Elements of Algebra: Including Sturm's TheoremA. S. Barnes & Company, 1847 - 368 σελίδες |
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Αποτελέσματα 1 - 5 από τα 28.
Σελίδα 24
... units contained in 2b , the number taken away from 4a , is too great by the number of units contained in 3c , and the result 26 is therefore too small by 3c ; this remainder must there- fore be corrected by adding 3c to it . Hence ...
... units contained in 2b , the number taken away from 4a , is too great by the number of units contained in 3c , and the result 26 is therefore too small by 3c ; this remainder must there- fore be corrected by adding 3c to it . Hence ...
Σελίδα 26
... units expressed by a , and the number of units expressed by b . Consequently , this result is numerically less than a . To distinguish this sum from an arithmetical sum , it is called the algebraic sum . Thus , the polynomial , 2a3-3a2b ...
... units expressed by a , and the number of units expressed by b . Consequently , this result is numerically less than a . To distinguish this sum from an arithmetical sum , it is called the algebraic sum . Thus , the polynomial , 2a3-3a2b ...
Σελίδα 27
Including Sturm's Theorem. cal difference between the sum of the units contained in the ad- ditive terms , and the sum of the units contained in the subtractive terms . It follows from this , that an algebraic sum may , in the numeri ...
Including Sturm's Theorem. cal difference between the sum of the units contained in the ad- ditive terms , and the sum of the units contained in the subtractive terms . It follows from this , that an algebraic sum may , in the numeri ...
Σελίδα 28
... units - in c d . Let us first multiply by c ; that is , take ab as many times as there are units in c . ting ac , which is too We begin by wri- great by b taken b a -- C d ac bc ad + bd ac bc ad + bd . ― - b c times ; for it is only the ...
... units - in c d . Let us first multiply by c ; that is , take ab as many times as there are units in c . ting ac , which is too We begin by wri- great by b taken b a -- C d ac bc ad + bd ac bc ad + bd . ― - b c times ; for it is only the ...
Σελίδα 47
... units in the denominator , and one of these parts is supposed to be taken as many times as there are units in the numerator . Thus , in the fractional expression a + b c + ď a given unit is supposed to be divided into as many equal ...
... units in the denominator , and one of these parts is supposed to be taken as many times as there are units in the numerator . Thus , in the fractional expression a + b c + ď a given unit is supposed to be divided into as many equal ...
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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 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 manner 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 required to find resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion transformed transposing unity unknown quantity whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 33 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Σελίδα 111 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 298 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Σελίδα 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.
Σελίδα 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.
Σελίδα 27 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.
Σελίδα 115 - ... equal to the square root of the numerator divided by the square root of the denominator.