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a b c algebraic characters Algebraic Quantities Arith arithmetic becomes binomial bº cº changing the signs coefficient consequently courier cube cube root deduce denominator denoted divided dividend and divisor division employed enunciation equa evident example exponent expression extract the root factors figures follows formula fraction francs given in art given number greatest common divisor indicated letters logarithm manner method multiplicand multiplied necessary negative number of arrangements observed obtain operation perfect square performed polynomials preceding article proposed equation proposed number quan question quotient radical sign reduced remainder represented resolve result second degree second member second term simple quantities solution sought square root subtract suppose taken tens third tion tities units unity unknown quantity vulgar fractions whence whole numbers write
Side 99 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Side 133 - Adding to the trial-divisor 3 ab, that is, three times the product of the first term of the root by the second, and...
Side 272 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...
Side 272 - A hare is 50 leaps before a greyhound, and takes 4 leaps to- the greyhound's 3, but 2 of the greyhound's leaps are as much as 3 of the hare's ; how many leaps must the greyhound take to catch the hare ? Ans. 300.
Side 249 - From what has preceded, we perceive that the value of a fraction is the quotient arising from the division of the numerator by the denominator, or from the expression of this division.
Side 272 - There is a fish whoso tail weighs 9 pounds, his head weighs as much as his tail and half his body, and his body weighs as much as his head and his tail ; what is the whole weight of the fish ? Ans.
Side 120 - Therefore, in the third and fourth forms, when q is greater than p2, that is, when the known term is negative, and greater than the square of half the coefficient of the first power of x, both values of the unknown quantity are impossible.
Side 106 - This process, founded upon what was laid down in article 96, that the square of a fraction is expressed by the square of the numerator divided by the square of the denominator, may evidently be applied to any kind of fraction whatever, and more readily to decimals than to others.