Elements of Algebra: Including Sturms' Theorem |
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Page 35
... dividend , the co - efficient of the quotient multiplied by 7 must give 35 , the co - efficient of the dividend ; hence , the new co - efficient 5 is found by dividing 35 by 7. Again , the exponent of any letter , as a , in the quotient ...
... dividend , the co - efficient of the quotient multiplied by 7 must give 35 , the co - efficient of the dividend ; hence , the new co - efficient 5 is found by dividing 35 by 7. Again , the exponent of any letter , as a , in the quotient ...
Page 36
... dividend , and affect each with an exponent equal to the excess of its exponent in the dividend over that in the divisor . From this rule we find , 48a3b3c2d 150a5b3cd3 = 4a2bcd ; 5a2b3cd . 12ab2c 30a3d2 Ans . 2x Ans . 5axy2 . 1. Divide ...
... dividend , and affect each with an exponent equal to the excess of its exponent in the dividend over that in the divisor . From this rule we find , 48a3b3c2d 150a5b3cd3 = 4a2bcd ; 5a2b3cd . 12ab2c 30a3d2 Ans . 2x Ans . 5axy2 . 1. Divide ...
Page 37
... dividend are found in the divisor , the numerator is reduced to unity ; for , in fact , both terms of the fraction are divided by the numerator . 52. It often happens , that the exponents of certain letters , are the same in the dividend ...
... dividend are found in the divisor , the numerator is reduced to unity ; for , in fact , both terms of the fraction are divided by the numerator . 52. It often happens , that the exponents of certain letters , are the same in the dividend ...
Page 38
... dividend . Hence , the dividend is the assemblage , after reduction , of the partial products of each term of the divisor by each term of the quotient , and consequently , the signs of the terms in the quotient must be such as to give ...
... dividend . Hence , the dividend is the assemblage , after reduction , of the partial products of each term of the divisor by each term of the quotient , and consequently , the signs of the terms in the quotient must be such as to give ...
Page 39
... dividend and the quotient di- rectly under the divisor . Divisor . Dividend . a2 2ax + x2 || α a2 - ax ax + x2 ― ax + x2 . -- Х α- X Quotient . We first divide the term a2 of the dividend by the term a of the divisor , the partial ...
... dividend and the quotient di- rectly under the divisor . Divisor . Dividend . a2 2ax + x2 || α a2 - ax ax + x2 ― ax + x2 . -- Х α- X Quotient . We first divide the term a2 of the dividend by the term a of the divisor , the partial ...
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Common terms and phrases
affected algebraic quantities arithmetical arrangements becomes binomial called co-efficient common difference consequently contain continued fraction contrary signs cube root decimal deduced denominator divide 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 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 resolved result rule second degree second member second term simplest form square root substituted subtract superior limit suppose take the equation taken third tion tities transformed transposing unity unknown quantity whence whole number
Popular passages
Page 30 - 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.
Page 275 - 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.
Page 27 - 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.
Page 179 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 180 - 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.
Page 90 - 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 would it take each person to perform the same work alone ? Ans.
Page 346 - 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.
Page 34 - I. Divide the coefficient of the dividend by the coefficient of the divisor.
Page 108 - Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Page 202 - 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.