Elements of Algebra: Tr. from the French of M. Bourdon, for the Use of the Cadets of the U. S. Military Academy, Τόμος 1E. B. Clayton, 1831 - 389 σελίδες |
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Σελίδα 26
... remainder by the first term of the divisor , which gives the second term of the quo- tient ; multiply the divisor by this second term , and subtract the product from the result of the first operation . Continue the same process until ...
... remainder by the first term of the divisor , which gives the second term of the quo- tient ; multiply the divisor by this second term , and subtract the product from the result of the first operation . Continue the same process until ...
Σελίδα 38
... remainder is still equal to that of the divisor , the division may be continued , by multiplying this remainder by 4 , in order to render the division of the two first terms possible . This done , the remainder becomes - 12ab2-4 a2b + ...
... remainder is still equal to that of the divisor , the division may be continued , by multiplying this remainder by 4 , in order to render the division of the two first terms possible . This done , the remainder becomes - 12ab2-4 a2b + ...
Σελίδα 39
... remainder is obtained of a lower degree than the divisor , with reference to the principal letter . See the following table . First Operation . -48 b3 + 48 a b2 - 16 a2b + 16a34b2-5 ab + a2 1st Rem . or , -- 12 ab2-4 a2b + 16 a3 12b - 3 ...
... remainder is obtained of a lower degree than the divisor , with reference to the principal letter . See the following table . First Operation . -48 b3 + 48 a b2 - 16 a2b + 16a34b2-5 ab + a2 1st Rem . or , -- 12 ab2-4 a2b + 16 a3 12b - 3 ...
Σελίδα 41
... two polynomials , the division may be performed without any preparation , and the first remainder will be 6 ba + 9b2 10 c -- 12 b c 5 c2 . • These transformations , which consist in decomposing a po- 6 Fractions . 41.
... two polynomials , the division may be performed without any preparation , and the first remainder will be 6 ba + 9b2 10 c -- 12 b c 5 c2 . • These transformations , which consist in decomposing a po- 6 Fractions . 41.
Σελίδα 43
... remainder , 51 ab3 + 29 , b ' . Suppressing b3 in this remain- der , it becomes - 51 a +29 b for a new divisor , or , changing the signs , which is permitted , 51 a - 29b : the new ... remainder ; this last remainder will be Fractions . 43.
... remainder , 51 ab3 + 29 , b ' . Suppressing b3 in this remain- der , it becomes - 51 a +29 b for a new divisor , or , changing the signs , which is permitted , 51 a - 29b : the new ... remainder ; this last remainder will be Fractions . 43.
Συχνά εμφανιζόμενοι όροι και φράσεις
absolute numbers affected algebraic algebraic quantities arithmetical binomial binomial formula coefficient common factor consequently contains contrary signs cube root deduce denote difference divide dividend division entire functions entire number entire polynomials enunciation equa equal equation involving example exponent expression extract formula fraction given number gives greater greatest common divisor greyhound Hence hypothesis infinite number logarithm manner method monomial multiplied necessary negative nomials nth root number of terms obtain perfect square performing positive preceding prime principle problem proposed equation proposed polynomials question quotient radical rational and entire reduced relative divisor remainder resolved result rule second degree second member second term solution square root substituting subtract suppose take the equation tion transformations unity unknown quantities verified whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 26 - In the first operation we meet with a difficulty in dividing the two polynomials, because the first term of the dividend is not exactly divisible by the first term of the divisor. But if we observe that the co-efficient 4...
Σελίδα 5 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Σελίδα 67 - It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.
Σελίδα 304 - 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 119 - There are other problems of the same kind, which lead to equations of a degree superior to the second, and yet they may be resolved by the aid of equations of the first and second degrees, by introducing unknown auxiliaries.
Σελίδα 14 - ... first term of the quotient ; multiply the divisor by this term, and subtract the product from the dividend.
Σελίδα 69 - 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 133 - 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 237 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Σελίδα 201 - ... multiply the last term by the ratio, subtract the first term from this product, and divide the remainder by the ratio diminished by unity.