New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges |
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Page 17
... remainders will be equal . 3. If equal quantities be multiplied by the same quan- tity , or equal quantities , the products will be equal . 4. If equal quantities be divided by the same quantity , or equal quantities , the quotients ...
... remainders will be equal . 3. If equal quantities be multiplied by the same quan- tity , or equal quantities , the products will be equal . 4. If equal quantities be divided by the same quantity , or equal quantities , the quotients ...
Page 24
... Remainder , is the quantity left after the subtraction is performed . In algebraic subtraction there may be distinguished two cases . CASE I. 57. When the quantities are positive . 1. Let it be required to take 3 a from 8 a . OPERATION ...
... Remainder , is the quantity left after the subtraction is performed . In algebraic subtraction there may be distinguished two cases . CASE I. 57. When the quantities are positive . 1. Let it be required to take 3 a from 8 a . OPERATION ...
Page 41
... term of the quotient . Multiply the whole divisor by this term , and subtract the prod- uct from the dividend . Regard the remainder as a new dividend , arrange it and find the next term of the quotient , in the 4 * DIVISION . 41.
... term of the quotient . Multiply the whole divisor by this term , and subtract the prod- uct from the dividend . Regard the remainder as a new dividend , arrange it and find the next term of the quotient , in the 4 * DIVISION . 41.
Page 42
... remainder will not contain the first term of the divisor . EXAMPLES . ( 2. ) a2 + 4 a2 b2 + 16 b1 a2 2 a b + 4 b2 a1 - 2ab + 4a2 b2 2 a3b + 16b + 2 ab a2 + 2ab + 462 4a2b2 + 8 a b3 4 a2 b2 4 a2 b2 - 8 a b3 + 16b + - 8 a b3 +16 b1 ( 3 ...
... remainder will not contain the first term of the divisor . EXAMPLES . ( 2. ) a2 + 4 a2 b2 + 16 b1 a2 2 a b + 4 b2 a1 - 2ab + 4a2 b2 2 a3b + 16b + 2 ab a2 + 2ab + 462 4a2b2 + 8 a b3 4 a2 b2 4 a2 b2 - 8 a b3 + 16b + - 8 a b3 +16 b1 ( 3 ...
Page 43
... remainder , however far the operation may be carried . 15. Divide a by 1 + x . Ans . a - a x + a x2 — a x3 + , etc. am − 1 fn +1 bm + n Ans . a1bm − 1 . 16. Divide am + n + an + 1bm – 1 an + 1 ― bn +1 . - by 17. Divide a + a® b2 + a + ...
... remainder , however far the operation may be carried . 15. Divide a by 1 + x . Ans . a - a x + a x2 — a x3 + , etc. am − 1 fn +1 bm + n Ans . a1bm − 1 . 16. Divide am + n + an + 1bm – 1 an + 1 ― bn +1 . - by 17. Divide a + a® b2 + a + ...
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Common terms and phrases
a²x² algebraic arithmetical progression binomial factors bushels cent Clearing of fractions coefficient common difference common logarithm Completing the square cube root decimal degree denominator denote Divide dividend equal equation Art EXAMPLES exponent expression Extracting the square Find the cube Find the square Find the sum find the values formula given equation Given x² greatest common divisor Greenleaf's imaginary inequality infinite series last term least common multiple logarithm loge miles Multiply negative nth root number of terms obtain OPERATION permutations polynomial positive problem proportion quadratic equation quan quotient radical sign ratio Reduce remainder required root Required the number required to find result rods second term simplest form solution square root Subtracting tity Transposing and uniting unknown quantity Whence whole number α₁
Popular passages
Page 41 - 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.
Page 61 - The LEAST COMMON MULTIPLE of two or more quantities is the least quantity that can be divided by each of them without a remainder.
Page 157 - Subtract the square of the root from the left period, and to the remainder bring down the next period for a dividend. 3d. Double the root already found, and place it on the left for a divisor. Find how many times the divisor is contained...
Page 79 - Reduce compound fractions to simple ones, and mixt numbers to improper fractions ; then multiply the numerators together for a new numerator, and the denominators for. a new denominator.
Page 141 - Hence, for raising a monomial to any power, we have the following RULE. Raise the numerical coefficient to the required power, and multiply the exponent of each letter by the exponent of the required power.
Page 82 - A Complex Fraction is one having a fraction in its numerator, or denominator, or both. It may be regarded as a case in division, since its numerator answers to the dividend, and its denominator to the divisor.
Page 275 - ... travel over, who gathers them up singly, returning with them one by one to the basket ? Ans.
Page 165 - Find the cube root of the first term, write it as the first term of the root, and subtract its cube from the given polynomial.
Page 255 - Hence -,- = -76" dn that is a" : b" = c" : dn THEOREM IX. 23 1 If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d...
Page 316 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.