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 11
... corresponding to the symbols employed . Addition . 13. Suppose that it is required to add together the expres- sions 3 a , 5 b , 2 c ; the result of this addition is : 3 a + 5 b + 2 c , an expression which cannot be reduced to a more ...
... corresponding to the symbols employed . Addition . 13. Suppose that it is required to add together the expres- sions 3 a , 5 b , 2 c ; the result of this addition is : 3 a + 5 b + 2 c , an expression which cannot be reduced to a more ...
Σελίδα 17
... corresponding product is affected with the sign + , and when they are affected with contrary signs , the product is affected with the sign - - Again , we say in algebraic language , that + multiplied by + , or multiplied by , gives + ...
... corresponding product is affected with the sign + , and when they are affected with contrary signs , the product is affected with the sign - - Again , we say in algebraic language , that + multiplied by + , or multiplied by , gives + ...
Σελίδα 49
... corresponding with the greatest expo- nent ; 3. Write those letters which are not common , with their re- spective exponents , in the terms of the fraction which contains them . From this new rule , we find , 48 a3b2c d3 3 36 a2b3c2 de ...
... corresponding with the greatest expo- nent ; 3. Write those letters which are not common , with their re- spective exponents , in the terms of the fraction which contains them . From this new rule , we find , 48 a3b2c d3 3 36 a2b3c2 de ...
Σελίδα 98
... corresponds with the second of the preceding No. , since by dividing the first equation by 3 , and the third by 2 , the coefficients of y and z become the same . We will now show how this system of equations has been formed : After ...
... corresponds with the second of the preceding No. , since by dividing the first equation by 3 , and the third by 2 , the coefficients of y and z become the same . We will now show how this system of equations has been formed : After ...
Σελίδα 99
... corresponds with the second in No. 75 , but does not satisfy the relation d " -d d ' - d a " -a a - a By applying the formulas , we would find 0 A B x = y ==== 0 ' 2 = Now let us operate directly upon the equations . Multiplying the ...
... corresponds with the second in No. 75 , but does not satisfy the relation d " -d d ' - d a " -a a - a By applying the formulas , we would find 0 A B x = y ==== 0 ' 2 = Now let us operate directly upon the equations . Multiplying the ...
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.