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16. A certain work being raised in 12 days, by working 4. hours each day; how long would it have been in raising by working 6 hours per day?

Ans. 8 days. 17. What quantity of corn can I buy for 90 guineas, at the rate of 68 the bushel ?

Ans. 39 qrs 3 bu. 18. A person, failing in trade, owes in all 9771; at which time he has, in money, goods, and recoverable debts, 420: 68 Strl ; now supposing these things delivered to his creditors, how much will they get per pound ?

Ans. 88 74d. 19. A plain of a certain extent having supplied a body of 3000 horse with forage for 18 days ; then how many days wouid the same plain have supplied a body of 2000 horse ?

Ans. 27 days. 20. Suppose a gentleman's income is 600 guineas a year, and that he spends 25s 6d per day, one day with another ; how much will he have saved at the year's end ?

Ans. 1641 129 6d. 21. Wbat cost 30 pieces of lead, each weighing. I cwt 121b, at the rate of 168 4d the cwt ?

Ans. 271 28 60. 22. The governor of a besieged place having provision for 54 days, at the rate of 1 flb of bread; but being desirous to prolong the siege to 80 days, in expectation of succour, in that case what must the ration of bread be? Ans. IIb.

23. At half a guinea per week, how long can I be boarded for 20 pounds ?

Ans. 387,26 wks. 24. How much will 75 chaldrons 7 bushels of coals come to, at the rate of 12 138 6d per chaldron ?

Ans. 1252 1980fd. 25. If the penny loaf weigh 8 ounces when the bushel of wheat costs 78 3d, what ought the penny loaf to weigh when the wheat is at 88 4d ?

Ans. 6 oz 15.36. dr. 26. How much a year will 173 acres 2 roods 14 poles of land give, at the rate of 1178 8d per acre ?

Ans. 2401 28 730d. 27. To how much amounts 73 pieces of lead, each weighing 1 cwt 3 qrs 7 lb, at 102 48 per fother of 194 cwt ?

Ans. 691 48 2d 141 q. 28. How many yards of stuff, of 3 qrs wide, will line a cloak that is 13 yards in length and 31 yards wide ?

Ans. 8 yds 0 qrs 23 nl. 29. If 5 yards of cloth cost 148 2d, what must be given for 9 pieces, containing each 21 yards 1 quarter?

Ans. 271 Is 103d. 30. If a gentleman's estate be worth 21071 12s a year ; what may he spene per day, to save 5001 in the year ?

Ans, 41 88 136 d.

31. Wanting

31. Wanting just an acre of land. cut off from a piece which is 13% poles in breadth, what length must the piece be?

Ans. Il po 4 yds 2 ft 0,1 in. 32. At 78 9fd per yard, what is the value of a piece of cloth containing 53 ells English I qu. Ans 251 18s 1 d.

33. If the carriage of 5 cwt 14 lb for 96 miles be 17 126 60 ; how far may I have 3 cwt I qr carried for the same money ?

Ans. 151 m 3 fur 3;s pol. 34. Bought a silver tankard, weighing 1 lb 7 oz 14 dwis; what did it cost me at 68 4d the ounce ?

Ans. 61 48 91d. 35. What is the half year's rent of 547 acres of land, at 158 6d the acre ?

Ans. 2117 198 3d. 36. A wall that is to be built to the height of 36 feet, was raised 9 feet high by 16 men in 6 days; then how many men must be employed to finish the wall in 4 days, at the same rate of working ?

Ans. 72 men. 37. What will be the charge of keeping 20 horses for a year, at the rate of 143d per day for each horse ?

Ans, 4411 Os 10d. 38. If 18 ells of stuff that is yard wide, cost 39.8 6d ; what will 50 ells, of the same goodness, cost, being yard wide ?

Ans. 71 68 31.d. 39. How many yards of paper that is 30 inches wide, will hang a room that is 20 yards in circuit and 9 feet high.

Ans. 72 yards. 40 If a gentleman's estate be worth 384! 168 a year, and the land-tax be assessed at 28 94d per pound, what is his net annual income ?

Ans. 3311 18 9d. 41. The circumference of the earth is about 25000 miles; at what rate per hour is a person at the middle of its surface carried round, one whole rotation being made in 23 hours 56 minutes ?

Ans. 10441 miles. 42. If a person drink 20 bottles of wine per month, when it costs 88 a gallon ; how many bottles per month may he drink, without increasing the expence, when wine costs 108, the gallon ?

Ans. 16 bottles. 43. What cost 43 qrs 5 bushels of corn, at 11 88 6d the quarter.

Ans. 621 38 33d. 44. How many yards of canvas that is ell wide will line 50 yards of say that is 3 quarters wide ?

Ans. 30 yds. 45. If an ounce of gold cost 4 guineas, what is the value of a grain ?

Ans. 2, pd. 46. If 3 cwt of tea cost 401 128 ; at how much a pound must it be retailed, to gain 10l by the whole ?

Ans. 3996



COMPOUND PROPORTION shows how to resolve such ques. tions as require two or more statings by Simple Proportion ; and these may be either Direct or Inverse.

In these questions, there is always given an odd number of terms, either five or seven, or nine, &c. These are distinguished into terms of supposition, and terms of demand, there being always one term more of the former than of the latter, which is of the same kind with the answer sought. The method is thus :

Ser down in the middle place that term of supposition which is of the same kind with the answer sought.Take one of the other terms of supposition, and one of the demanding terms which is of the same kind with it; then place one of them for a first term, and the other for a third, according to the directions given in the Rule of Three.- Do the same with another term of supposition, and its corresponding demanding term ; and so on if there be more terms of each kind; setting the numbers under each other which fall all on the left-hand side of the middle term, and the same for the others on the right-hand side. — Then, to work

By several Operations.—Take the two upper terms and the middle term, in the same order as they stand, for the first Rule-of-Three question to be worked, whence will be found a fourth term. Then take this fourth number, so found, for the middle term of a second Rule-of-Three question, and the next two under terms in the general stating in the same order as they stand, finding a fourth term for them.

And so on, as far as there are any numbers in the general stating, making always the fourth number, resulting from each simple stating, to be the second term in the next following one. So shall the last resulting number be the answer to the question.

By one Operation --Multiply together all the terms standing under each other, on the left-hand side of the middle term ; and, in like manner, multiply together all those on the right-hand side of it. Then multiply the middle term by the latter product, and divide the result by the former product ; so shall the quotient be the answer sought.

Vol. I.




1. How many men can complete a trench of 135 yards long in 8 days, when 16 men can dig 54 yards in 6 days?

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The same by two Operations.

As 54:16::155: 40 As 8:40::6:30


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2. If 1001 in one year gain 52 interest, what will be the interest of 7502 for 7 years


Ans. 2621 108. 3 If a family of 8 persons expend 2001 in 9 months ; how much will serve a family of 18 people 12 months ?

lo: Ans. 3001. 4. If 278 be the wages of 4 men for 7 days ; what will be the wages of 14 men for 10 days?

Ans. 61 158. 5. If a footman travel 130 miles in 3 days, when the days are 12 hours long; in' how many days, of 10 hours each, may he travel 360 miles ?

Ans. 9 days.

Ex. 6. If 120 bushels of corn can serve 14 horses 56 days ; how many days will 94 bushels serve 6 horses ?

Ans. 102 days. 7. If 3000 lb. of beef serve 340 men 15 days; how many ibs will serve 120 men for 25 days? Ans. 1764 lb 1111 02.

8. If a barrel of beer be sufficient to last a family of 8 persons 12 days ; how many barrels will be drank by 16 persons in the space of a year ?

Ans. 60% barrels. 9. If 180 men, in 6 days, of 10 hours each, can dig a trench 200 yards long, 3 wide, and 2 deep ; in how many days, of 8 hours long, will 100 men dig a trench of 360 yards long, 4 wide, and 3 deep?

Ans. 15 days.



A FRACTION, or broken number, is an expression of a part, or some parts, of something considered as a whole.

It is denoted by two numbers, placed one below the other, with a line between them :

3 numerator Thus,

which is named 3-fourths. 4 denominator The denominator, or number placed below the line, shows how many equal parts the whole quantity is divided into; and it represents the Divisor in Division. And the Numerazor, or number set above the line, shows bow many of these parts are expressed by the Fraction : being the remainder after division. —Also, both these numbers are, in general, named the Terms of the Fraction.

Fractions are either Proper, Improper, Simple, Compound, er Mixed.

A Proper Fraction, is when the numerator is less than the denominator ; as, ), or f, or }, &c.

An Improper Fraction, is when the numerator is equal 10, or exceeds, the denominator ; as, ģ, or {, or }, &c.

A Simple Fraction, is a single expression, denoting any number of parts of the integer; as, ģ. or i

A Compound Fraction, is the fraction of a fraction, or several fractions connected with the word of between them ; as, f of j, or of of 3, &c.

A Mixed Number, is composed of a whole number and a fraction together; as, 3, or 12, &c.

A whole

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