## Algebraical Problems Producing Simple and Quadratic Equations, with Their Solutions: Designed as an Introduction to the Higher Branches of Analytics. To which is Added an Appendix, Containing a Collection of Problems on the Nature and Solution of Equations of Higher Dimensions |

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addition Alff answer the conditions arithmetic means arithmetic progression arithmetic series Assume bought bushels casks coefficient common difference common ratio completing the square corresponding positive integral cost cube digits distance equal extracting the root extracting the square find corresponding positive find the least find the values Find two numbers former gain geometric progression geometric series Given 3a greater guineas harmonic mean harmonic progression least common multiple length less moidores number of days number of gallons number of shillings number of terms number of yards paid pence person pieces positive integral values problem proportion quadratic received remaining Required the number respectively second equation sheep sold square root squaring both sides subtraction tegral values third three numbers Transform the equation transposition travelled unknown quantity values of x wheat whence whole number

### Popular passages

Page 26 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.

Page 150 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.

Page 209 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.

Page 2 - Any quantity may be transposed from one side of an equation to the other, if, at the same time, its sign, be changed.

Page 383 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...

Page 252 - The sum of the squares of the extremes of four numbers in arithmetical progression is 200, and the sum of the squares of the means is 136. What are the numbers ? Ans.

Page 218 - Two partners A and B gained £18 by trade. A's money was in trade 12 months, and he received for his principal and gain £26. Also B's money, which was £30, was in trade 16 months.

Page 219 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately 1 Ans.

Page 148 - A person employed 4 workmen, to the first of whom he gave 2 shillings more than to the second ; to the second 3 shillings more than to the third ; and to the third 4 shillings more than to the fourth. Their wages amounted to 32 shillings. What did each receive ? Ans.

Page 376 - A's 160, and B's 110. Prob. 39. At an election for two members of congress, three men offer themselves as candidates ; the number of voters for the two successful ones are in the ratio of 9 to 8 ; and if the first had had 7 more, his majority- over the second would have been to the majority of the second over the third as 12 : 7. Now if the first and third had formed a coalition, and had one more voter, they would each have succeeded by a majority of 7.