Elements of Algebra: Including Sturm's TheoremA. S. Barnes & Company, 1847 - 368 σελίδες |
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Σελίδα 8
... Exponents ..... 233 Multiplication of Quantities with any Exponent 234 Division 235 Formation of Powers . 236 Extraction ... Exponent .. 244-245 Applications of the Binomial Theorem 245--246 Summation of Series .. Summation of Infinite ...
... Exponents ..... 233 Multiplication of Quantities with any Exponent 234 Division 235 Formation of Powers . 236 Extraction ... Exponent .. 244-245 Applications of the Binomial Theorem 245--246 Summation of Series .. Summation of Infinite ...
Σελίδα 13
... exponent of a , and denotes the number of times which a enters into the product as a factor . Hence , the exponent of a quantity shows how many times the quantity is a factor . It also indicates the number of times , plus one , that the ...
... exponent of a , and denotes the number of times which a enters into the product as a factor . Hence , the exponent of a quantity shows how many times the quantity is a factor . It also indicates the number of times , plus one , that the ...
Σελίδα 16
... exponents of the letters which enter this term . For example , the term 8a2bcd3 is of the seventh degree , since the sum of the exponents , 2 + 1 + 1 + 3 = 7 . 26. A polynomial is said to be homogeneous , when all its terms are of the ...
... exponents of the letters which enter this term . For example , the term 8a2bcd3 is of the seventh degree , since the sum of the exponents , 2 + 1 + 1 + 3 = 7 . 26. A polynomial is said to be homogeneous , when all its terms are of the ...
Σελίδα 17
... exponents . 29. When a polynomial contains several similar terms , it may often be reduced to a simpler form . Take the polynomial It may be written ( Art . 24 ) - But 4a2b 2a2b reduces to Hence , 4a2b3a2c + 7a2c 4a2b - 4a2b -- - 3a2c + ...
... exponents . 29. When a polynomial contains several similar terms , it may often be reduced to a simpler form . Take the polynomial It may be written ( Art . 24 ) - But 4a2b 2a2b reduces to Hence , 4a2b3a2c + 7a2c 4a2b - 4a2b -- - 3a2c + ...
Σελίδα 18
... exponents . The reduction of similar terms is an operation peculiar to al- gebra . Such reductions are constantly made in Algebraic Addition , Subtraction , Multiplication , and Division . 30. In the operations of algebra , there are ...
... exponents . The reduction of similar terms is an operation peculiar to al- gebra . Such reductions are constantly made in Algebraic Addition , Subtraction , Multiplication , and Division . 30. In the operations of algebra , there are ...
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affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator dividend division entire number enunciation equa equal equation involving example exponent factors figure formula fourth given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm manner method monomial multiply nth root number of terms obtain operation ounces perfect square positive roots preceding problem progression proposed equation quan quotient real roots Reduce remainder required to find resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion transformed transposing unity unknown quantity whence whole number
Δημοφιλή αποσπάσματα
Σελίδα 277 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Σελίδα 29 - Hence, for the multiplication of polynomials we have the following RULE. Multiply all the terms of the multiplicand by each term of the multiplier, observing that like signs give plus in the product, and unlike signs minus.
Σελίδα 348 - 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 33 - The square of the difference of two quantities is equal to the square of the first minus twice the product of the first by the second, plus the square of the second.
Σελίδα 111 - 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 298 - ... is equal to the sum of the products of the roots taken three and three ; and so on.
Σελίδα 204 - 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 182 - If the product of two quantities is equal to the product of two other quantities, two of them may be made the extremes, and the other two the means of a proportion.
Σελίδα 27 - We have seen that multiplying by a whole number is taking the multiplicand as many times as there are units in the multiplier.
Σελίδα 115 - ... equal to the square root of the numerator divided by the square root of the denominator.