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according added algebraic applicable arithmetical assume becomes binomial called cents changed coefficients combinations complete consider contain continued cube root denominator derived difference diminished distance Divide dividend divisible dollars equal equation example exponent expression factors fifth figure find the values four fraction geometrical give Given greater greatest common divisor Hence increased inequality infinite series involving known last term least less logarithm manner means method miles multiplied negative obtain operation perform permutations polynomial positive preceding principle Prob problem progression proportional proposed quadratic quotient radical raise ratio Reduce remainder represent Required Resolve result RULE second term seen simple solved square root substitute subtract successive suppose surd term third tion units unity unknown quantity values of x variation Whence whole zero
Page 28 - 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 47 - To reduce a mixed number to an improper fraction, — RULE : Multiply the whole number by the denominator of the fraction, to the product add the numerator, and write the result over the denominator.
Page 25 - In the multiplication of whole numbers, place the multiplier under the multiplicand, and multiply each term of the multiplicand by each term of the multiplier, writing the right-hand figure of each product obtained under the term of the multiplier which produces it.
Page 142 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.
Page 38 - 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 355 - The number of deaths in a besieged garrison amounted to 6 daily ; and allowing for this diminution, their stock of provisions was sufficient to last 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the...
Page 235 - Whence it follows, that the cube of a number composed of tens and units, is equal to the cube of the tens, 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 172 - The first term, a, is called the antecedent of b the ratio ; the last term, b, is called the consequent of the ratio. Hence it appears that the theory of ratios is included in the theory of fractions ; and a ratio may be considered as a fraction whose numerator is the antecedent, and whose denominator is the consequent.