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 ARITHMETIC K. 385 Joint operation. The two fimpfe quefHons into which the compound We now proceed to ftate the queftion, Horf. days. horf. queftion is refolved, are ftated, and wrought feparately, by placing the divi* 21 16 : : 14 * as follows. H. B. H. Days fors on the left hand, bulh. 56 and the other ex— If 14 : 56 : : 20 If 16 : tremes on the right; 112 then multiply and divide, as diredted in 14)1120(808. Rule HI. and the 1008 H2 anfwer comes out of 168 the fame name with days. ~) the middle term, 112 |o)2688|o(24 An. viz. 24 days. 224 Anf, 120 bulhels, as before. II. The Rule of Five Inverfe. The queftions that fall under this rule have commonly (o) one of the proportions inverfe, and the other direft, and The two fimple queftions into which the compound fometimes the upper, and fometimes the lower, is the queftion is refolved, are ftated and wrought feparately, inverfe proportion; and in fome few queftions both pro- as follows. portions are inverfe. Now, though the three rules de- +Horf. day. horj. Bujh. d. h. tv. lujh. livered above make^no difference betwixt direft and in- #20 : 16 ; : 14* 56 : u—4—48 :120 verfe ; yet, to bring the learner to fome meafure of ac14 24 quaintance with this ufeful diftindtion, we fh^JI, in ftating the following queftions, expofe the fame to view, by af64 fixing an afteriflt to the extremes of every inverfe pro16 portion. ^ueji. If 14 horfes eat 56 bufhels of corn in 16 2)0)2214 (11 days. 268 days, in how many days will 20 horfes eat 120 bulhels 60 24 hours. at that rate ? 9j6(4 In this queftion the fuppofition is, that 14 horfes eat 16128 56 bulhels in 16 daysj and the demand is. In how many 16 120 days 20 horfes will eat 120 bulhels. 60 — 6|o) The number fought is days, and the term in the fup56(1935360(345610 pofition of the fame kind is 16 days; and accordingly 96[o(48 min. 168.... place 16 days in the middle. The remaining four terms are extremes; which clafs into fimilar pairs, by ma255 24)576(24 48 days. king each pair confilt of one term taken from the fuppo224 — lition, and another of the fame kind taken from the de96 mand. Thus, 14 horfes and 20 horfes make one pair; 313 96 again, 56 bulhels and 120 bulhels make another pair. 280 —• Out of the fimilar pairs, joined with the middle term, form fo many fimple queftions; namely, 336 (o) 1. If 14 horfes eat a certain number of bulhels in 16 -33<> days, in how many days will 20 horfes eat the fame quantity ? (°) 2. If 56 bulhels are eat up in 16 days, in how many days will 120 bulhels be eat up by the fame eaters ? III. The Rule of Seven, Nine, &c. In the firft fimple queftibn it is plain, that the anfwer mu ft be lefs than the middle term; for 20 horfes will Quest. If 15 men eat i56d. worth of bread in 6 ,eat the fame number of bulhels in fewer days than 14 days, when wheat is fold at 12 s. per bulhel, in how horfes; and fo the greateft extreme, viz. 20, is the di- many days will 30 men eat 520 d. worth of bread when vifor; and becaufe 20 is an extreme found in the de- wheai is at 10 s. per bulhel ? mand, the proportion is inyerfe. This queftion belongs to the rule of feven, the numIn the fecond fimple queftion it is alfo obvious, that ber fought is days, and the term of the fame kind in the anfwer muft be greater than the middle term ; for 120 the fuppofition is 6 days, which place in the middle. bulhels will require more days to be eat up in than 56 T he remaining fix terms are extremes, which dais into bulhels ; and therefore the leaft extreme, viz 56, is the fimilar pairs, by taking one term of each pair out of divifor; and becaufe 56 is an extreme found in the fup- the fuppofition, and another of the fame kind out of the pofition, the proportion is direft. Von. I. No. 17. 3 demand. 5E Out