Elements of Algebra: Including Sturms' Theorem |
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Page 30
... each product with a sign contrary to that of the corresponding term in the multiplicand ; this gives - - 12a4b + 15a3b2 + 24a2b3 6ab4 - The same operation is also performed with the term - 30 [ CHAP . II . ELEMENTS OF ALGEBRA .
... each product with a sign contrary to that of the corresponding term in the multiplicand ; this gives - - 12a4b + 15a3b2 + 24a2b3 6ab4 - The same operation is also performed with the term - 30 [ CHAP . II . ELEMENTS OF ALGEBRA .
Page 38
... corresponding terms of the dividend and divisor have the same sign , their quotient will be affected with the sign + , and when they are affected with contrary signs , their quotient will be affected with the sign ; again , for the sake ...
... corresponding terms of the dividend and divisor have the same sign , their quotient will be affected with the sign + , and when they are affected with contrary signs , their quotient will be affected with the sign ; again , for the sake ...
Page 84
... corresponding values of x , y , being substituted in the given equation , 5x - 3y = 12 will satisfy it equally well : hence , there are an infinite number of values for x and y which will satisfy the equation , and conse- quently , the ...
... corresponding values of x , y , being substituted in the given equation , 5x - 3y = 12 will satisfy it equally well : hence , there are an infinite number of values for x and y which will satisfy the equation , and conse- quently , the ...
Page 97
... b The double sign ± , is read plus or minus , and nus or plus . The upper signs correspond to the , is read , mi- case in which the laborer received , and the lower signs , to 7 CHAP . IV . ] 97 EQUATIONS OF THE FIRST DEGREE .
... b The double sign ± , is read plus or minus , and nus or plus . The upper signs correspond to the , is read , mi- case in which the laborer received , and the lower signs , to 7 CHAP . IV . ] 97 EQUATIONS OF THE FIRST DEGREE .
Page 108
... corresponding numbers of the second . We may also re- mark that , the square of a number expressed by a single figure , will contain no figure of a higher denomination than tens . The numbers of the last line , 1 , 4 , 9 , 16 , & c ...
... corresponding numbers of the second . We may also re- mark that , the square of a number expressed by a single figure , will contain no figure of a higher denomination than tens . The numbers of the last line , 1 , 4 , 9 , 16 , & c ...
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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.