Elements of algebra1860 |
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Page 12
... reduced to an equation ; i . e . , the additions , subtractions , multiplications , etc. , which were stated , and said to produce a certain result , have been exhibited , and the result is the equality of certain quantities produced by ...
... reduced to an equation ; i . e . , the additions , subtractions , multiplications , etc. , which were stated , and said to produce a certain result , have been exhibited , and the result is the equality of certain quantities produced by ...
Page 14
... reduced to ordinary rule of three . If the minute - hand gain by 55 spaces in an hour , in how long does it gain by 5 ? and the answer is - in the eleventh part of an hour , or 5 minutes . ADDITIONAL EXAMPLES , ARITHMETICAL AND ...
... reduced to ordinary rule of three . If the minute - hand gain by 55 spaces in an hour , in how long does it gain by 5 ? and the answer is - in the eleventh part of an hour , or 5 minutes . ADDITIONAL EXAMPLES , ARITHMETICAL AND ...
Page 32
... Reduce to their simplest form , by clearing of brackets , the following expressions : - 7. 1- { 2− ( 1 − x + x3 ) } . - - 8. a- [ 2a- { 3a — ( 4a — 5 ) } ] . 9. a [ a + b { a + b + c − ( a + b + c + d - - a + b + c + d + e ) ...
... Reduce to their simplest form , by clearing of brackets , the following expressions : - 7. 1- { 2− ( 1 − x + x3 ) } . - - 8. a- [ 2a- { 3a — ( 4a — 5 ) } ] . 9. a [ a + b { a + b + c − ( a + b + c + d - - a + b + c + d + e ) ...
Page 57
... Reduce to a decimal . The result is .1111 9 ) 1.000 .1111 • • ; but how far soever it may be carried , the division will never terminate , so that cannot really be expressed as a decimal ; yet the quantity .1111 . . . ... may be ...
... Reduce to a decimal . The result is .1111 9 ) 1.000 .1111 • • ; but how far soever it may be carried , the division will never terminate , so that cannot really be expressed as a decimal ; yet the quantity .1111 . . . ... may be ...
Page 66
... . Ex . 11 . Reduce to their simplest forms : - 1. 2 ' x 42 . 2. 2 - 1 × ( 1 ) 2 . -1 3. ( 23 ) −1 × ( 41 ) 3 . 4. ( 2-1 ) x ( ) 1 × 4- 5. ( 2- ) × ( 4-3 ) - ! 6. 3 / 4 × √34 × ( 22 ) 2 . 7. ( ( ( 2 - 1 ) -1 ) -1 ) - ! - ...
... . Ex . 11 . Reduce to their simplest forms : - 1. 2 ' x 42 . 2. 2 - 1 × ( 1 ) 2 . -1 3. ( 23 ) −1 × ( 41 ) 3 . 4. ( 2-1 ) x ( ) 1 × 4- 5. ( 2- ) × ( 4-3 ) - ! 6. 3 / 4 × √34 × ( 22 ) 2 . 7. ( ( ( 2 - 1 ) -1 ) -1 ) - ! - ...
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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
Popular passages
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Page 231 - But wheat rising 2s. per bushel, and work being scarce, the family find the sum saved would not buy as much wheat as their former savings by two bushels ; when it appears that at this rate the sum annually saved would be less by five guineas than by the former. Now the two youngest dying it is found that if the remaining members of the family saved each one shilling less than the oldest child had done before the rise of wheat, their monthly account with the bank would not be affected by the deaths...
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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...