An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 73
... wine at 9 shillings , with 12 gallons of that at 5 shillings . 38. A wine merchant has two kinds of wine ; the one costs a shillings per gallon , the other b shillings . How must he mix both these wines together , in order to have n ...
... wine at 9 shillings , with 12 gallons of that at 5 shillings . 38. A wine merchant has two kinds of wine ; the one costs a shillings per gallon , the other b shillings . How must he mix both these wines together , in order to have n ...
Page 76
... wines is just that of the required mixture , and , of course , needs none of the other wine added to it to make it of the required value ; and zero , must , there- fore , be regarded as a true solution . 4. In what cases would the value ...
... wines is just that of the required mixture , and , of course , needs none of the other wine added to it to make it of the required value ; and zero , must , there- fore , be regarded as a true solution . 4. In what cases would the value ...
Page 78
... wines are of the same value , they should give a mixture of a value differ- ent from their common value . 3. In what case would the denominators of the fractional values of the unknown quantities in example 41 of art . 126 become zero ...
... wines are of the same value , they should give a mixture of a value differ- ent from their common value . 3. In what case would the denominators of the fractional values of the unknown quantities in example 41 of art . 126 become zero ...
Page 79
... wines and the mix- ture are all of the same value ; in whatever proportion , therefore , the wines are mixed together , the mixture Cases in which the value of an unknown quantity is CH . III . § III . ] EQUATIONS OF THE FIRST DEGREE . 79.
... wines and the mix- ture are all of the same value ; in whatever proportion , therefore , the wines are mixed together , the mixture Cases in which the value of an unknown quantity is CH . III . § III . ] EQUATIONS OF THE FIRST DEGREE . 79.
Page 83
... wine is less than that of the required mixture . Secondly . When b > c ; that is , when the price of the least expensive wine is more than that of the mixture . In either case the problem is altogether impossible , for two wines cannot ...
... wine is less than that of the required mixture . Secondly . When b > c ; that is , when the price of the least expensive wine is more than that of the mixture . In either case the problem is altogether impossible , for two wines cannot ...
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Common terms and phrases
126 become zero 3d root arithmetical progression 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 given number 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