Elements of Algebra: Including Sturms' Theorem |
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Page 32
... letter ; and the term produced by the multiplica- tion of the two terms which contain the lowest exponent of this letter . For , these two partial products will contain this letter , affected with a higher and lower exponent than ...
... letter ; and the term produced by the multiplica- tion of the two terms which contain the lowest exponent of this letter . For , these two partial products will contain this letter , affected with a higher and lower exponent than ...
Page 35
... letter , as a , in the quotient , added to the exponent of the same letter in the divisor , must give the exponent of this letter in the dividend : hence , the ex- ponent in the quotient is found by subtracting the exponent in the ...
... letter , as a , in the quotient , added to the exponent of the same letter in the divisor , must give the exponent of this letter in the dividend : hence , the ex- ponent in the quotient is found by subtracting the exponent in the ...
Page 37
... letter b is affected with the same expo- nent in the dividend and divisor : hence , it will divide out , and will not appear in the quotient . But if it is desirable to preserve the trace of this letter in the quotient , we may apply to ...
... letter b is affected with the same expo- nent in the dividend and divisor : hence , it will divide out , and will not appear in the quotient . But if it is desirable to preserve the trace of this letter in the quotient , we may apply to ...
Page 39
... letter a . 10a4 + 10a - Dividend . 48a3b + 26a2b2 + 24ab3 8a3b 6a262 40a3b + 32a2b2 + 24ab3 40a3b + 32a2b2 + 24ab3 ... letter a , is derived , without re- duction from the two terms of the divisor and quotient , affected 1 with the ...
... letter a . 10a4 + 10a - Dividend . 48a3b + 26a2b2 + 24ab3 8a3b 6a262 40a3b + 32a2b2 + 24ab3 40a3b + 32a2b2 + 24ab3 ... letter a , is derived , without re- duction from the two terms of the divisor and quotient , affected 1 with the ...
Page 41
... letter . Now , we avoid the trouble of looking out these terms by writing , in the first place , the terms of the dividend and divisor in such a manner that the exponents of the same letter shall go on diminishing from left to right ...
... letter . Now , we avoid the trouble of looking out these terms by writing , in the first place , the terms of the dividend and divisor in such a manner that the exponents of the same letter shall go on diminishing from left to right ...
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Common terms and phrases
affected algebraic quantities arithmetical arithmetical means arithmetical progression binomial co-efficient common difference consequently contain contrary signs cube root decimal deduced denominator denote derived polynomials divide dividend division entire number enunciation equa equation involving example expression extract the square factors figure find the square find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple letter logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose take the equation third tion transformed transposing unity unknown quantity whence whole number ах
Popular passages
Page 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.
Page 277 - 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 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.
Page 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.
Page 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.
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 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.
Page 36 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
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 204 - 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.