A.B. fir. gal. qt. 39 I 2 I 24 3 6 II. ALE and BEER MEASURE. 2. 3. B.B.fir. gal. qts. pts. Hhds. gal. qts. 769 17 I 2 Refulting from a Comparifon of the preceding Rules. PROB. 1. Having the fum of two numbers, and one of them given, to find the other. Rule. Subtract the given number from the given fum, and the remainder will be the number required. Let Let 288 be the fum | From 288 the Sum, of two numbers; one of which is 115, the. other is required? Take 115 the given number. Rem. 173 the other. PROB. 2. Having the greater of two numbers, and the difference between that and the lefs given, to find the lefs. Rule. Subtract the one from the other. Take 198 the difference. Let the greater number | From 325 the greater, be 325, and the difference between that and the other, 198: What is the oth er? Rem. 127 the lefs. PROB. 3. Having the leaft of two numbers given, and the difference between that and a greater, to find the greater. Rule. Add them together.. Given S127 the lefs number. Sum 325 the greater number required. PROB. 4 Having the fum and difference of two numbers given, to find thofe numbers. Rule. To half the fum add half the difference, and the fum is the greater, and from half the fum take half the difference, and the remainder is the lefs.-Or, from the fum take the difference, and, half the remainder is the leaft: To the least add the given difference, and the fum is the greatest. What are those two numbers, whose fum is 48, and difference 14? 2)48 Sum = 24 2.) 14 24+7 31 the greater, and 24-7 17 the lefs. Or 48—14÷2 — 17, and 17+14 = 31. PROB. PROB. 5. Having the fum of two numbers and the difference of their fquares given, to find those numbers. Rule. Divide the difference of their fquares by the fum of the numbers, and the quotient will be their difference: You will then have their fum and difference to find the numbers by Prob. 4. What two numbers are those, whose fum is 32, and the difference of whofe fquares is 256? PROB. 6. Having the difference of two numbers and the difference of their fquares given, to find those numbers. Rule. Divide the difference of their fquares by the difference of the numbers, and the quotient will be their fum, then proceed by Prob. 4. What are thofe two numbers, whofe difference is 20, and the difference of whofe fquares is 2000 ? 20) 2000(100 Sum. 50+10= 60, the greater, and 50-10 40, the lefs. PROB. 7. Having the product of two numbers, and one of them given, to find the other. Rule. Divide the product by the given number, and the quotient will be the number required. 1 Let Let the product of two numbers be 288 and one of them 8; I demand the other? 8)288 Anf. 36 PROB. 8. Having the dividend and quotient, to find the divifor. Rule. Divide the dividend by the quotient. COR. Hence we get another method of proving Di PROB. 9. Having the Divifor and Quotient given, to By a due confideration and application of these Problems only, many queftions may be refolved in a fhort and elegant manner, although fome of them are generally fuppofed to belong to higher rules. APPLICATION of the preceding Rules. 1. The leaft of two numbers is 19418, and the difference between them is 238; What is the greater, and sum of both ? 19418+2384 = 21802 greater, and 19418+21802 41220 fum. 2. Suppose a man born in the year 1743; When will he be 57 years of age? 1743+57 1800 Anf. What |