Elements of Algebra: For the Use of Schools and Junior Classes in Colleges |
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Page 22
... true answer . As we have defined to signify increased by , and diminished by , there is a necessary connection between these symbols . For instance , if the thing which is increased be " A's present age , " the interpre- tation of +4 ...
... true answer . As we have defined to signify increased by , and diminished by , there is a necessary connection between these symbols . For instance , if the thing which is increased be " A's present age , " the interpre- tation of +4 ...
Page 23
... true this result originated in the absurdity of the statement of the question ; we say absurdity in this case , because no consideration was required to convince us that one of the true conditions was reversed . But similar questions ...
... true this result originated in the absurdity of the statement of the question ; we say absurdity in this case , because no consideration was required to convince us that one of the true conditions was reversed . But similar questions ...
Page 43
... such when it occurs . It will be observed that many of the results admit of generalization . The first , for example , is true of the nth powers of n quantities . EXAMPLES . 1. x2 + y2 2xy . For ( INEQUALITIES . 43 Inequalities.
... such when it occurs . It will be observed that many of the results admit of generalization . The first , for example , is true of the nth powers of n quantities . EXAMPLES . 1. x2 + y2 2xy . For ( INEQUALITIES . 43 Inequalities.
Page 57
... . ... may be considered as equal to , and this arises not from the circum- stance that .111 . . is near to , but from the fact that the two following propositions hold true : 1st , That the INTERMINABLE DIVISION . 57 Definition of Limit.
... . ... may be considered as equal to , and this arises not from the circum- stance that .111 . . is near to , but from the fact that the two following propositions hold true : 1st , That the INTERMINABLE DIVISION . 57 Definition of Limit.
Page 58
... true result , for the true result is greater than 2 , and ours gets more and more near to 2. Thus the first proposition is satisfied the two expressions 3 and 1.99 . . approach nearer and nearer the farther the division is carried ; but ...
... true result , for the true result is greater than 2 , and ours gets more and more near to 2. Thus the first proposition is satisfied the two expressions 3 and 1.99 . . approach nearer and nearer the farther the division is carried ; but ...
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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 175 - 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.
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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...
Page 232 - 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.
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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...