An Elementary Treatise on Algebra |
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Page 13
... Corollary . The continued product of several monomials is , as in examples 8 and 9 , positive , when the number of negative factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary ...
... Corollary . The continued product of several monomials is , as in examples 8 and 9 , positive , when the number of negative factors is even ; and it is negative , as in example 10 , when the number of negative factors is odd . 33. Corollary ...
Page 15
... Corollary . If the rule for the exponents is applied to the case in which the exponent of a letter in the dividend is equal to its exponent in the divisor , when , for instance , am is to be divided by am , the exponent of the letter in ...
... Corollary . If the rule for the exponents is applied to the case in which the exponent of a letter in the dividend is equal to its exponent in the divisor , when , for instance , am is to be divided by am , the exponent of the letter in ...
Page 16
... Corollary . When , in example 6 of art . 30 , the ex- ponent n of a in the divisor is greater than its exponent m in the dividend , the exponent m -n in the quotient is nega- tive ; and a negative exponent is thus substituted for the ...
... Corollary . When , in example 6 of art . 30 , the ex- ponent n of a in the divisor is greater than its exponent m in the dividend , the exponent m -n in the quotient is nega- tive ; and a negative exponent is thus substituted for the ...
Page 20
... Corollary . The quotient can be obtained with equal facility by using the terms which contain the lowest powers of a letter instead of those which con- tain the highest powers . In this case , it is more convenient to place the term ...
... Corollary . The quotient can be obtained with equal facility by using the terms which contain the lowest powers of a letter instead of those which con- tain the highest powers . In this case , it is more convenient to place the term ...
Page 22
... Corollary . The division of a " - b " by a - b may be continued for the purpose of showing the form of the quotient , an bn a- b an - an - ban - 1 + an - 2b + an - 362 + & c ..... + abn - 2 + bn - 1 an - 1b - bn an - 1b - an - 2 2 an ...
... Corollary . The division of a " - b " by a - b may be continued for the purpose of showing the form of the quotient , an bn a- b an - an - ban - 1 + an - 2b + an - 362 + & c ..... + abn - 2 + bn - 1 an - 1b - bn an - 1b - an - 2 2 an ...
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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 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 у³
Popular passages
Page 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.
Page 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.
Page 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...
Page 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.
Page 63 - A term may be transposed from one member of an equation to the other by changing its sign.
Page 1 - ALGEBRA. CHAPTER I. FUNDAMENTAL PROCESSES OF ALGEBRA. SECTION I. Definitions and Notation. 1. Algebra, according to the usual definition, is that branch of mathematics in which the quantities considered are represented by the letters of the alphabet, and the operations to be performed upon them are indicated by signs. In this sense it would embrace almost the whole science of mathematics, elementary geometry alone being excepted. It is, consequently, subject in common use to some limitations, which...
Page 113 - The derivative of the sum of two functions is the sum of their derivatives.
Page 127 - Subtract the square of the root from the first period, and to the remainder bring down the second period for a dividend. III. Double the root already found and place it on the left for a divisor.
Page 271 - The characteristic of the logarithm of a decimal fraction is a negative number* and is equal to the number of places by which its first significant figure is removed from the place of units. Thus the logarithm of...
Page 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. 260. Corollary. The two equations...