Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical ExamplesA.S. Barnes & Burr, 1860 - 400 σελίδες |
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Αποτελέσματα 1 - 5 από τα 51.
Σελίδα 21
... determined by taking the sum of the exponents of the letters which enter it . For example , the term Sa2bcd3 is of the seventh degree , since the sum of the expo- nents , 2 + 1 + 1 + 3 , is equal to 7 . 26. A polynomial is said to be ...
... determined by taking the sum of the exponents of the letters which enter it . For example , the term Sa2bcd3 is of the seventh degree , since the sum of the expo- nents , 2 + 1 + 1 + 3 , is equal to 7 . 26. A polynomial is said to be ...
Σελίδα 45
... determined . We may then consider it as a new dividend , and reason upon it as upon the proposed dividend . We will there- fore divide the term 40a3b , which contains the highest power 5a2 of the divisor . of a , by the term This gives ...
... determined . We may then consider it as a new dividend , and reason upon it as upon the proposed dividend . We will there- fore divide the term 40a3b , which contains the highest power 5a2 of the divisor . of a , by the term This gives ...
Σελίδα 53
... determine the form of the quotient . If we continue for the second the operation for division , we shall find am - 2 term of the quotient , and am - 262 — bm for the second remainder ; also , am - 362 for the third term of the quotient ...
... determine the form of the quotient . If we continue for the second the operation for division , we shall find am - 2 term of the quotient , and am - 262 — bm for the second remainder ; also , am - 362 for the third term of the quotient ...
Σελίδα 89
... determined by assuming a value for the second . Thus , from the equation , we may deduce x + 2y = 4 , x = 4 - 2y , but cannot find a value for x without assuming one for y . If , however , we have another equation between the two un ...
... determined by assuming a value for the second . Thus , from the equation , we may deduce x + 2y = 4 , x = 4 - 2y , but cannot find a value for x without assuming one for y . If , however , we have another equation between the two un ...
Σελίδα 90
... determine the values of three unknown quantities , we must have three equa- tions ; and generally , to determine the values of n unknown quantities we must have n equations . Elimination . 83. Elimination is the operation of combining ...
... determine the values of three unknown quantities , we must have three equa- tions ; and generally , to determine the values of n unknown quantities we must have n equations . Elimination . 83. Elimination is the operation of combining ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
algebraic expression algebraic quantities approximating fraction arithmetical arithmetical progression becomes binomial 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 99 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Σελίδα 364 - 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 118 - X 6 62 + 3 x 3; and taken 3 tens times, 32 + 2 (3 X 6) + 6s gives 3 x 6 + 32 ; and their sum is, 33 + 2 (3 x 6) + 63 : that is, Rule. — The square of a number is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.
Σελίδα 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
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 200 - Subtract the cube of this number from the first period, and to the remainder bring down the first figure of the next period for a, dividend.
Σελίδα 242 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Σελίδα 215 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Σελίδα 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
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.