An Elementary Treatise on Algebra: Theoretical and PracticalCollins and Hannay, 1824 - 516 σελίδες |
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Σελίδα 82
... integral one , and reci- procally . So that , we have - = bx = bxa ̈1 = ba ̈1 , 1 b α 1 a = bx = bxa - d = bad , and a - 2b - 2d - 2 . 1 b ad 1 . X da a3b2 da - 1 • 1 X. a2 ba In like manner any quantity may be transferred from the ...
... integral one , and reci- procally . So that , we have - = bx = bxa ̈1 = ba ̈1 , 1 b α 1 a = bx = bxa - d = bad , and a - 2b - 2d - 2 . 1 b ad 1 . X da a3b2 da - 1 • 1 X. a2 ba In like manner any quantity may be transferred from the ...
Σελίδα 86
... integral quotient , and R the remainder , if A is not exactly divisible by B. The fraction B R being changed into q + cannot be reduced un- B ' less that R B or its reciprocal B R is reducible , be- cause q is an integral quantity which ...
... integral quotient , and R the remainder , if A is not exactly divisible by B. The fraction B R being changed into q + cannot be reduced un- B ' less that R B or its reciprocal B R is reducible , be- cause q is an integral quantity which ...
Σελίδα 104
... integral part by the denomina- tor of the fraction , and to the product annex the numerator with its proper sign : under this sum place the former denominator , and the result is the improper fraction required . 2h Ex . 1. Reduce 3x - + ...
... integral part by the denomina- tor of the fraction , and to the product annex the numerator with its proper sign : under this sum place the former denominator , and the result is the improper fraction required . 2h Ex . 1. Reduce 3x - + ...
Σελίδα 107
... integral part ; and put the remaining terms of the numerator , if any , over the denominator for the fractional part ; then the two joined together with the proper sign between them . will give the mixed quantity required . x3 + 2ax2 + ...
... integral part ; and put the remaining terms of the numerator , if any , over the denominator for the fractional part ; then the two joined together with the proper sign between them . will give the mixed quantity required . x3 + 2ax2 + ...
Σελίδα 108
... integral part , x3 b and is the fractional part ; therefore x + 2a + - b is the mixed quantity required . 8 4 Ex . 2. Reduce x2 + x + y1 + y3 x2 + x2y2 + y1 8 to a whole quan- tity . Dividend . x3 + x1y1 + y3 8 6 x2 + x®y2 + x1y1 ...
... integral part , x3 b and is the fractional part ; therefore x + 2a + - b is the mixed quantity required . 8 4 Ex . 2. Reduce x2 + x + y1 + y3 x2 + x2y2 + y1 8 to a whole quan- tity . Dividend . x3 + x1y1 + y3 8 6 x2 + x®y2 + x1y1 ...
Άλλες εκδόσεις - Προβολή όλων
An Elementary Treatise on Algebra: Theoretical and Practical James Ryan,Robert Adrain Πλήρης προβολή - 1824 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a²+ab+b² according added algebraic quantities arithmetical becomes binomial changing the signs coefficients common denominator completing the square compound quantity consequently cube root demonstrated difference divi divided dividend division equa equal exponent expression extracting the root factors find the values formula fourth fraction required greater greatest common divisor greatest common measure Hence improper fraction least common multiple less letter logarithm lowest terms lues magnitudes manner mixed quantity multiplied number of terms numbers or quantities observed operation positive prefixed Prob problem proper sign proportionals proposed equation quadratic quadratic equations quan quotient radical sign ratio Reduce remainder Required the square required to find result RULE shillings side simple equations square root substituting subtracted surd third tion tity transposition unity unknown quantity values of x whence whole number