An Elementary Treatise on Algebra: To which are Added Exponential Ewquations and Logarithms1855 - 288 páginas |
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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 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 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
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 268 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 127 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend. V. Double the whole root already found, for a new divisor, and continue the operation as before, until all the periods are brought down.
Página 192 - One hundred stones being placed on the ground in a straight line, at the distance of 2 yards from each other, how far will a person travel who shall bring them one by one to a basket, placed at 2 yards from the first stone ? Ans.
Página 45 - Thus, in the, proportion a : b = b : c, b is a mean proportional between a and c, and ca third proportional to a and b.
Página 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Página 232 - I. 296. Descartes' Theorem. A complete equation cannot have a greater number of positive roots than there are variations in the row of signs of its terms, nor a greater number of positive roots than there are permanences in this row of signs. Proof. If the equation is that of art. 295, the values of «, U, U', &c.
Página 172 - Ans. When we have that is, the square of the sum of two numbers cannot be greater than twice the sum of their squares.
Página 109 - ... finally, if the dollar were adjudged to the third regiment, each man of the other two regiments would receive $£. What is the number of men in each regiment? Ans. 780 men in the first, 1716 in the second, and 2028 in the third regiment. 10. To find three numbers such that if 6 be added to the first and second, the sums are to one another as 2 : 3 ; if 5 be added to the first and third, the sums are as 7 : 11 ; but if 36 be subtracted from the second and third, the remainders are as 6 : 7. Ans....
Página 3 - ... 7. The root of a quantity is the quantity which, multiplied a certain number of times by itself, produces the given quantity ; and the index of the root is the number of times which the root is contained as a factor in the given quantity. The sign */~ is called the radical sign, and when prefixed to a quantity indicates that its root is to be extracted, the index of the root being placed to the left of the sign and a little above it. The index 2 is generally omitted, and the radical sign, without...