DOUBLE RULE OF THREE, Teaches to refolve such questions as require two or more statings, by simple proportion; and that, whether direct or inverse: It is composed (commonly) of 5 numbers to find a fixth, which if the proportion be direct, must bear such proportion to the 4th and 5th, as the 3d bears to the ist and 2d; but if inverse the 6th number must bear fuch proportion to the 4th and 5th, as the ist bears to the 2d and 3d. Always place the three conditional terms in this order; That number which is the principal cause of gain, loss, or action, poffefses the first place; that which denotes the space of time, or distance of place, the second; and that, which is the gain, loss or action, the third; this being done, place the other two terms, which move the question, under those of the fame name, and if the blank place or term fought, fall under the third place, then the question is in direct proportion; therefore, RULE 1. Multiply the three last terms together, for a dividend, and the two first for a divifor But if the blank fall under the first or second place; then, the proportion is inverse; therefore, RULE 2. Multiply the first, second and last terms together for a dividend, and the other two for a divisor, and the quotient will be the answer. EXAMPLES. 1. If 1001. gain 61. in a year; what will 400l. gain in 9 months? £. P. Mo. £. Int. 100: 12:: 6 Terms in the supposition, or conditional terms. 400:9 Terms which move the question, Here the blank falling under the third place, the question is in direct proportion, and the answer must be found by the first rule; therefore, 400×9×6=21600 For the dividend, and 2. If tool. will gain 61. in a year; in what time will 4001. gain. 181. ? 100: 12::6 Terms in the supposition. 400: :: 18 Terms which move the question. Here the blank falling under the 2d place, the questSon is in reciprocal or inverse proportion, and the answer must be fought by the second Rule: Therefore, 3. If 4001. gain 181. in 9 months; what is the rate per cent. per annum ? Pr. mo. Int. 400: 9 :: 18 100: 12 18 96 12 400 216 9 100 36/00) 216/00(61. Anf. 216 4. What principal, at 6 per cent. per ann. will gain 18l. in 9 months ? Pr. mo. Int. 5. If 8 men spend 321. in 13 weeks; what will 24 men spend in 52 weeks? M. W. 6. If the freight of 9 hhds. of sugar, each weighing 12 Cwt. 20 leagues, cost 161; what must be paid for the freight of 50 tierces ditto, each weighing 21⁄2 Cwt. 100 leagues ? hhds. leag. £.• P £92 11 10 Ans. 7. There 7. There was a certain edifice completed in a year by 20 workmen; but the fame being demolished, it is necessary that just such another should be built in 5 months; I demand the number of men to be employed about it? Men. mo. Ed. 20:12:: I 5 :: 1 48 men, Ans. feet long, 6 feet high in what time will 24 8. If 6 men build a wall 20 and 4 feet thick, in 16 days; men build one 200 feet long, 8 feet high, and 6 feet thick ? 1. If 78 pence Massachusetts be worth I French crown; how many Massachusetts pence are worth 320 French crowns? 2. Fr. Cr. d. Fr C. As I: 78 :: 320 : 24960d. Ans. If 24 yards at Boston make 16 ells at Paris, how many ells at Paris will make 128 yards at Boston ? Par. Boft. Par. Boft. As 24yds.: 16ells. :: 128yds.: 85ells, Anf. 3. If 60lb. at Boston make 56lb. at Amsterdam; how many lb at Boston will be equal to 350 at Amsterdam? Amf. Bost. Amf. Boft. 1b. lb. lb. lb. As 56:60:: 350: 375 Anf. CONJOINED CONJOINED PROPORTION Is when the coins, weights or measures of several countries are compared in the same question; or, in other words, it is joining many proportions together, and by the relation, which several antecedents have to their confequents, the proportion between the first antecedent and the last confequent is discovered, as well as the proportion between the others in their several respects. This Rule may generally be fo abridged by cancelling equal quantities on both sides, and abrieviating commenfurables, that the whole operation may be performed with very little trouble-and it may be proved by as many statings in the Single Rule of Three as the nature of the question may require. CASE I. When it is required to find how many of the first fort of coin, weight, or meafure, mentoned in the question, are equal to a given quantity of the last. RULE. Place the numbers alternately, that is, the antecedents at the left hand, and the consequents at the right, and let the last number stand on the left hand; then multiply the left hand column continually for a dividend, and the right hand for a divisor, and the quotient will be the answer. EXAMPLES. 1. Suppose 100 yards of America 100 yards of England, and 100 yards of England 50 canes of Thoulouse, and 100 canes of Thoulouse=160 ells of Geneva, and 100 ells of Geneva 200 ells of Hamburgh; how many yards of America are equal to 379 ells of Hamburgh? Antecedents. |