An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 2
... less , or the negative sign , and placed between two quantities denotes that the quantity which follows it is to be subtracted from the one which precedes it . Thus 7-2 is 7 minus or less 2 and denotes the remain . der after subtracting ...
... less , or the negative sign , and placed between two quantities denotes that the quantity which follows it is to be subtracted from the one which precedes it . Thus 7-2 is 7 minus or less 2 and denotes the remain . der after subtracting ...
Page 4
... less than ; and the expression in which either of these signs occurs is called an inequality . Thus , the inequality ab denotes that a is greater than b ; and the inequality ab denotes that a is less than b ; the greater quantity being ...
... less than ; and the expression in which either of these signs occurs is called an inequality . Thus , the inequality ab denotes that a is greater than b ; and the inequality ab denotes that a is less than b ; the greater quantity being ...
Page 28
... less , and the remainder , which is less than either of the given quantities , is , by the preceding article , divisible by the greatest common divisor . In the same way , from this remainder and the divisor a still smaller remainder ...
... less , and the remainder , which is less than either of the given quantities , is , by the preceding article , divisible by the greatest common divisor . In the same way , from this remainder and the divisor a still smaller remainder ...
Page 36
... less than this product . For , by art . 55 , Fractions may be reduced to a common denomi- nator , which is a common multiple of their denomi- nators , by multiplying both their terms by the quo- tients , respectively obtained from the ...
... less than this product . For , by art . 55 , Fractions may be reduced to a common denomi- nator , which is a common multiple of their denomi- nators , by multiplying both their terms by the quo- tients , respectively obtained from the ...
Page 54
... less in a page , and 3 letters less in each line , then each page would contain 145 letters less . How many lines are there in each page ? and how many letters in each line ? Solution . Let x = the number of lines in a page , - y the ...
... less in a page , and 3 letters less in each line , then each page would contain 145 letters less . How many lines are there in each page ? and how many letters in each line ? Solution . Let x = the number of lines in a page , - y the ...
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Common terms and phrases
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 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