A Treatise on Algebra
J. Murphy & Company, 1857 - Algebra - 216 pages
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according added addition affected algebraical applicable arithmetical arranged become binomial called changed coefficient consequently considered constantly containing corresponding demonstrate denominator determined difference divided divisible divisor dollars double easily elimination equa equal equal to zero equivalent evidently exactly example exponent expressed fact factors figures follows formula four fourth fractional given equation gives greater Hence imaginary infer instance known last term less likewise logarithms manner method multiplied namely necessarily negative numerical value observe obtained operation period permutations polynomial positive preceding Problem progression proportion quotient radical ratio reduced regard remainder represent resolution resolved roots rule second member second term similar simple square square root substituted subtract succession Suppose supposition symbols taken terms taken third tion units unity unknown quantity variable whole number write
Page 164 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 164 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Page 83 - ... the second term of the quotient is obtained by dividing the first term of the remainder by the first term of the divisor.
Page 156 - If four numbers are in proportion, the sum of the terms of the first ratio is to either term of the first ratio as the sum of the terms of the second ratio is to the corresponding term of the second ratio ; that is, the numbers are in proportion by Composition.
Page 144 - IN ARITHMETICAL PROPORTION THE SUM OF THE EXTREMES is EQUAL TO THE SUM OF THE MEANS. 24. GEOMETRICAL' PROPORTION is AN EQUALITY OF GEOMETRICAL RATIOS, AND ARITHMETICAL PROPORTION AN EQUALITY OF ARITHMETICAL RATIOS.
Page 164 - Hence the fundamental laws that the logarithm of the product is equal to the sum of the logarithms of the factors and that the logarithm of 1 is 0 do not apply to his tables.
Page 42 - Since the dividend may be regarded as the product of two factors, one of which is the divisor...
Page 82 - By multiplying a + b by а — b we obtain the identity (a + 6)(a-6)=a2-62, a result which may be verbally expressed as follows : The product of the sum and the difference of any two quantities is equal to the difference of their squares. Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.
Page 6 - ... of algebraic analysis, and thus prepare the mind of the student who would afterwards apply himself to higher studies.
Page 70 - Since the square root of 1 is 1, and the square root of any number less than...