## An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |

### From inside the book

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Page 10

... product of am br cq , an br c3 , and am + nb . Ans . a2m + 2 n bp + r + 1cq + 8 . 30. Problem . To find the product of two poly- nomials . Multiplication of Polynomials . Solution .

... product of am br cq , an br c3 , and am + nb . Ans . a2m + 2 n bp + r + 1cq + 8 . 30. Problem . To find the product of two poly- nomials . Multiplication of Polynomials . Solution .

**Denote**the aggregate of 10 [ CH . I. § IV . ALGEBRA . Page 11

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**Denote**the aggregate of all the positive terms of one factor by A and of the other by B , and those of their negative terms respectively by C and D ; and , then , the fac- tors are A Cand B - D . Now , if A - C is multiplied by B it is ... Page 46

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**Denote**the value of each of the ratios in the continued proportion of the preceding article by M , and we have whence M = A : B = C : D = E : F , & c .; A = BxM C = DxM E = F × M , & c .; and the sum of these equations is A + C + E + ... Page 65

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**denote**any known quantities , whether positive or negative , and x is the unknown quantity . Proof . When an equation of the first degree with one unknown quantity is reduced , as in art . 118 , its first mem- ber is composed of two ... Page 85

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**denote**similar quantities , accents or numbers being placed to its right or left , above or below , so as to ...**denote**different quantities , though they generally are supposed to imply some similarity between the Indeterminate ...### Other editions - View all

### Common terms and phrases

126 become zero 3d root arithmetical mean arithmetical progression Binomial Theorem coefficient commensurable roots common difference contained continued fraction continued product Corollary deficient terms denote derivative Divide dividend division equal roots equal to zero equation x² factor Find the 3d Find the 4th Find the continued Find the greatest Find the number Find the square Find the sum Free the equation Geometrical Progression given equation gives greatest common divisor Hence imaginary roots last term least common multiple letter logarithm monomials multiplied number of real number of terms polynomial positive roots preceding article Problem quantities in example quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Second Degree Solution Solve the equation square root Sturm's Theorem subtracted Theorem unity unknown quan unknown quantity variable whence