## Elements of algebra |

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added addition algebraic amount appear arithmetical arrangement assumed bushel called changing coefficient common common multiple complete consequently contain cost cube decimal denominator determine difference distance divided division divisor double equal equation example expression Extract factor feet Find the value five former four fraction gain gallons geometric given gives greater greatest common measure half hence increased involve latter least leave less means meets miles minutes Multiply negative obtain operations performed person positive problem Professor progression PROP prove question quotient ratio received reduced remainder represent Required respectively result rules satisfy sell sheep side simple solution solved square root stroke student subtract suppose symbol thing third tion travelled true unknown quantity whole number write yards

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Página 173 - To divide a given straight line into two parts, so that the rectangle contained by the -whole, and one of the parts, may be equal to the square of the other part.

Página 229 - 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...

Página 230 - But in 30 days the scurvy made its appearance, and carried off three men every day, and at the same time a storm arose, which protracted the voyage three weeks. They were however just enabled to arrive in port, without any diminution in each man's daily allowance of water. Required the time of the passage, and the number of men alive when the vessel reached harbour.

Página 217 - ... 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...

Página 211 - ... 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...