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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Σελίδα 17
... hence , or consequently . 14. If a quantity is taken several times , as a + a + a + a + a , it is generally written but once , and a number is then placed before it , to show how many times it is taken . Thus , a + a + a + a + a may be ...
... hence , or consequently . 14. If a quantity is taken several times , as a + a + a + a + a , it is generally written but once , and a number is then placed before it , to show how many times it is taken . Thus , a + a + a + a + a may be ...
Σελίδα 22
... hence - 5a2b 8a2b5a2b 5a2b 3a2b ******** - 3a2b . In like manner we may reduce the similar terms of any poly . nomial . Hence , for the reduction of a polynomial containing sets of similar terms , to its simplest form , we have the ...
... hence - 5a2b 8a2b5a2b 5a2b 3a2b ******** - 3a2b . In like manner we may reduce the similar terms of any poly . nomial . Hence , for the reduction of a polynomial containing sets of similar terms , to its simplest form , we have the ...
Σελίδα 35
... Hence , ac bc is the product of a b by c . - But the true product is a b taken c - - d times : hence , the last product is too great by a b taken d times ; that is , by ad bd , which must , therefore , be subtracted . Subtracting this ...
... Hence , ac bc is the product of a b by c . - But the true product is a b taken c - - d times : hence , the last product is too great by a b taken d times ; that is , by ad bd , which must , therefore , be subtracted . Subtracting this ...
Σελίδα 38
... hence , each term of the product is of the 8th degree . This remark serves to discover any errors in the addition of the exponents . 2d . If no two terms of the product are similar , there will be no reduction amongst them ; and the ...
... hence , each term of the product is of the 8th degree . This remark serves to discover any errors in the addition of the exponents . 2d . If no two terms of the product are similar , there will be no reduction amongst them ; and the ...
Σελίδα 41
... hence , it is 5 . Again , the exponent of each letter in the quotient must be such that when added to the exponent of the same letter in the divisor , the sum will be the exponent of that letter in the dividend . Hence , the exponent of ...
... hence , it is 5 . Again , the exponent of each letter in the quotient must be such that when added to the exponent of the same letter in the divisor , the sum will be the exponent of that letter in the dividend . Hence , the exponent of ...
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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.