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added addition algebraic binomial cents changed Clearing coefficient common denominator consequently containing cube root Define denominator denote difference Divide dividend division entire quantity equa equal equation equivalent EXAMPLES Expand Explain the operation exponent expression Extract factors figures find the values formulas four fourth fraction Given gives greatest common divisor Hence indicated known least common multiple less letter logarithm means Multiply NOTE obtain parenthesis polynomial positive prime proportion quan quotient radical Raise ratio Reduce remainder Repeat the Rule represent Resolve result similar simple solution of Problem solved square root Substituting subtracted taken Theorem third tion tity transposing twice units unknown quantity values of x Whence write written
Page 53 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 54 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 287 - The logarithm of a product is equal to the sum of the logarithms of its factors.
Page 153 - This may be effected, as is evident from the definition of a power, by taking the given quantity as a factor as many times as there are units in the exponent of the required power.
Page 268 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 287 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 169 - Find the greatest square in the first- period on the left, and place its root on the right after the manner of a quotient in division. Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend.
Page 257 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards; but if the circumference of each wheel...
Page 257 - 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. Ans. 20 and 40.
Page 116 - For, if we have given ab' = a'b, then, dividing by bb', we obtain Corollary. The terms of a proportion may be written In any order which will make the product of the extremes equal to the product of the means.