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affected algebraic quantities arithmetical arithmetical progression arrangements binomial binomial theorem called co-efficient common difference consequently continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equation involving example exponent figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm manner method monomial multiplicand multiplied number of terms obtain operation ounces perfect power perfect square permutations positive roots preceding problem progression proposed equation quan quotient radical sign real roots Reduce remainder required to find resolved result rule satisfy second degree second member second term simplest form square root substituted subtract superior limit suppose supposition taken third tion total number transformed unity unknown quantity whence whole number
Page 271 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Page 23 - 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.
Page 35 - ... the first term of the quotient ; multiply the• divisor by this term, and subtract the product from the dividend. II. Then divide the first term of the remainder by the first term of the divisor...
Page 198 - In each succeeding term the coefficient is found by multiplying the coefficient of the preceding term by the exponent of a in that term, and dividing by the number of the preceding term.
Page 86 - 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.
Page 104 - 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.
Page 12 - HOW divided, of the algebraic analysis may be divided into two classes : those which are known or given, and those which are unknown or sought. The Howrepre- known are uniformly represented by the first letters of the alphabet, a, b, c, d, &c. ; and the unknown by the final letters, x, y, z, v, w, &c.