An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 66
... 0 , an obvious absurdity , unless B is zero . The sign is , therefore , rather to be regarded as the expression of the peculiar species of absurdity which arises from diminishing the denominator of a fraction till it becomes zero . 94 ...
... 0 , an obvious absurdity , unless B is zero . The sign is , therefore , rather to be regarded as the expression of the peculiar species of absurdity which arises from diminishing the denominator of a fraction till it becomes zero . 94 ...
Page 74
... 94 become zero ? and what would this value signify ? Ans . When or when n = 0 , a = 0 ; and , in either case , this value signifies that the couriers are together at the outset ; and zero must , therefore , be regarded as a real ...
... 94 become zero ? and what would this value signify ? Ans . When or when n = 0 , a = 0 ; and , in either case , this value signifies that the couriers are together at the outset ; and zero must , therefore , be regarded as a real ...
Page 75
... Zero . 3. In what cases would the value of one of the unknown quantities in example 38 of art . 94 become zero ? and what would this value signify ? Ans . When , either a = c , or b = c ; and , in either case , these equations indicate ...
... Zero . 3. In what cases would the value of one of the unknown quantities in example 38 of art . 94 become zero ? and what would this value signify ? Ans . When , either a = c , or b = c ; and , in either case , these equations indicate ...
Page 76
... become equal to each other , as required by the ratio m : n = m : m 1 . 96. When the solution of a problem gives , for the values of one of its unknown quantities , any fractions , the denominators of which are zero ... 94 be- come zero ...
... become equal to each other , as required by the ratio m : n = m : m 1 . 96. When the solution of a problem gives , for the values of one of its unknown quantities , any fractions , the denominators of which are zero ... 94 be- come zero ...
Page 77
... 94 become zero ? and what is the corresponding absur- dity of the enunciation ? Ans . When a = 0 , and the absurdity is , that the squares of two equal numbers should differ . 97. Corollary . When the solution of a problem gives for the ...
... 94 become zero ? and what is the corresponding absur- dity of the enunciation ? Ans . When a = 0 , and the absurdity is , that the squares of two equal numbers should differ . 97. Corollary . When the solution of a problem gives for the ...
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Common terms and phrases
3d root 94 become zero approximate values arithmetical progression binomial Binomial Theorem coefficient commensurable roots common denominator continued fraction continued product Corollary courier deficient terms denote distance gone dividend equal roots equal to zero Examples of putting factor Find the 3d Find the continued Find the greatest Find the square Find the sum Free the equation gallons Geometrical Progression given equation given number gives greatest common divisor Hence imaginary roots last term least common multiple less logarithm merator monomials negative roots number of real number of terms obtained polynomial positive roots preceding article Problem proportion putting Questions quantities in example Questions into Equations quotient radical quantities ratio real root reduced remainder required equation required number Scholium Solution Solve the equation square root subtracted suppressed tained Theorem third three equations tity unity unknown quan unknown quantity whence wine
Popular passages
Page 47 - In any proportion the terms are in proportion by Composition and Division ; that is, the sum of the first two terms is to their difference, as the sum of the last two terms is to their difference.
Page 54 - There is a number consisting of two digits, the second of which is greater than the first, and if the number be divided by the sum of its digits, the quotient is 4...
Page 149 - Multiply the divisor, thus increased, by the last figure of the root; subtract the product from the dividend, and to the remainder bring down the next period for a new dividend.
Page 197 - Problem. To find the last term of an arithmetical progression when its first term, common difference, and number of terms are known. Solution. In this case a, r, and n are supposed to be known, and I is to be found.
Page 262 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 62 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 44 - Arrange the terms in the statement so that the causes shall compose one couplet, and the effects the other, putting ( ) in the place of the required term. II. If the required term be an extreme, divide the product of the means by the given extreme ; if the required farm be a mean, divide the product of the extremes by the given mean.
Page 46 - Likewise, the sum of the antecedents is to their difference, as the sum of the consequents is to their difference.
Page 99 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f?
Page 206 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.