Say, if 9990l. 121. pay 20s, in the pound, what will 27961. 104. 20 55939 20 199812)1115600(5 999060 12 199812)1434480(7 1398684 35796 143184 In performing this example, the first and third numbers are reduced into fhillings, and multiplying the fecond and third numbers together, and dividing by the first, the quotient is 5, which is of the fame denomination with the second number, viz. fhillings; and there is a remainder of 119540 fail lings, which is reduced into pence, and then divided by the first number as before, and it quotes 7 pence, and there yet remains 35796 pence, which, reduced into farthings, does not contain the divifor once; thefe pence, therefore, remain over and above the 5s. and 7d. in the pound which the bankrupt pays. The foregoing examples will be found fufficient to inftruct the learner in the nature and method of working this rule; I fhall therefore give a few examples for practice, leaving the operation to be performed by the learner. Example 5. If 56%. of indigo coft 11. 45. what will 1c08b. coft at that rate? Say, if 561b. coft 224. what will 1008/%. cost ?— Answer 40323. or 2014 125. Example 6. If a debtor owes his creditors 5937. 125. and compounds at 7s. 6d. in the pound, what will pay his creditors at that rate? Say, Say, if 20s. can be paid by god. what will pay 11872s.? -Anfwer 2221. 125. Example 7. If 100l. gain 67. intereft in 12 months, how much will 340/. gain in the fame time at that rate of intereft? If 100l. gain 61. what will 340l. gain? Anfwer 201. 85. Example 8. A draper bought 6 packs of cloth, each pack containing 12 pieces, for which he paid 10Sol. being 85. 4d. per ell Flemish how many yards were there in each piece? : If 100d. purchases 3 grs. what will 259200d. purchase?— Anfwer 7776 grs. which divided by 72, the number of pieces in the whole, it quotes 108 grs. or 27 yards in each piece. The general ufe of this rule is, from having the rate, value, proportion, produce, intereft, gain or lofs of one or any other number of things, to find the rate, value, proportion, produce, interest, gain or loss of one or any other number of the fame things in a direct proportion. SECT. VIII. OF THE SINGLE RULE OF THREE INVERSE. THE rule of three inverfe is that which teaches how fron three given numbers to find a fourth, which thall bear the fame rate or proportion to the second number as the first does to the third; or the third number bears the fame proportion to the second as the first does to the fourth. Rule. Multiply the first and second numbers together, and divide the product by the third. The method of placing the numbers in this rule is the fame as that of the rule of three direct, and therefore need not be repeated. In order to discover whether a queftion belong to the direct or inverse rule, it must be remembered that the first and Z 2 third third numbers are called the extremes; if, therefore, the fourth number be greater than the fecond, the less extreme must be the divifor; but if it be less, the greater extreme must be the divifor. And when the firft number is the divifor, the work belongs to the rule of three direct; but when the third number is the divifor, it belongs to the rule of three inverfe; as in the following examples. Example 1. If 8 men perform any certain piece of work in 6 days, how many men will perform the fame work in 3 days? If 6 days require 8 men, what will 3 days require? 6 In this example I confider, that if to do the work in 6 days it requires the labour of 8 men, then, to do the fame work in 3 days, it will require more men, confequently the fourth number will be greater than the fecond, therefore I divide the product of the first and fecond numbers multiplied together by the third number (the leaft extreme), and the quotient is 16 (men) for the answer. The proof of questions in this rule, as well as the foregoing rule, is performed by back stating the question; but it must be observed, in all questions in the direct rule, the proof is wrought by the rule of three direct; and in queftions of the inverse rule the proof is wrought by the rule of three inverfe. Thus, to prove the foregoing example, I fay, if 16 men require 3 days to perform the work, how many days will S - men require to perform it? If 16 men require 3 days, what will 8 men require? Example 2. If a loaf at a certain price weighs 4lb. when wheat is 65. per bufhel, what should it weigh when wheat is 45. 6d. per bufhel? If 72d. per bushel give 9 half lbs. what will 54d. give? 9 54)648(12 In this example, I multiply 72 pence, the price of the bufhel of wheat, by 9, the number of the half pounds in the loaf, and dividing by 54 pence, the price of the bufhel of wheat at the other price, the answer is 12 half pounds or 6 pounds for the weight of the loaf at that price of the ,wheat. In London the price of the loaf is varied, and the weight continues the fame. Questions which concern the price are wrought by making the price the fecond number. Example 3. If a board be 8 inches broad, how much in length will make a fquare foot? If 12 in. in breadth require 12 in. in length, what will 8 in. in breadth require? 12 Example 4. How many yards of fhalloon at 3qrs. wide are fufficient to line throughout the garments made with 1000 yards of cloth at 7qrs. wide? If 7qrs. wide require 1000yds. what will 39rs wide require? Qu. 5. If 150l. be lent for nine months, how long should gol. be lent to gain the fame intereft at the fame rate?Anfwer 15 months. Qu. 6. If a colonel be befieged in a town with 1000 men, having provifions for only 2 months, how many muft he difmifs, that the provifion may ferve the remainder 5 months? -Anfer 600, and retain 400. Qu. 7. If a perfon perform a journey (travelling at an uniform rate) in 24 days, by travelling 12 hours per day, how how long will it take to perform the fame journey by travelling 16 hours per day at the fame rate ?—Anf. 18 days. Qu. 8. If a carrier carry 12 cwt. 72 miles for 51. how miles will he carry 18 cwt. for the same money?— many Anfwer 48 miles. - This rule ferves to find a fourth number to the given three, in an inverted proportion. And it particularly answers feven forts of questions: viz. 1. Having the value of two different forts of coin, it fhews how many pieces of the one are equal in value to a given number of the other. 2. From two different values of one commodity, and the value of an article made from the fame commodity at one value thereof, to find the weight, measure, &c. of the fame article; or, on the contrary, from the values of the commodity and the weight, measure, &c. of the article, to find the value thereof (the 2d example is of this nature). 3. From the breadths of two equal rectangular figures, and the length of one of them, to find the length of the other; or, from the two lengths and one breadth, to find the other breadth (of this nature are the third and fourth examples). 4. From the given weight, expenfe of carriage, and number of miles carriage of any goods, to find the number of miles any other weight could be carried for the fame price: from a given weight and price, and two diftances, to find the weight anfwerable to the other diftance (of this nature is the eighth question). 5. From two fums of money lent, and the time for which one of them is lent, to find the time for which the other fhould be lent; or, from the two different times, and the fum which is lent for one of them, to find the fum which fhould be lent for the other time (of this nature is the fifth example). 6. From the quantity of work which a given. number of men can perform in a given time, to find the number of men that can perform it in any other given time; or, from the number of men, to find the time any other given number would require (of this nature is the firft example). 7. From the quantity of provifions, or money, and the |