Elements of algebra1860 |
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Page 47
... denominator , the product is the numerator , it follows that a quotient and a fraction are the same thing ; so that a ÷ b is equivalent to the fraction The remembrance of the rules of arithmetical fractions will consequently assist the ...
... denominator , the product is the numerator , it follows that a quotient and a fraction are the same thing ; so that a ÷ b is equivalent to the fraction The remembrance of the rules of arithmetical fractions will consequently assist the ...
Page 69
... denominator is 2 raised to the power of the number of terms , and the numerator is less by 1 than the denominator . our inference . This is Our second step consists in assuming that this is the true law , viz . , that for any number ...
... denominator is 2 raised to the power of the number of terms , and the numerator is less by 1 than the denominator . our inference . This is Our second step consists in assuming that this is the true law , viz . , that for any number ...
Page 85
... a . Hence we have the following DEFINITION : -A fraction is such , that when multiplied by the denominator , the product is the numerator . REDUCTION . The fundamental proposition of reduction of fractions is ON FRACTIONS . 85 Fractions.
... a . Hence we have the following DEFINITION : -A fraction is such , that when multiplied by the denominator , the product is the numerator . REDUCTION . The fundamental proposition of reduction of fractions is ON FRACTIONS . 85 Fractions.
Page 86
... denominator of a fraction be multiplied by the same quantity , the fraction is unaltered in value . α Let be the fraction , where a and b are integers , then b pa a b pb a For x b = a ( Def . ) But b or pa pb a > b = a ( Multiplication ) ...
... denominator of a fraction be multiplied by the same quantity , the fraction is unaltered in value . α Let be the fraction , where a and b are integers , then b pa a b pb a For x b = a ( Def . ) But b or pa pb a > b = a ( Multiplication ) ...
Page 87
... denominator by the same quantity . a be the original fraction , is an equivalent reduced For , if pa pb b one . ca2 Ex . 1 . --- cb2 a2 - b2 a - b 3 . = = c ( a + b ) 2 ̄ ̄ ( a + b ) 2 ̄ a + b a3 3 b3 a2 + ab + b2 = a - b . a 2 . 4 ...
... denominator by the same quantity . a be the original fraction , is an equivalent reduced For , if pa pb b one . ca2 Ex . 1 . --- cb2 a2 - b2 a - b 3 . = = c ( a + b ) 2 ̄ ̄ ( a + b ) 2 ̄ a + b a3 3 b3 a2 + ab + b2 = a - b . a 2 . 4 ...
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A's money a+b+c a²b² a²x a²x² algebraic arithmetic series arithmetical progression ax² bushel coefficient common difference contain cube root decimal denominator distance divided division divisor equal example expression factor Find the least Find the sum Find the value fraction gallons geometric geometric series geometrical progression greatest common measure hence increased infinity least common multiple least number less miles an hour Multiply Newmarket number of terms numerical quantity obtain operations person problem PROP quadratic QUADRATIC EQUATIONS question quotient remainder represent Required the number result second equation sheep shew side solution solved square root subtract suppose surd symbol third three times B's tion travelled unknown quantity whole number x³y xy³ yards دو وو
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Page 219 - ... pounds per chain, as there were chains in the street leading to A. The sewer however being insufficient to carry off the water, an additional drain was made from a point in this street, distant 4 chains from the bridge A, which entered the river at the same point with the sewer, and was equally inclined to the river and sewer. Now it was found that a drain down the middle of each street, at the rate of £9 per chain would have cost only £54 more than the expense of the sewer. Required the lengths...
Page 213 - ... way that he bought it, he privately clips off one twenty-fifth part, He may now legally sell it as a light guinea, and he finds that in consequence of the rise of pure gold in the ratio of 239 : 249 he just gains the clippings by his purchase. It is required to find the ratio of pure gold and alloy in the guinea, and also the relative value of equal quantities of pure gold and. alloy, it being known that the sum of the squares of the numbers •which express the two ratios, exceeds eleven times...