Elements of Algebra: Including Sturms' TheoremA. S. Barnes, 1845 - 368 σελίδες |
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affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide dividend division entire number enunciation equa equal equation involving example exponent factors figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm method monomial multiply nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient real roots Reduce remainder resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion tities transformed transposing unity unknown quantity whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 30 - 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.
Σελίδα 275 - 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.
Σελίδα 27 - 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.
Σελίδα 179 - 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.
Σελίδα 180 - 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.
Σελίδα 90 - 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.
Σελίδα 346 - 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.
Σελίδα 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Σελίδα 108 - 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.
Σελίδα 202 - 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.