Elements of Algebra: Including Sturm's TheoremA. S. Barnes & Company, 1847 - 368 σελίδες |
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Σελίδα 13
... example , ala is the first power of a , a2 = axa is the second power , or square of a , a3 = a × a × a is the third ... example of the use of the exponent in algebra , let it be required to express that a number a is to be multiplied ...
... example , ala is the first power of a , a2 = axa is the second power , or square of a , a3 = a × a × a is the third ... example of the use of the exponent in algebra , let it be required to express that a number a is to be multiplied ...
Σελίδα 14
... example shows the brevity of the algebraic language . 16. The root of a quantity , is a quantity which being multi- plied by itself a certain number of times , will produce the given quantity . The sign , is called the radical sign ...
... example shows the brevity of the algebraic language . 16. The root of a quantity , is a quantity which being multi- plied by itself a certain number of times , will produce the given quantity . The sign , is called the radical sign ...
Σελίδα 15
... example , 3a - 5b , and 2a2 - 3cb + 462 , are polynomials . A polynomial composed of two terms , is called a binomial ; and a polynomial of three terms is called a trinomial . 21. The numerical value of an algebraic expression , is the ...
... example , 3a - 5b , and 2a2 - 3cb + 462 , are polynomials . A polynomial composed of two terms , is called a binomial ; and a polynomial of three terms is called a trinomial . 21. The numerical value of an algebraic expression , is the ...
Σελίδα 16
... 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 same degree . The polynomial 3a 2b + c - -- 4ab + b2 ...
... 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 same degree . The polynomial 3a 2b + c - -- 4ab + b2 ...
Σελίδα 22
Including Sturm's Theorem. - EXAMPLES . 1. Add together the polynomials , 3a2 · 2b2-4ab , 5a2 — b2 + 2ab , The term 3a2 ... example . Passing then to the term and 3ab 3c2 - 262 . 3a2 4ab2b2 - 5a2 + 2ab + 3ab Z ? 262-3c 8a2 + ab 562 · 3c2 ...
Including Sturm's Theorem. - EXAMPLES . 1. Add together the polynomials , 3a2 · 2b2-4ab , 5a2 — b2 + 2ab , The term 3a2 ... example . Passing then to the term and 3ab 3c2 - 262 . 3a2 4ab2b2 - 5a2 + 2ab + 3ab Z ? 262-3c 8a2 + ab 562 · 3c2 ...
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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.