An Elementary Treatise on Algebra: To which are Added Exponential Equations and LogarithmsJames Munroe and Company, 1860 - 284 páginas |
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Página 76
... body starts , the first body hav- ing just arrived at the point of departure of the second , and 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 33 ...
... body starts , the first body hav- ing just arrived at the point of departure of the second , and 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 33 ...
Página 79
... body has passed round the circle once , twice , & c . , oftener than the first body ; which is here impos- sible . 3 In what case would all the terms of the fractiona . values of the unknown quantities in example 33 of art , 126 become ...
... body has passed round the circle once , twice , & c . , oftener than the first body ; which is here impos- sible . 3 In what case would all the terms of the fractiona . values of the unknown quantities in example 33 of art , 126 become ...
Página 81
... body moves faster than the second , in which case the second cannot overtake it . The enunciation may be corrected for this case by supposing the bodies to travel in the opposite direction to Cases of negative value of unknown quantity ...
... body moves faster than the second , in which case the second cannot overtake it . The enunciation may be corrected for this case by supposing the bodies to travel in the opposite direction to Cases of negative value of unknown quantity ...
Página 82
... body to pursue the second . Examples 31 and 32 are not , however , impossible in this case for , from the very nature of their circular mo- tion , the first body is necessarily pursuing the second even in their present direction ; the ...
... body to pursue the second . Examples 31 and 32 are not , however , impossible in this case for , from the very nature of their circular mo- tion , the first body is necessarily pursuing the second even in their present direction ; the ...
Página 83
... body would be obliged to change its direction , and move in the same direction with the first , and even with this change of enunciation the problem is impossible , if the second body moves slower than the first . But as it is , the ...
... body would be obliged to change its direction , and move in the same direction with the first , and even with this change of enunciation the problem is impossible , if the second body moves slower than the first . But as it is , the ...
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An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1837 |
An Elementary Treatise on Algebra: To which are Added Exponential Equations ... Benjamin Peirce Visualização integral - 1837 |
Palavras e frases frequentes
126 become zero 3d root approximate values coefficient commensurable roots contain continued fraction continued product Corollary courier decimals deficient terms denote derivative dividend equal roots equal to zero Find the 3d Find the continued Find the greatest Find the square Find the sum Free the equation gallons given equation gives greatest common divisor Hence last term least common multiple letter logarithm monomials Multiply negative exponents nth root number of real number of terms Obtain one equation positive roots preceding article Problem proportion quantities in example Questions into Equations quotient radical quantities ratio real roots reduced remainder required equation required number row of signs Scholium Solution Solve the equation square root Sturm's Theorem substitution subtracted suppressed Theorem three equations unity unknown quan unknown quantity whence wine
Passagens conhecidas
Página 48 - 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.
Página 55 - 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...
Página 130 - The rule of art. 28, applied to this case, in which the factors are all equal, gives for. the coefficient of the required power the same power of the given coefficient, and for the exponent of each letter the given exponent added to itself as many times as there are units in the exponent of the required power. Hence...
Página 127 - 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.
Página 159 - A certain capital is let at 4 per cent. ; if we multiply the number of dollars in the capital, by the number of dollars in the interest for 5 months, we obtain 11?041§.
Página 172 - Ans. 15 and 26. 31. What two numbers are they, whose sum is a, and the sum of whose squares is b 1 Ans.
Página 232 - An equation of any degree whatever cannot have a greater number of positive roots than there are variations in the signs of Us terms, nor a greater number of negative roots than there are permanences of these signs.
Página 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Página 45 - Given three terms of a proportion, to find the fourth. Solution. The following solution is immediately obtained from the test. When the required term is an extreme, divide the product of the means by the given extreme, and the quotient is the required extreme. When the required term is a mean, divide the product of the extremes by the given mean, and the quotient is the required mean.
Página 196 - Hence, to find the sum, multiply the first term by the difference between unity and that power of the ratio whose exponent is equal to the number of terms, and divide the product by the difference between unity and the ratio. Examples in Geometrical Progression.