An Elementary Treatise on Algebra: To which are Added Exponential Equations and Logarithms |
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Page 19
... dividend and di- visor are arranged according to the powers of the letter x ; the divisor is placed at the right of the dividend with the quotient below it . As each term of the quotient is obtained , its product by the divisor is ...
... dividend and di- visor are arranged according to the powers of the letter x ; the divisor is placed at the right of the dividend with the quotient below it . As each term of the quotient is obtained , its product by the divisor is ...
Page 23
... dividend , or in both , which contain the same highest power of the letter accord- ing to which the terms are arranged . In this case , these terms are to be united in one by taking out their common factor ; and the com- pound terms ...
... dividend , or in both , which contain the same highest power of the letter accord- ing to which the terms are arranged . In this case , these terms are to be united in one by taking out their common factor ; and the com- pound terms ...
Page 24
... dividend , the coefficient a2 - 2 a b + b2 of x2 in the first remainder , and the coefficient a2 + 2 ab 62 of x in the second re- - mainder , by the coefficient a - - b of x in the divisor . Ans . ( a + b ) x2 + ( a — b ) x — ( a — b ) ...
... dividend , the coefficient a2 - 2 a b + b2 of x2 in the first remainder , and the coefficient a2 + 2 ab 62 of x in the second re- - mainder , by the coefficient a - - b of x in the divisor . Ans . ( a + b ) x2 + ( a — b ) x — ( a — b ) ...
Page 26
... dividend over the divisor with a line between them , it is called a fraction ; its dividend is called the numerator of the fraction , and its divisor the de- nominator of the fraction ; and the numerator and denominator of a fraction ...
... dividend over the divisor with a line between them , it is called a fraction ; its dividend is called the numerator of the fraction , and its divisor the de- nominator of the fraction ; and the numerator and denominator of a fraction ...
Page 29
... dividend , that is , of the preceding remainder and its divisor ; hence , it is the same with that of any divisor and its dividend , or with that of the given quantities . 61. Corollary . When the remainders decrease to unity , the ...
... dividend , that is , of the preceding remainder and its divisor ; hence , it is the same with that of any divisor and its dividend , or with that of the given quantities . 61. Corollary . When the remainders decrease to unity , 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