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 1
... denote the numbers upon which we are to reason . They are used both to abridge the reasoning , and generalize it ... denoted by a augmented by the number denoted by b . 3d . The sign , which is called minus , and is used to indi- cate ...
... denote the numbers upon which we are to reason . They are used both to abridge the reasoning , and generalize it ... denoted by a augmented by the number denoted by b . 3d . The sign , which is called minus , and is used to indi- cate ...
Σελίδα 2
... denoted by one or more letters , and shows the number of times , plus ONE , that this second number is added to itself . 7th . The exponent , which is employed when a number , de- noted by a letter , is multiplied into itself any number ...
... denoted by one or more letters , and shows the number of times , plus ONE , that this second number is added to itself . 7th . The exponent , which is employed when a number , de- noted by a letter , is multiplied into itself any number ...
Σελίδα 3
... denoted by the letter is to be multiplied by itself , or the number of times this letter is a factor in a product . The power of a number , is the product resulting from the multiplication of this number by itself any number of times ...
... denoted by the letter is to be multiplied by itself , or the number of times this letter is a factor in a product . The power of a number , is the product resulting from the multiplication of this number by itself any number of times ...
Σελίδα 4
... 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 have the equality or equation 2x + 19 67 . Now , if ...
... 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 have the equality or equation 2x + 19 67 . Now , if ...
Σελίδα 6
... denote this fraction by supposing a < b . Let m represent the number to be added to the two terms , it a + m becomes b + m In order to compare the two fractions , they should be reduced to the same denominator , which can be done by ...
... denote this fraction by supposing a < b . Let m represent the number to be added to the two terms , it a + m becomes b + m In order to compare the two fractions , they should be reduced to the same denominator , which can be done by ...
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.