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 10
... affected with the same exponents , are called similar terms . Thus , 7 ab and 3 ab , 4a3 b , and 5 a3 b2 , are similar terms . 8 a2 b and 7 a b2 are not similar terms , for although they are composed of the same letters , yet the same ...
... affected with the same exponents , are called similar terms . Thus , 7 ab and 3 ab , 4a3 b , and 5 a3 b2 , are similar terms . 8 a2 b and 7 a b2 are not similar terms , for although they are composed of the same letters , yet the same ...
Σελίδα 12
... affected with the same exponents , are called similar terms . Thus , 7 ab and 3 ab , 4 a3 b2 , and 5 a3 b2 , are similar terms . 8 a2 b and 7 a b2 are not similar terms , for although they are composed of the same letters , yet the same ...
... affected with the same exponents , are called similar terms . Thus , 7 ab and 3 ab , 4 a3 b2 , and 5 a3 b2 , are similar terms . 8 a2 b and 7 a b2 are not similar terms , for although they are composed of the same letters , yet the same ...
Σελίδα 14
... affecting each letter with an exponent equal to the sum of the two exponents with which this letter is affected in the two ... affected in this factor . The reason for the rule relative to the coefficients is evident . But in order to ...
... affecting each letter with an exponent equal to the sum of the two exponents with which this letter is affected in the two ... affected in this factor . The reason for the rule relative to the coefficients is evident . But in order to ...
Σελίδα 15
... affected with coeficients and exponents , ob- serve the rule given for the multiplication of monomials . ( No. 16. ) For example : ( 3a2 + 4 a b + b2 ) ( 2 a + 5b ) gives for a product 6 a3 +8 a2 b + 2ab + 15a2 b + 20 a b2 +5 b3 , or ...
... affected with coeficients and exponents , ob- serve the rule given for the multiplication of monomials . ( No. 16. ) For example : ( 3a2 + 4 a b + b2 ) ( 2 a + 5b ) gives for a product 6 a3 +8 a2 b + 2ab + 15a2 b + 20 a b2 +5 b3 , or ...
Σελίδα 16
... affected ; also , to multiply all the terms of the mul- tiplicand by the subtractive terms of the multiplier , but affect the partial products with signs contrary to those with which the terms of the multiplicand are affected . With ...
... affected ; also , to multiply all the terms of the mul- tiplicand by the subtractive terms of the multiplier , but affect the partial products with signs contrary to those with which the terms of the multiplicand are affected . With ...
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.