Then 9 X 9.962625= 89.663625, its weight in air. A folid inch of filver is 5.556769 ounces troy. 14.5 75.163625 ounces of gold. 9.962625) 75.163625 (7.5546, space taken up by the gold. 2.6094, by the filver, as above. Sum 10.164, by both. Then 10.1649 1.164. 9= '.* 9) 1.164 (.1293. Q. E. F. 15. Hiero, king of Sicily, ordered his jeweller to make him a crown, containing 63 ounces of gold; the workman thought fubftituting part filver therein a proper perquifite ; which taking air, Archimedes was appointed to examine it, who, on putting it into a veffel of water, found it raised the fluid, or that itself contained 8.2245 cubic inches of metal; and having discovered that the cubic inch of gold more critically weighed 10.36 ounces, and that of filver but 5.85 ounces; he, by calculation, found what part of his majefty's gold had been changed; and you are defired to repeat the process ? 10.36)63.00 (6.08108 inches in folidity, had it been gold. 5.85)63.00 (10.76923 folid inches, if all filver. Then, by alligation, 8.2245{ 6.08108 10.76923 2.54473 22.14342 4.68815 4.68815) 2.54473 (.5428, part gold. 4.68815) 2.14342 (.4572, part filver. •.•.5428 X 63 = 34.1884 34 oz. 3 dwt. 224 gr. of gold. And.4572 X63 28.8036 28 16 = 13 of filver. Q. E. F. Since gold and filver are always weighed, bought and fold, by troy weight, which weights are feldom in the poffeffion of gentlemen in the country, graziers, or farmers; therefore to prevent their being impofed on by Jews, and other itinerant traders, I fhall give an example concerning the reduction of troy into averdupoife weight. In the year 1696 an experiment was made by authority (by a balance which would turn with fix grains put into either scale) when it was found, that 15 pounds averdupoise weight, were equal to 181b. 2 ozs. 15 dwts. troy = 105000 grains. = ... 15) 105000 (7000 grains troy 16 oz. averdupoife. 1 oz. averdupoife. I oz. averdupoise. Firft, fuppofe a filver tankard weighs 2 lb. 11 oz. 8 dr. averdupoife, its weight in ounces troy is required? CHAPTER III. POSITION; OR, THE RULE OF FALSE. T HE rule of pofition, or fuppofition, is fo called, because we fuppofe fome uncertain number, in order, that by reasoning from them we may gain the true number; and because thofe fuppofitions are taken at adventure, it is alfo called the rule of falfe. Y fingle pofition are folved fuch questions as require only one fuppofition to difcover the true refult. Bonly RULE. When you have made choice of your pofition, work it according to the nature of the queftion as if it were the true number; and if by the ordering your pofition. you find the refult either too much or too little, you may then find out the number fought by this proportion; viz. as the refult of your pofition is to the position, fo is the given number to the number fought. 1. Three perfons, viz. A, B, C, thus difcourfe together concerning their age; fays B to A, I am as old. and half as old again as you; then fays C to B, but I am twice as old as you; A replied, I am fure the fum of all our ages is 165: now I demand each man's age? 165 2. Three perfons, Andrew, Benjamin and Charles, are to go a journey of 235 miles; of this journey Andrew is to go a certain number of miles unknown; Benjamin is to go four times as many miles as Andrew, and three miles more; and Charles is to go twice as many miles as Benjamin, and five miles more: how many miles muft each of these persons travel severally? 3= (Benjamin. } Alfo 17 X 43 71 miles Benjamin. And 71 x 2 + 5 = 147 235 Charles. 3. There were in company together four perfons, Adam, Edward, Charles and William; Adam told Charles that he was older than him by two years; Edward told them, that he was as old as both of them together, and four years older; William, hearing them, said, I am just 96 years old, and that that is equal to all your ages: how old was each of them feverally? 4. The captain, lieutenant and cornet of a troop have taken among them from fome enemy 478 crowns, which they agree to share in this manner; the captain is to have 24 times as much as the cornet, wanting only seven crowns; and the lieutenant is to have five times as much as the cornet, wanting three crowns; what is each officer's fhare? Suppofe the cornet to have Then 8 x 53 And 8 X 24-7 81 Again, 7+ 3 = 10 37 Alfo 478 +10= 488 185 And 230+ 10 = 240 5. Let 273 1. be divided amongst four perfons, viz. Andrew, Bennet, Chriftopher and Daniel; Andrew is to have a fhare unknown; Bennet is to have twice as much as Andrew, and 30 1. more; Chriftopher is to have three times as much as Andrew, wanting 52 1. and Daniel is to have five times as much as Andrew, and 201. more; how must this 273 1. be divided amongst them, fo that every one may have his true fhare? 220 20: 275: 25, Andrew's Then will 25 x 2 + 30 = 80, Bennet's Likewife 25 X 3 52 = 23, Chriftopher's 25 X 5+20= 145, Daniel's And £273 share. 6. Admit three merchants build a fhip, which coft 13601. A pays a certain part unknown; B paid 2 as much, wanting 15.5 1. and C paid as much as both A and B, and 75.251. over; how much did each man pay? 1. Suppose A paid 100 B 100 X 2.5 15.5 234.5 75.25—31 = 44.25 1360—44.25=1315.75 744.25 — 44.25 = 700 1. s. d. ... 700: 100:: 1315.75: 187.964286 187 19 31, A Then 187.964286x2.5-15.5=454.410713=454 8 21, B And 642-375+ 75.25=717.625 1360. =717 12 6, C 7. As I walk'd forth to take the air, , and, if you please, One tenth, and too; 209 These being made one fum by you, In this proportion, as 15 to 3. paid. And |