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

### From inside the book

Results 1-5 of 7

Page 67

... equal to any quantity whatever , and is called an indeterminate expression . The given equation is , indeed , in this case 0x x +

... equal to any quantity whatever , and is called an indeterminate expression . The given equation is , indeed , in this case 0x x +

**0**=**0**, an equation which is satisfied by any value whatever of x , and is called an identical equation .**126**... Page 75

...

...

**126 become**.**zero**? and what would this value signify ? Solution . As the value of the unknown quantity of the example is the fraction , which is its answer ; it is zero , when b na a or , clearing from fractions , when that is , when na = ... Page 76

... zero is , therefore , to be regarded as a real solution . 3. In what cases would the value of one of the unknown quantities in example 38 of art .

... zero is , therefore , to be regarded as a real solution . 3. In what cases would the value of one of the unknown quantities in example 38 of art .

**126 become zero**? and what would this value signify ? Ans . When either a = c , or b = c ... Page 77

...

...

**become**equal to each other , as required by the ratio m : n = m : m = 1 . 129. When the solution of a problem gives , for the values of one of its unknown quantities , any fractions , the denominators of which are**zero**, while the ... Page 78

...

...

**126 become zero**? and what is the corresponding absurdity of the enunciation ? Ans . When a 0 , and the absurdity is , that the squares of two equal num- bers should differ . 131. Corollary . When the solution of a problem gives for 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