Elements of algebra1860 |
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Page 1
... operations , it is impos- sible to carry on a continuous train of reasoning by means of which the various data are successively introduced in their pro- per places , and the conclusions to which they respectively lead , combined and ...
... operations , it is impos- sible to carry on a continuous train of reasoning by means of which the various data are successively introduced in their pro- per places , and the conclusions to which they respectively lead , combined and ...
Page 2
... operations are suffered to remain without representation . In the former case , then , the mind has , without assistance , to pursue the track , and to keep in view both the previous operations and the results which are to be obtained ...
... operations are suffered to remain without representation . In the former case , then , the mind has , without assistance , to pursue the track , and to keep in view both the previous operations and the results which are to be obtained ...
Page 3
... operations tacitly performed on things not known , nor susceptible of representation . We may proceed as follows : - A's money is four times B's . Now , whilst B's is increased by £ 15 , let A's be increased in such a manner that it ...
... operations tacitly performed on things not known , nor susceptible of representation . We may proceed as follows : - A's money is four times B's . Now , whilst B's is increased by £ 15 , let A's be increased in such a manner that it ...
Page 4
... operations have been performed on it , and conclusions deduced from them ; and although these operations are simply those of multiplication and addition , yet the mind has nevertheless to fix itself on B's money , as though it were a ...
... operations have been performed on it , and conclusions deduced from them ; and although these operations are simply those of multiplication and addition , yet the mind has nevertheless to fix itself on B's money , as though it were a ...
Page 5
Philip Kelland. thus to relieve the mind from a repetition of operations , and to confine it , at each separate step , to the arguments which that step demands . 5. That , therefore , which constitutes the transition from Arithmetic to ...
Philip Kelland. thus to relieve the mind from a repetition of operations , and to confine it , at each separate step , to the arguments which that step demands . 5. That , therefore , which constitutes the transition from Arithmetic to ...
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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 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...