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

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**Equal Roots**. III . Real Roots . , 186 186 195 a or 201 p the 201 en 210 214 el CHAPTER IX . CONTINUED FRACTIONS . CO ti W 248 EXPONENTIAL EQUATIONS AND LOGARITHMS . SECTION I. Exponential Equations . 263 II . Nature and Properties of ... Page 21

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**equal**to the lowest exponent which it has in any term , and indeed by means of negative exponents any mono- mial may ...**Roots**CH . I. § V. ] 21 DIVISION . Page 90

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Case in which the

To which are Added Exponential Equations and Logarithms Benjamin Peirce. Case in which the

**roots**of two Equations ...**equal**. But this is impossible , unless x = 0 . The value of y would , likewise , be zero , if we had A ' M = A M ... Page 123

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**root**nearly**equal**to 3. Solve the equation 132 , 6 . Ans . -5-87205266 . x4 + 8 x2 + 16 x = 440 , which has two**roots**, the first being nearly 4 and the second nearly -4 . 4. Solve the equation Ans . 3-97601 and 2 x4 - 20 x = - 19 , 4 ... Page 130

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**ROOTS**. SECTION I. : Powers and**Roots**of Monomials . 193. Problem . To find any power of a monomial . Solution . The rule of art . 28 , applied to this case , in which the factors are all**equal**, gives for the coefficient of the ...### 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