28. PROOF.-Beginning at the top, add each column, downwards, and if the second result is the same as the first, the work is supposed to be right.

OBS. The object of beginning at the top and adding downwards, is, that the figures may be taken in a different order from that in which they were added before; otherwise, if a mistake has been made the first time adding, we should be liable to fall into the same again. But the order being reversed, the presumption is, that any mistake which may have been made will thus be detected; for it can hardly be supposed that two mistakes exactly equal will occur.

20. Find the sum of 256, 763, and 894, and prove the operation.

21. Find the sum of 8054, 5730, and 3056, and prove the operation.

22. Find the sum of 74502, 83000, and 62581, and prove the operation.

23. Find the sum of 68056, 31067, 680, and 200, and prove the operation.

24. Find the sum of 50563, 8276, 75009, 31, and 856, and prove the operation.

25. Find the sum of 65031, 2900, 35221, and 870, and prove the operation.

29. From the preceding illustrations and principles we derive the following

GENERAL RULE FOR ADDITION.

I. Write the numbers to be added under each other; so that units may stand under units, tens under tens, &c. (Art. 21.)

II. Begin at the right hand, and add each column separately. When the sum of a column does not exceed 9, write it under the column; but if the sum of a column exceeds 9, write the units' figure under the column added, and carry the tens to the next column. (Arts. 23, 25.)

QUEST.-28. How is addition proved? Obs. Why add the columns downwards, instead of upwards? 29. What is the general rule for addition?

III. Proceed in this manner through all the orders, and finally set down the whole sum of the last or the left hand column. (Art. 25.)

EXAMPLES FOR PRACTICE.

1. A man bought a quantity of flour for 38 dollars, a ton of hay for 14 dollars, and a firkin of butter for 12 dollars. How much did he give for the whole?

2. A grocer bought three boxes of honey. The first box contained 22 pounds, the second 15, and the third 9 pounds. How many pounds were there in all?

3. A man being asked his age, answered, that he had 3 children whose united ages were just equal to his own age. The eldest was 18, the second 16, and the third 14 years old. What was his age?

4. A man bought 5 hogsheads of molasses for 238 dollars, and sold it so as to gain 75 dollars. How much did he sell it for?

5. A lady purchased materials for 3 dresses. For the first she paid 15 dollars, for the second, 9 dollars, and for the third, 7 dollars. How much did she pay for them all?

6. A boy bought a cap for 12 shillings, a pair of gloves for 6 shillings, a pair of boots for 16 shillings, and a book for 6 shillings. How much did he give for the whole?

7. A gentleman owns 3 houses. For the first he receives a rent of 150 dollars, for the second 175, and for the third 225 dollars. What is the sum of all the rents?

8. A shopkeeper commenced business with 1530 dollars. After trading for some time, he found that he had gained 950 dollars. How much had he then?

9. A man bought a horse for 87 dollars, a carriage for 75 dollars, and a harness for 28 dollars. How much did he give for the whole?

10. What number of dollars are there in four purses; the first containing 25 dollars, the second 73, the third 84, and the fourth 96 ?

11. A poor man having lost his house by fire, to help him repair his loss, one man gave him 25 dollars, another 15, another 10, another 5, and another 3. How much did he receive in all?

12. In a certain school there were three classes in arithmetic. The first class contained 8 scholars, the second 11, and the third 14. How many scholars were studying arithmetic?

13. A merchant, on closing his business for the day, found he had received 23 dollars from one customer, 57 from another, 31 from another, and 25 from various othHow much did he receive that day?

ers.

14. A laborer, in pursuit of employment, walked 7 miles the first day, 10 the second, 12 the third, 15 the fourth, and 20 the fifth day. How far had he then walked?

15. A man, owning a large farm, gave to one of his sons 112 acres, to another 123, to the third 147, and had 200 acres left. How large was his farm at first?

16. A man bought a barrel of oil for 30 dollars, and sold it so as to gain 15 dollars, How much did he sell it for? 17. A lad bought a geography for 50 cents, a grammar for 25 cents, an arithmetic for 13 cents, and a slate for 10 cents. How much did he give for them all?

18. A gentleman purchased a carpet for 38 dollars, a dozen chairs for 36 dollars, a bureau for 15 dollars, and a table for 12 dollars. What did his bill amount to?

19 A merchant had 4 notes; one for 157 dollars, another for 368, another for 576, and another for 1687 dollars. What was the whole amount of his notes ?

20. A gentleman bought a cloak for 56 dollars, a coat for 25 dollars, a vest for 9 dollars, a hat for 7 dollars, and a pair of boots for 5 dollars. What did he give for the whole?

21. A fashionable lady purchased a cashmere shawl for 469 dollars, a watch for 237 dollars, a pocket handkerchief for 87 dollars, and a bonnet for 53 dollars. What was the amount of her bill?

22. A farmer had 375 sheep and 168 lambs in one pasture, in another 379 sheep and 197 lambs. How many sheep had he? How many lambs? How many sheep and lambs together?

23. Four men entered into partnership; one furnished 2878 dollars, another 1784 dollars, a third 1265 dollars, and the fourth 894 dollars. What was the amount of their stock?

24. A man sold three house lots; for one he received 975 dollars, for another 763 dollars, and for the third 586 dollars. What did the whole amount to?

25. A gentleman purchased a store for 4500 dollars, and paid 75 dollars for repairs and 150 dollars for having it enlarged. For how much must he sell it in order to gain 175 dollars?

26. A gentleman paid 75 dollars for one piece of cloth, 67 dollars for another, 54 dollars for another, and 48 dollars for another. How much did he pay for all?

27. A certain orchard contains 56 apple-trees, 19 peachtrees, 23 plum-trees, and 15 cherry-trees. How many trees are there in the orchard?

28. The distance from New York to Albany is 150 miles, from Albany to Utica 93 miles, from Utica to Rochester 158 miles, and from Rochester to Buffalo 75 miles. How far is it from New York to Buffalo ?

29. A man being asked his age, said he was 17 years old when he left the academy, he spent 4 years in college, 3 years in a law school, practised law 15 years, was a member of congress 18 years, and it was 16 years since he retired from business. How old was he?

30. A shopkeeper, having a note to pay, found it more convenient to pay in small sums: at one time he paid 184 dollars, at another 268 dollars, at another 379 dollars, at another 467 dollars, and there were 350 dollars still unpaid. What was the amount of his note ?

31. A gentleman owns a house and lot worth 10800 dollars, a store worth 5450 dollars, a house-lot worth 3700 dollars, and has 15000 dollars in personal property. What is the whole amount of his property?

32. A man left his estate to his wife, his three sons, and two daughters. To his wife he gave 10350 dollars, to his sons 5450 dollars apiece, and his daughters 3500 dollars apiece. How large was his estate?

33. A merchant, on looking over his accounts, found he owed one man 750 dollars, another 648, another 597, another 486, another 379, and another 287 dollars. What was the amount of his debts?

34. A man bought a span of horses for 275 dollars, a

carriage for 150 dollars, and a harness for 87 dollars. How much did he give for the whole ?

25. A man bought 268 bushels of wheat for 287 dollars, 187 bushels of corn for 98 dollars, and 156 bushels of oats for 128 dollars. How much did he give for the whole ?

36. A farmer, wishing to stock his farm, paid 197 dollars for a span of horses, 86 dollars for a yoke of oxen, 175 dollars for cows, and 169 dollars for sheep. How much did he give for the whole ?

37. A butcher sold to one customer 157 pounds of meat, to another 159, to another 149, to another 97, and to another 68. How much did he sell in all?

38. A carpenter received for one job 879 dollars, for another 786, for another 693, for another 587, for another 476, and for another 368 dollars. How much did he re

ceive in all?

39. A grocer bought 375 dollars worth of molasses,

dollars worth of tea, 158 dollars worth of coffee, and 137 dollars worth of spices.

What was the amount worth of sugar, 287

his bill?

40. A merchant bought calico to the amount of 568 dollars, silks to the amount of 479 dollars, and broadcloths to the amount of 784 dollars. He sold them so as to gain 134 dollars on the calico, 178 dollars on the silks, and 242 dollars on the broadcloths. How much I did he sell them for? What was the amount of his gains?

41. A merchant pays 560 dollars a year for store rent, 386 dollars to one clerk, 267 to another, and 369 dollars for various other expenses. What does it cost him a year to carry on his business?

42. A man receives 568 dollars rent for one store, 479 for another, and 276 for another. How much does he receive for them all?

43. The distance from Boston to Springfield is 98 miles, from Springfield to Pittsfield is 53 miles, from Pittsfield to Albany is 49 miles, from Albany to Auburn is 173 miles, and from Auburn to Buffalo is 152 miles. How far is it from Boston to Buffalo ?