Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems, and Practical ExamplesA. S. Barnes & Company, 1857 - 400 σελίδες |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 76
... denominators . Hence , the transformed equation is x 2. Reduce + entire terins . 5 4x + 5x 60 = 400 . X - 3 - to an equation involving only Ans . 7x + 5x 140 = 105 . 3. Reduce entire terms . α с b + f 76 [ CHAP . IV . ELEMENTS OF ALGEBRA .
... denominators . Hence , the transformed equation is x 2. Reduce + entire terins . 5 4x + 5x 60 = 400 . X - 3 - to an equation involving only Ans . 7x + 5x 140 = 105 . 3. Reduce entire terms . α с b + f 76 [ CHAP . IV . ELEMENTS OF ALGEBRA .
Σελίδα 135
... transformed , by the aid of the following prin- ciples . 1st . Let the a , and , denote any two radicals of the second degree , and denote their product by p ; whence , √ax √ b = p ( 1 ) . Squaring both members of equation ( 1 ) ...
... transformed , by the aid of the following prin- ciples . 1st . Let the a , and , denote any two radicals of the second degree , and denote their product by p ; whence , √ax √ b = p ( 1 ) . Squaring both members of equation ( 1 ) ...
Σελίδα 328
... transformed équation , having its co - efficients very great , as may be seen by reducing the transformed equation resulting from the supposi tion k9000 . Having solved the transformed equation , and found the values of y , the ...
... transformed équation , having its co - efficients very great , as may be seen by reducing the transformed equation resulting from the supposi tion k9000 . Having solved the transformed equation , and found the values of y , the ...
Σελίδα 329
... transformed into an incomplete equation , in which the second term shall be wanting . For , let there be the general equation , Suppose xm + Pxm − 1 + Qxm − 2 + x = u + x ' , • + Tx + U = 0 . u being a new unknown quantity , and x ...
... transformed into an incomplete equation , in which the second term shall be wanting . For , let there be the general equation , Suppose xm + Pxm − 1 + Qxm − 2 + x = u + x ' , • + Tx + U = 0 . u being a new unknown quantity , and x ...
Σελίδα 330
... transformed equation , ( Art . 263 ) , m m 1 2 x2 + ( m1 ) Px + Q = 0 , from which we obtain two values for x ' , which substituted in the transformed equation , reduce it to the form , um + P'um - 1 + R'um - 3 • · + T'u + U ' = 0 ...
... transformed equation , ( Art . 263 ) , m m 1 2 x2 + ( m1 ) Px + Q = 0 , from which we obtain two values for x ' , which substituted in the transformed equation , reduce it to the form , um + P'um - 1 + R'um - 3 • · + T'u + U ' = 0 ...
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algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes called co-efficient common difference contrary signs cube root deduce denote the number derived polynomial Divide dividend entire number equal exactly divisible example exponent extract the square figures Find the factors find the values following RULE formula fractional unit given equation given number gives greater number greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple logarithm mixed quantity monomial multiplicand and multiplier nth power nth root number of terms obtain operation perfect square positive roots preceding problem proposed equation quotient radical sign real roots Reduce the polynomial remainder required to find result second degree second member second term simplest form square root substituted subtract suppose taken third transformed equation unknown quantity whence whole number X₁
Δημοφιλή αποσπάσματα
Σελίδα 121 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Σελίδα 174 - For, we can find the value of one of the unknown quantities in terms of the other and known quantities...
Σελίδα 286 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Σελίδα 39 - 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 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.
Σελίδα 200 - RULE. I. Separate the given number into periods of three figures each, beginning at the right hand ; the left hand period will often contain less than three places of figures.
Σελίδα 100 - If A and B together can perform a piece of work in 8 days, A and c together in 9 days, and B and c in 10 days, how many days will it take each person to perform the same work alone.
Σελίδα 35 - We have, then, for the multiplication of polynomials, the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier in succession, aff'ccting the product of any two terms with the sign plus, when tlieir signs are alike, and with the sign minus, when their signs
Σελίδα 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Σελίδα 200 - The cube of a number is equal to the cube of the tens, plus three times the product of the square of the tens by the units, plus three times the product of the tens by the square of the units, plus the cube of the units.