quotient rational reduced remain represented Required the sum required to divide required to find resolved result rule side simple solution square number square root substituting subtracted surd taken taking third tion triangle unknown quantity usual value of x Whence whole numbers

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Page 13 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.

Page 38 - ... be the power required. Or, multiply the quantity into itself as many times, less one, as is denoted by the index of the power, and the last product will be tJie answer. 175, When the sign of any simple quantity is +, all the powers of it will be + ; and when the sign is — , all the even powers .will be +, and the odd powers — , as is evident from multiplication.

Page 128 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.

Page ii - In conformity to the act of 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 ;

Page 44 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power...

Page 35 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.

Page 129 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.

Page 17 - If there is a remainder after the last division, write it over the divisor in the form of a fraction, and annex it with its proper sign to the part of the quotient previously obtained.

Page 128 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.

Page 243 - N .•. def. (2), x— x1 is the logarithm of that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power of n. N" =a