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added addition ages algebraic amount ANALYSIS arithmetical base binomial called cent changing coefficient common common divisor compound interest contains cost cube decimal denote difference Divide dividend division divisor dollars equal equation exponent expressed Extracting factors figure FORMULA four fourth fraction gain Given giving greater greatest half Hence hour increased indicated infinite integer invested involved last term length less letter logarithm means method miles minus monomial Multiply negative Note number of terms OPERATION parenthesis placed polynomial positive preceding prefix present worth prime factors principles problem progression proportion quadratic quotient radical ratio receive Reduce remainder removed Resolve result rule share shows side simple SOLUTION square root Substituting subtract subtrahend taken third Transposing twice unit unknown quantity unlike whole Write
Σελίδα 202 - 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.
Σελίδα 22 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.
Σελίδα 42 - 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.
Σελίδα 109 - Prob. 29. In the composition of a quantity of gunpowder, The nitre was 10 Ibs. more than f of the whole. The sulphur 4^ Ibs.
Σελίδα 139 - 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.
Σελίδα 208 - From the preceding, it appears, that the sum of the extremes is equal to the sum of any other two terms equally distant from the extremes.
Σελίδα 64 - Divide the greater number by the less, the divisor by the remainder, and thus continue to divide the last divisor by the last remainder until there is no remainder ; the last divisor will be the greatest common divisor.
Σελίδα 50 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.