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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 divide dividend division entire number enunciation equa equation involving equation x2 example exponent figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm manner merator method monomial multiplied n'h root number of terms number of variations 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 satisfy second degree second member second term simplest form square root substituted subtract superior limit suppose supposition take the equation taken third tion transformed transposing unity unknown quantity whence whole number
Page 27 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.
Page 174 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Page 279 - 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 51 - To reduce fractions having different denominators to equivalent fractions having a common denominator. RULE. Multiply each numerator into all the denominators except its own, for the new numerators, and all the denominators together for a common denominator. EXAMPLES. 1. Reduce ^, £, and |, to a common denominator.
Page 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.
Page 206 - 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 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.
Page 115 - ... equal to the square root of the numerator divided by the square root of the denominator.