32. Bought 30 pieces of broad cloth for 130l. and fold them again for 150l. Now, if they had coft 150l. how muit they have been fold to have yielded gain at the fame

33. A fhip failed 48 leagues in 24 hours, how many leagues will the fail in a week at the fame rate? Anf. 336 leagues.

34. A Merchant hath owing him 9681. and his debtor agrees to pay him 13s. for every pound; the question is what must he pay him for the whole debt, and what must the Merchant lofe by compofition or abatement ?

Anf. The debtor muft pay 6291. 4s. The Merchant muft lofe 3381. 16s.

35. As I was beating on the foreft grounds,

Up ftarts a hare before my two greyhounds:
The dogs being light of foot, did fairly run
Unto her fifteen rods just twenty-one :
The distance that she started up before
Was four fcore, fixteen rods just, and no more
Now this I'd have you unto me declare,

How far they ran before they caught the hare.

Anf. 336 rods. For 21-15-6 rods the dogs gain at the hare in running 21 rods; but the queftion is how far muft they run to gain 96 rods at her, i. e. to overtake her, which is thus folved. As 6: 21:: 96: 336.

I

XIII. The Rule of Three Inverse.

NVERSE, or reciprocal, proportion is, when of four numbers the 3d bears the fame ratio or proportion to the first as the 2d. does to the 4th.

Therefore the lefs the 3d. term is, in refpect to the first, the greater will the 4th term be, in respect to the fecond.

The

The preparation and difpofition of the terms differ nothing here from the Rule of Three Direct, only the operation is inverse. The only difficulty is in knowing when a queftion belongs to one rule, and when to the other; in order to which obferve the following directions.

Having ftated the question, obferve whether the 3d term, being more than the ift, requires more, or being less requires lefs; if fo, the question belongs to the direct rule: but if the 3d term being more than the Ift, requires lefs, or being lefs, requires more, it then belongs to the Rule of Three Inverfe, and in fuch case, the fourth term must be found by an inverse operation, i. e. by xing the firft and fecond terms together, anding the product by the third term.

EX A MP LE S.

1. If 10 yards of cloth, half yard wide, will make a garment, how many yards 5 quarters wide, will make a lining for the faid garment?

Here it is manifeft, that by how much more this lining has of breadth, so much less muft it have in length: there fore the third term being more than the firft, and requiring the fourth to be lefs, this is more requires lefs.

qr.

qr. yds.
If 2: 10:5

10x2÷54 yds. the Anf.

2: If 4 yards of cloth 5 quarters wide, will make a garment; how many yards, half yard wide, will line the fame garment t?

Here it is obvious, that by how much lefs the lining has of breadth, fo much more it must have of length: therefore this is lefs requires more.

If

qr. yds. qr.

4ds :: 2:

5x4÷2-10yds. the Anf.

This rule may be proved by inverting this question as above, or thus, the product of the first and second terms, will always be equal to the product of the third and fourth, when the work is right. Thus in queft. 1ft 10×2=5X4.

CON

CONTRACTIONS.

1. Divide the fecond term by the third, xing the quote into the first, and the product is the answer.

3. If 24 men in 37 days do a piece of work, in how long time will 9 men do the like?

If 24: 279: 72 the Anf. Thus 27÷9=3, and 24×372 the Anf. as before.

II. Divide the firft term by the third, ing the fecond by the quote and the product is the Antwer.

4. If a friend lend me 2800l for 8 months, how long fhould I lend him 700l. to requite him.?

1. m. 1. m.

If 2800 8700: 32 the Anf.

Thus 2800 700-4 and 8x432 months the Anf.

III. When the third term and either of the other two can be exactlyed by fome common for; then them and take the quotes instead of these terms; proceeding thus as oft as you can.

5. If 378 oxen will eat up the grafs of a field in 36 days, how long will 18 oxen be eating up the fame ?

Anf. 756 days; by xing aft and ad terms together,

. If the penny white loaf ought to weigh ounces troy, when wheat is at 4s. 6d. a bufhel; what ought it to weigh when wheat is at 65. gd. a bufhel. Anf. 6 jubce

7. Suppoft

7. Suppofe 3 cocks, or 4 hens, will eat up a certain quantity of corn in 56 days, how long will i cock and 1 hen be in eating up the fame ?

Because of 3 cocks, or 4 hens, fome number must be found that is divifible by 3 and by 4 without remainder, fuch is the number 12; (for 3 x412) make then 3 cocks or 4 hens equivalent to 12 chickens, and you will have cock equivalent to 4 chickens, 1 hen to 3 chickens, and I cock and hen to 7 chickens; in which cafe the question will ftand thus: If 12 chickens will eat up a certain quantity of corn in 56 days, how long will 7 chickens be in eating up the lame? Anf. 96 days.

8. There are 2400 foldiers in a garrifon in a befieged town, who have only provifions for 9 months; how many must be disbanded that the provifions may serve 16 months? Anf. 1050.

9. At what price per bufhel is wheat, when the penny white loaf weighs 5 ounces, 8 dwts. if it weighs 9 ounces when wheat is at 4s. 6d. a bufhel ? Anf. 75. 6d.

10. If 11. 25. worth of wine will fuffice a club of 12 men when the wine is fold after the rate of 251. 4s a hhd; how many men will 11. 2s. worth ferve, when the wine is fold after the rate of 181. 18s. a hlid? Anf. 16 men.

Here follows a collection of queftions put down promifcuoufly in both rules; wherein the learner is left to himfelf to distinguish the particular rale, whether Direct or Inverfe, which each queftion belongs to.

1. If the expence in houfe-keeping, during 6 weeks amount to 91. 3s. 6d. how long will 100l, lalt at that rate Anf. 65 weeks, 2 days, 18

138

367

hours,

2. If 736 dollars, at 4s. 6d. each, were given in exchange for 144 Jacobufes, what was the value of 1 Jacobus? Anf. 235.

3. If 5 oxen, or 7 colts, will eat up a clofe in 87 days, in what time will 2 oxen and 3 colts eat up the fame ? (vide Saunderson's Algebra)

Because of the 5 oxen, or 7 colts, fome number must be found that can be÷ed by 5 and by 7 without remainder, fuch is the number 35=7×5; make then 5 oxen or 7 colts equivalent to 35 heifers, and you'll have 1 ox equivalent to 7 heifers, colt to 5 heifers, 2 oxen = 14 heifers, 3 colts 15 heifers, and 2 oxen + 3 colts

14+15=29 heifers, and the queftion will ftand thus: If 35 heifers will eat up a clole in 87 days, in what time will 29 heifers eat up the fame? Anf. in 105 days.

4 If4lb of tea coft 11. 135. 4d. what will 4 parcels cost, each weighing 2 c. 3 qr. 21 lb? Anf. 5481. 6s. 8d.

5. If a field will graze 18 horfes for feven weeks, how long will it graze 42 horfes? Anf. 3 weeks.

6. If 2 c. 3 qr 21 lb. of fugar coft 61. 1s. 8d. what will 12 c. 2 qr. coft at the fame rate? Anf. 251. 175. 8d. 323-9.

47

7. If 60 gallons of water in one hour's time fall into a ciftern, containing 200 gallons, and by a pipe in the fame ciftern there runs out 45 gallons in one hour; in how many hours will the cistern be filled, if both the cocks keep running? Anf. 13 hours 20 min.

8. If a piece of ordnance fhoot 144lb. of powder at a time; how many pounds will discharge it 68 times? and what will the powder come to, at 11 d. per lb? Anf. 1003lb. of powder. Value 471. 34d.

9. If a fquare pipe 4 inches wide, will discharge a cer tain quantity of water in one hours time; in what time will another fquare pipe, 2 inches wide, discharge the faine quantity from the fame current ?

The discharge of water through pipes, all other things being the fame, is as the area of their orifices. The ori

G.

fice