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added algebraic already arithmetical becomes called cents changed CHECK coefficient common factor complete consider contains cost cube definition denominator difference digits distance dividing division divisor dollars eliminating equal equation equivalent evident example exponent expression factor figure Find Find the number fraction given gives graphs greater Hence hour identity increased indicated integral laws length less letters logarithm lowest means method miles an hour minutes Multiplying negative obtained positive pounds preceding problem progression prove quadratic quotient rational Reduce remainder represent result rods satisfy seen Simplify solution Solve Solve the equation square root Substituting subtracted surd tens term third traveled twice units unknown numbers write written zero
Page 85 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 74 - The square of the sum of two numbers is equal to the square of the first, plus twice the product of the first and the second, plus the square of the second.
Page 412 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 205 - What fraction is that, whose numerator being doubled, and the denominator increased by 7, the value becomes f ; but the denominator being doubled, and the numerator increased by 2, the value becomes -jj-?
Page 357 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 355 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Page 74 - The product of the sum and difference of two numbers is equal to the difference of their squares.
Page 68 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 241 - ... plus three times the product of the square of the tens by the units, plus three times the product of the tens by the square of the units, plus the cube of the units. This being the case, the cube of the tens...
Page 35 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.