Elements of algebra1860 |
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Page 6
... half , though not a number , is a numerical quantity . We understand the word quantity , then , to be a term which has its rise and use in the adoption of an unit of measure . Thus , if the unit of measure be one foot , the quantity ...
... half , though not a number , is a numerical quantity . We understand the word quantity , then , to be a term which has its rise and use in the adoption of an unit of measure . Thus , if the unit of measure be one foot , the quantity ...
Page 15
... half that of the father ? 6. A merchant has spirits at 9s . a gallon , and also at 13s . a gallon . In what proportions must he mix them so as to be worth 10s . 6d . a gallon ? What 7. A , B , and C are to share an estate of £ 3500 ; A ...
... half that of the father ? 6. A merchant has spirits at 9s . a gallon , and also at 13s . a gallon . In what proportions must he mix them so as to be worth 10s . 6d . a gallon ? What 7. A , B , and C are to share an estate of £ 3500 ; A ...
Page 16
Philip Kelland. have twice as much as B , and C half as much as A and B to- gether . 15. A post is of its length in the ground , in the water , and 7 feet above the water . What is its length ? 16. At an election there were 1300 voters ...
Philip Kelland. have twice as much as B , and C half as much as A and B to- gether . 15. A post is of its length in the ground , in the water , and 7 feet above the water . What is its length ? 16. At an election there were 1300 voters ...
Page 61
... half of B's money , his will then be four times B's . Re- quired each ? 25. Divide £ 350 between A , B , and C , so that A may have £ 15 more than B , and B £ 22 more than C. 26. What number is that which , when increased by 10 and by 3 ...
... half of B's money , his will then be four times B's . Re- quired each ? 25. Divide £ 350 between A , B , and C , so that A may have £ 15 more than B , and B £ 22 more than C. 26. What number is that which , when increased by 10 and by 3 ...
Page 70
... half the product of the last number , and the next higher number . Assume that the sum of n numbers is n ( n + 1 ) . If this be true , then the sum of n + 1 numbers will be found by adding the n + 1th number to it , and will in ( n + 1 ) ...
... half the product of the last number , and the next higher number . Assume that the sum of n numbers is n ( n + 1 ) . If this be true , then the sum of n + 1 numbers will be found by adding the n + 1th number to it , and will in ( n + 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
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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...