Elements of Algebra: Including Sturms' Theorem |
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Page 7
Including Sturms' Theorem Charles Davies. ARTICLES Discussion of Equations of the Second Degree . 141-150 Problem of ... term in a Decreasing Series 163 Sum of two Terms equi - distant from Extremes 164 To find Sum of all the Terms ...
Including Sturms' Theorem Charles Davies. ARTICLES Discussion of Equations of the Second Degree . 141-150 Problem of ... term in a Decreasing Series 163 Sum of two Terms equi - distant from Extremes 164 To find Sum of all the Terms ...
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... term , is called a dimension of the term ; and the degree of a term is the number of these factors or dimensions . Thus , 3a is a term of one dimension , or of the first degree . 5ab is a term of two dimensions , or of the second degree ...
... term , is called a dimension of the term ; and the degree of a term is the number of these factors or dimensions . Thus , 3a is a term of one dimension , or of the first degree . 5ab is a term of two dimensions , or of the second degree ...
Page 30
... term 2a2 of the second ; this gives the polynomial 8a5 - 10a4b - 16a3b2 + 4a2b3 , the signs of which are the same as those of the multiplicand . Passing then to the term 3ab of the multiplier , multiply each term of the multiplicand ...
... term 2a2 of the second ; this gives the polynomial 8a5 - 10a4b - 16a3b2 + 4a2b3 , the signs of which are the same as those of the multiplicand . Passing then to the term 3ab of the multiplier , multiply each term of the multiplicand ...
Page 32
... term of the multiplier will produce as many terms as there are terms in the multiplicand . Thus , in example 16th ... second , plus the square of the second . Let a denote one of the quantities and b the 32 [ CHAP . II . ELEMENTS ...
... term of the multiplier will produce as many terms as there are terms in the multiplicand . Thus , in example 16th ... second , plus the square of the second . Let a denote one of the quantities and b the 32 [ CHAP . II . ELEMENTS ...
Page 34
... term within a parenthesis for the other factor . 1. Take , for example , the polynomial ab + ac ; in which , it is plain , that a is a factor of both terms : hence ab + ac = a ( b + c ) . 2. Take , for a second example , the ...
... term within a parenthesis for the other factor . 1. Take , for example , the polynomial ab + ac ; in which , it is plain , that a is a factor of both terms : hence ab + ac = a ( b + c ) . 2. Take , for a second example , the ...
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affected algebraic quantities arithmetical means arithmetical progression binomial called co-efficient common difference consequently contain contrary signs cube root Cx² decimal deduced denominator denote divide dividend division entire number enunciation equa equal equation involving example exponent expression extract the square factors figure find the values formula fourth fraction given equation given number gives greater greatest common divisor hence inequality last term least common multiple less logarithm monomial multiplicand multiplied negative nth root number of terms obtain operation ounces perfect square permutations problem proportion proposed equation quan quotient radical sign Reduce remainder result rule satisfy second degree second member second term simplest form square root substituted subtract suppose supposition take the equation third tion tities total number transposing unity unknown quantity whence whole number ах
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.