New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges
R.S. Davis & Company, 1864 - Algebra - 394 pages
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added algebraic arithmetical assume becomes binomial called cent changed Clearing coefficient common divisor complete consequently containing cube root denominator denote determine difference distance Divide dividend division equal equation EXAMPLES Expand exponent expression Extracting the square factors figures find the values formula four fourth fraction give Given greater greatest Hence imaginary increased indicates infinite interest least less letter logarithm manner means method miles Multiply negative obtain OPERATION positive principles problem progression proportion quadratic equation quotient radical Raise ratio Reduce remainder represent result rods RULE School solution solved square root Substituting Subtracting suppose taken third tion transformed Transposing units unknown quantity values of x Whence whole
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.