New Higher Algebra: An Analytical Course Designed for High Schools, Academies, and Colleges |
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Page 12
... denotes a power , and the denominator a root , thus , b indicates the fifth power of the fourth root of b , or the fourth root of the fifth power of b . SYMBOLS OF RELATION . 21. The SYMBOLS OF RELATION are signs used to indi- cate the ...
... denotes a power , and the denominator a root , thus , b indicates the fifth power of the fourth root of b , or the fourth root of the fifth power of b . SYMBOLS OF RELATION . 21. The SYMBOLS OF RELATION are signs used to indi- cate the ...
Page 45
... denoting the numbers and operations which occur in Arithmetic . 84. In SYMBOLICAL ALGEBRA the rules of Arithmetical Algebra are assumed to hold universally , and it is then determined what must be denoted by the symbols and the ...
... denoting the numbers and operations which occur in Arithmetic . 84. In SYMBOLICAL ALGEBRA the rules of Arithmetical Algebra are assumed to hold universally , and it is then determined what must be denoted by the symbols and the ...
Page 65
... denote any fraction ; then , ab = α . b Now , if we multiply its numerator by any quantity b , we have a ba b = a b , and , in like manner , if we divide its denominator by b , we obtain also a b . Hence , in both cases the value of the ...
... denote any fraction ; then , ab = α . b Now , if we multiply its numerator by any quantity b , we have a ba b = a b , and , in like manner , if we divide its denominator by b , we obtain also a b . Hence , in both cases the value of the ...
Page 66
... denotes that , al- 123 ) , is to be added The sign written before the dividing line has been termed the apparent sign of the fraction , and that depend- ing upon the value expressed by the fraction itself has been termed the real sign ...
... denotes that , al- 123 ) , is to be added The sign written before the dividing line has been termed the apparent sign of the fraction , and that depend- ing upon the value expressed by the fraction itself has been termed the real sign ...
Page 84
... denoted by the exponent of the highest power of the unknown quantity in the equation . Thus , An equation of the first degree is one having no higher power of the unknown quantity than its first power ; as , x + 14 = 28 - 4 , or cx = a2 ...
... denoted by the exponent of the highest power of the unknown quantity in the equation . Thus , An equation of the first degree is one having no higher power of the unknown quantity than its first power ; as , x + 14 = 28 - 4 , or cx = a2 ...
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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.