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 3
... greater or less than another . Thus ab is read , a greater than b ; a < b , a less than b , that is , the opening of the sign must be towards the greater quantity . From the preceding explanations , we see that Algebra may be regarded ...
... greater or less than another . Thus ab is read , a greater than b ; a < b , a less than b , that is , the opening of the sign must be towards the greater quantity . From the preceding explanations , we see that Algebra may be regarded ...
Σελίδα 4
... greater by adding 19 to it . This being the case , denote the least number by x : the greater may then be designated by x + 19 : hence their sum is x + x + 19 , or 2 x + 19. But from the enunciation , this sum is to be 67. Therefore we ...
... greater by adding 19 to it . This being the case , denote the least number by x : the greater may then be designated by x + 19 : hence their sum is x + x + 19 , or 2 x + 19. But from the enunciation , this sum is to be 67. Therefore we ...
Σελίδα 5
... greater by adding the half difference to the half sum , and the less , by subtracting the half difference from the half sum . Thus , when the given sum is 237 , and the difference 99 , 237 99 , 237 + 99 336 99 , 138 the greater is 2 + ...
... greater by adding the half difference to the half sum , and the less , by subtracting the half difference from the half sum . Thus , when the given sum is 237 , and the difference 99 , 237 99 , 237 + 99 336 99 , 138 the greater is 2 + ...
Σελίδα 6
... greater than the first . Let the proposed fraction be , if 3 be added to its two terms , it becomes . These two fractions reduced to the same denominator , become , and the second fraction is evi- dently greater than the first . To ...
... greater than the first . Let the proposed fraction be , if 3 be added to its two terms , it becomes . These two fractions reduced to the same denominator , become , and the second fraction is evi- dently greater than the first . To ...
Σελίδα 7
... greater than the part a m of the first , since b > a . is greater than the first . Q. E. D. Hence the second fraction We see , moreover , from the preceding reasoning , that must be a proper fraction in order that the theorem may be ...
... greater than the part a m of the first , since b > a . is greater than the first . Q. E. D. Hence the second fraction We see , moreover , from the preceding reasoning , that must be a proper fraction in order that the theorem may be ...
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.