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affected algebraic quantities arithmetical arithmetical means arithmetical progression becomes binomial binomial theorem called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator denote divide dividend division entire number enunciation equa equal equation involving example exponent extract the square figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm manner method monomial multiplied negative number of terms obtain operation ounces perfect power perfect square permutations preceding problem progression proposed equation quan quotient radical sign Reduce remainder result rule second degree second member second term simplest form square root substituted subtract suppose take the equation third tion tities total number transposing trinomial units unity unknown quantity whence whole number
Side 32 - 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.
Side 29 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Side 181 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Side 182 - 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.
Side 92 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Side 348 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Side 36 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Side 110 - 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.