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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Αποτελέσματα 1 - 5 από τα 39.
Σελίδα 16
... respect to the partial multiplication of a term of the multiplicand by a term of the multiplier , observe the rules given for monomials . ( No. 16. ) . Take , for an example , the two polynomials : and 4a3 - 5a3b - 8ab2 + 2b3 2a2-3 ab ...
... respect to the partial multiplication of a term of the multiplicand by a term of the multiplier , observe the rules given for monomials . ( No. 16. ) . Take , for an example , the two polynomials : and 4a3 - 5a3b - 8ab2 + 2b3 2a2-3 ab ...
Σελίδα 18
... respect to the exponents . For example , if it is found that in one of the terms of a product that should be homogeneous , the sum of the exponents is equal to 6 , while in all the others their sum is 7 , there is a manifest error in ...
... respect to the exponents . For example , if it is found that in one of the terms of a product that should be homogeneous , the sum of the exponents is equal to 6 , while in all the others their sum is 7 , there is a manifest error in ...
Σελίδα 26
... respect to the manner in which the operations are disposed and performed , yet there is this essen- tial difference between them , that in arithmetical division the figures of the quotient are obtained by trial , while in algebrai- cal ...
... respect to the manner in which the operations are disposed and performed , yet there is this essen- tial difference between them , that in arithmetical division the figures of the quotient are obtained by trial , while in algebrai- cal ...
Σελίδα 36
... respect to each other ; that is to say , they no longer contain a common factor . This proposition is evident ; for let A and B be the given polynomials , D their common divisor , A ' and B ' the quotients , we have A = AxD and B = B1 ...
... respect to each other ; that is to say , they no longer contain a common factor . This proposition is evident ; for let A and B be the given polynomials , D their common divisor , A ' and B ' the quotients , we have A = AxD and B = B1 ...
Σελίδα 43
... respect to each other , that is , they have not a common factor . In fact it results from the second principle ( 35 ) , that the greatest common divisor must be a factor of the re- mainder of each operation ; therefore it should divide ...
... respect to each other , that is , they have not a common factor . In fact it results from the second principle ( 35 ) , that the greatest common divisor must be a factor of the re- mainder of each operation ; therefore it should divide ...
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.