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

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**Solution**of Equations of the First Degree , with one 59 unknown quantity . 65 IV . Equations of the First Degree containing two or more unknown quantities . 85 CHAPTER IV . NUMERICAL EQUATIONS . SECTION I. Indeterminate Coefficients ... Page 7

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**Solution**. The following**solution**requires no de- monstration . The quantities to be added are to be written after each other with the proper sign between them , and the polynomial thus obtained can be reduced to its simplest form by ... Page 8

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**Solution**. Let A denote the aggregate of all the positive terms of the quantity to be subtracted , and B the aggregate of all its negative terms ; then A - B is the quantity to be subtracted , and let C denote the quantity from which it ... Page 9

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**Solution**. The required product is indicated by writing the given monomials after each other with the sign of multi- plication between them , and thus a monomial is formed , which is the continued product of all the factors of the given ... Page 18

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**Solution**. The term of the dividend , which contains the highest power of any letter , must be the product of the term of the divisor which contains the highest power of the same letter , multiplied by the term of the quotient which ...### 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