1. 2. 4. APOTHE CAR LE S' WEIGHT. 3. ID 3 3 3 gr. 1 3 3 9 gr. it 3 3 gr. 71 9 3 1 13 65 10 6 2 1 84. III 37 4 I 16 31 8 4 20 65 9 3 1 17 8 I. 2. 3. Yds. ft. in. Mil.fur. pol. Deg. m. fur. p. yds.ft.in. bar. 28 2 10 76 3 11 38 41 3 29 2 1 7 2 67 2 II 27 3.21 19 35 5 31 3 I 9 I I. 7. TIME. 3. 2 5 19 27 31 4 2 19 19 9 3 4 20 19 49 48 9 1. 2. 8. L AND, or SQUARE ME AS U R E. 3. A. R. Pol. A. R. Pol. A. R. Pol. ft. 29 29 17 56 3 19 27 24 25 17 36 29 210 2 in. 110 129 I O 21 9. SOLID SOLID ME A SU R e. 3. in. in.. 127 1349 I IOO 10. WINE M E A SU R E. 3: Ton.gal. qt: pt. Tier. gal. qt, Tum. bhd. gal. 79 19 17 532 19 38 3 12 29 197 47 I 2 I I I I I 2 I 1. ALE and Beer MEASURE. I. 2. 3. A.B. fir.gal. qt. B.B.fir. gal: qts. pts. Hhds. gal. qts. 39 3 5 769 17 24 3 6 19 7 391 42 3 I 2 I 21 12. DR Y ME A S'U R... 3. Qu. bu. pk. qt. Bu. pk. qts. pts. Chal. bu. pk. qts. 56 91 3 39 93 3 24 25 3 2 PRO B L E M S PROB. I. Having the sum of two numbers, and one of them given, to find the other. Rule. Subtract the given number from the given sum, and the remainder will be the number required. Let Let 288 be the sum From 288 the Sum, of two numbers ; one Take 115 the given number. of which is 115, the other is required ? Rem. 173 the other. Prob. 2. Having the greater of two numbers, and the difference between that and the less given, to find the less. Rule. Subtract the one from the other. Let the greater number From 325 the greater, be 325, and the difference | Take 198 the difference. between that and the other, 198 : What is the oth- Rem. 127 the less. er ? Prob. 3. Having the least of two numbers given, and the difference between that and a greater, to find the greater. Rule. Add them together. Given 127 . Suia 325 the greater number required. PROB. 40 Having the sum and difference of two numbers given, to find those numbers. Rule. To half the fum add half the difference, and the sum is he greater, and from half the sum take half the difference, and the remainder is the less.-Or, from the sum take the difference, and, half the remainder is the least : To the least add the given difference, and the fum is the greatest. What are those two numbers, whose sum is 48, and difference 14 ? 2)48 2.)14 diff. = Sum = 24 7 24+7= 31 the greater, and 24-7 = 17 the less. Or 48--14--2 = 17, and 17+ 14 = 31. PROB PROB. 5. Having the sum of two numbers and the difference of their squares given, to find those numbers. Rule. Divide the difference of their squares by the sum of the numbers, and the quotient will be their differ. ence : You will then have their sum and difference to find the numbers by Prob. 4. What two numbers are those, whose sum is 32, and the difference of whose squares is 256? Half fum 16 4 Greater 20 32 256(8 difference. 256 Lefs I2 Prob. 6. Having the difference of two numbers and the difference of their squares given, to find those num. bers. Rule. Divide the difference of their squares by the difference of the numbers, and the quotient will be their fum, then proceed by Prob. 4. What are those two numbers, whose difference is 20, and the difference of whose squares is 2000 ? 20),2000(100 Sum. 50+10= 60, the greater, and 50-10 = 40, the less. 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. Let Let the product of two numbers be 288 8)288 and one of them 8 ; I demand the other ? Ans . 36 PROB. 8. Having the dividend and quotient, to find the divisor. Rule. Divide the dividend by the quotient. Cor. Hence we get another method of proving Divihon. Given § 288 the Dividend. 36)288(8 Divisor. 1 36 the Quotient. 288 Required the Divifor? PROB. 9. Having the Divisor and Quotient given, to find the Dividend. Rule. Multiply them together. Given 8 Required the Dividend ? 288 the Dividend. 36 By a due confideration and application of these Problems only, many questions may be resolved in a short and elegant manner, although some of them are generally fupposed to belong to higher rules. APPLICATION of the preceding Rules. 1. The least 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 sum. 2. Suppose a man born in the year 1743 ; When will he be 57 years of age ? 1743 +57 = 1800 Ang. What |