An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 5
... number of its dimensions . The degree of a term is , therefore , found by ... terms are of the same degree . Thus , 3 a - 2b + c is homogeneous of the ... terms of the quantity are to be considered together . Thus , ( a + b + c ) ...
... number of its dimensions . The degree of a term is , therefore , found by ... terms are of the same degree . Thus , 3 a - 2b + c is homogeneous of the ... terms of the quantity are to be considered together . Thus , ( a + b + c ) ...
Page 13
... number of negative factors is odd . 33. Corollary . The product of the sum of two numbers by their difference is ... terms from which it is obtained ; and , therefore , by art . 15 , the degree of each term of the product is equal ...
... number of negative factors is odd . 33. Corollary . The product of the sum of two numbers by their difference is ... terms from which it is obtained ; and , therefore , by art . 15 , the degree of each term of the product is equal ...
Page 23
... term by diminishing the exponent of a by unity and increasing that of b by unity ; and the number of terms is equal to the exponent n . 51. Corollary . If b is put equal to a in the preceding quotient , each of its terms becomes equal ...
... term by diminishing the exponent of a by unity and increasing that of b by unity ; and the number of terms is equal to the exponent n . 51. Corollary . If b is put equal to a in the preceding quotient , each of its terms becomes equal ...
Page 47
... number of times in the above sum , provided its consequent is also repeated the same number of times . 95. Corollary ... Terms to that CH . II . § IV . ] 47 PROPORTIONS .
... number of times in the above sum , provided its consequent is also repeated the same number of times . 95. Corollary ... Terms to that CH . II . § IV . ] 47 PROPORTIONS .
Page 48
... Terms to that of two last . Moreover , in finding these sums and differences , each antecedent may be multiplied by any number , provided its consequent is multiplied by the same number . 97. Corollary . These rules may also be applied ...
... Terms to that of two last . Moreover , in finding these sums and differences , each antecedent may be multiplied by any number , provided its consequent is multiplied by the same number . 97. Corollary . These rules may also be applied ...
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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 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 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