## 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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Algebra answer arise arithmetical mean arithmetical progression arithmetical series binomial coefficients consequently cube root cubic equation decimal denominator denoted determined divisor equa equal EXAMPLES FOR PRACTICE expression factors find the difference find the root find the square find the sum find the value find two numbers former formula four roots frac fraction geometrical mean geometrical progression geometrical series give given equation given number greatest common measure Hence infinite series integral last term latter logarithms method multiplied negative nth root number of terms observed orders of differences perpendicular PROBLEM proportion quadratic equation quadratic surd question quotient rational remain Required the product Required the sum required to divide required to find resolved result rule second term side simple form square number square root substituting subtracted taken third tion transposition unknown quantity Whence whole numbers

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Side 25 - 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.

Side 48 - ... 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.

Side 148 - 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.

Side vi - 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 ;

Side 56 - ... and the quotient will be the next term Of the root. Involve the whole of the root, thus found, to its proper power...

Side 45 - 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.

Side 149 - 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.

Side 27 - 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.

Side 148 - 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.

Side 263 - 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