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added addition algebraic arithmetical 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 number of terms obtain parenthesis polynomial positive prime proportion quadratic quotient radical Raise ratio Reduce remainder Repeat the Rule represent Resolve result similar simple Solve square root Substituting subtracted taken Theorem third tion tity transposing twice units unknown quantity values of x Whence write
Page 283 - The logarithm of a product is equal to the sum of the logarithms of its factors.
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 276 - ... that is, Any term of a geometric series is equal to the product of the first term, by the ratio raised to a power, whose exponent is one less than the number of terms. EXAMPLES. 1.
Page 266 - ... two triangles are to each other as the products of their bases by their altitudes.
Page 71 - The LEAST COMMON MULTIPLE, of two or more quantities is the least quantity that can be divided by each of them without a remainder. Define a Multiple. Define a Common Multiple of two or more quan.
Page 263 - 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 = e :f Now ab = ab (1) and by Theorem I.
Page 105 - If the same operations are performed upon equal quantities, the results will be equal. Hence, — Both members of an equation may be increased, diminished, multiplied, or divided by the same quantity, without destroying the equality.
Page 255 - 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 151 - To raise a whole number or a decimal to any power, use it as a factor as many times as there are units in the exponent.
Page 320 - f- to find the values of x and y. (*Vf-2a;y=1295. > 9. Find two numbers such that their sum, their product, and the difference of their squares shall be equal to one another.