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AUTHOR OF PRACTICAL AND MENTAL ARITHMETIC, THE PRODUCTIVE GRAMMAR,
THE PRODUCTIVE GEOGRAPHY, &c.

STEREOTYPE EDITION

HARTFORD:

PUBLISHED BY JOHN PAINE.
1842.

HARVAR
UNIVERSI
LIBRARY
47*130

IT IS NOT EASY TO DEVISE A Cure for such a STATE OF THINGS, (THE DECLINING TASTE FOR SCIENCE;) BUT THE MOST OBVIOUS REMEDY IS TO PROVIDE THE EDUCATED CLASSES WITH A SERIES OF WORKS ON POPULAR AND PRACTICAL SCIENCES, FREED FROM MATHEMATICAL SYMBOLS AND TECHNI CAL TERMS, WRITTEN IN SIMPLE AND PERSPICUOUS LANGUAGE, AND ILLUSTRATED BY FACTS AND EXPERIMENTS WHICH ARE LEVEL TO THE CAPACITY OF ORDINARY MINDS." QUARTERLY REVIEW.

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THE FIRST THING TO BE REQUIRED IN A SYSTEM OF POPULAR INSTRUCTION, IS, THAT IT SHOULD BE INTELLIGIBLE; THAT CHILDREN AND YOUTH SHOULD UNDERSTAND WHAT THEY LEARN. UNDERSTAND WHAT THEY LEARN? IT MAY BE ASKED; WHAT ELSE CAN THEY DO? WE ANSWER, THAT THEY MAY COMMIT IT TO MEMORY, MAY RECITE IT, MAY EVEN MAKE A FAIR SHOW OF KNOWLEDGE, AND YET KNOW NOTHING. WE HAVE NOT THE LEAST HESITATION IN SAYING, THAT TWO OR THREE YEARS, IN THE EDU CATION OF ALMOST EVERY INDIVIDUAL IN THIS COUNTRY, HAVE BEEN THROWN AWAY UPON STUDYING WHAT THEY DID NOT UNDERSTAND." NORTH AMERICAN REVIEW.

Entered according to Act of Congress, in the year 1841,
BY JOHN PAINE,

in the Clerk's Office of the District Court of Connecticut.

HARTFORD,

STEREOTYPED BY

RICHARD H. HOBBS.

ARITHMETIC.

PART FIRST:

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Three thousand

Four thousand
Five thousand
Six thousand

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VIII or 150MMM... 8000

IX OF LOOMMMM... 9000

x or ccost....

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M or ccccɔɔ.1000000

* Or, IIII for 4; vIIII for 9; xxxx for 40; LXXXX for 90; and CM for 900,
† Every ɔ annexed to 15 increases its value 10 times: as 10, is 500, 10ɔ is 5000; in like
manner the prefixing of c and the annexing of ɔ to crɔ increases it 10 times as co, 1000,
ccɔɔ, 10000; lastly a line over any number increases it 1000 times: as, D, 500, D, 500000.

NOTE. L. stands for the Latin language; G. for the Greek and F. for the French.
1 ARITHMETIC, [G. arithmétiké.] Computing, calculating or reckoning by numbers.
2 MENTAL, [L. mentis.] Pertaining to the mind; intellectually.

3 NUMERATION, [L. numeratio.] Numbering; the method or act of numbering.
4 REPRESENTED, Exhibited; described; personated; to supply the place of
5,CHARACTER, A mark; a stamp; a letter; reputation; a personage.

QUESTIONS ON THE FOREGOING.

2. What does Number show? 1. How is it represented? 1. What letters and what figures stand for one, four, five and nine! What for ten? Ans. The figure 1 and 0 called naught or cipher.

3. What letters and what figures stand for eleven? For twelve? Fifteen? Twenty? Forty? Fifty? Ninety? What different numbers may be represented by the figures 1 and 5 written together? Ans. Fifteen and fifty-one; as, 15:51.

4. What different numbers may be expressed by the figures 1 and 9? 2 and 5? What number is expressed by c? by D? by M? What by C, D, and M, with a dash over each.

5. What figures stand for one hundred? For two hundred? One thousand? Ten thousand? One hundred thousand? One million?

ADDITION.'

QUESTIONS.

II. 1. Thomas has 3 dollars and Rufus 5 dollars. How many dollars have they both? Say 3 and 5 are 8.

A. 8 dollars. 2. A farmer has 5 cows in his yard, and 6 in the pasture. How many cows has he in both places?

3. A man bought a hat for 5 dollars, and a pair of boots for 7 dollars. How many dollars did he pay for both?

4. A man lost 7 dollars, and then had 8 dollars left? How many dollars had he at first?

5. A man gave 8 dollars for a saddle, 5 dollars for a bridle, and 2 dollars for a whip. What did the whole cost him?

6. Suppose there are 8 oranges in a basket, 5 on a table, and 4 in my pockets. How many will they all make?

7. A grocer sold to one man 6 barrels of flour, to another 9 barrels, and still had 5 barrels left. How many barrels had he at first?

8. In a certain class are 6 large boys, 7 small ones, and 10 girls. How many scholars are there in the class?

9. A boy has 10 dollars, his father gave him 10 more, and he has 5 owing to him. How many will they all make?

10. Thomas read 19 pages of history in one day, 12 in another, and 9 in another. How many pages did he read in all?

11. Suppose you are 10 years old, and that your brother was 10 years old when you were born. What is his age now?

12. A man gave 10 dollars more for his horse than for his wagon, and the wagon cost him 30 dollars. What did they both cost him? 13. How many are 10 and 30 and 40? 60 and 10 and 20? 100 and 200 and 400? 600 and 300 and 100?

1 ADDITION, [L. additio.] Any thing added; adding; joining; uniting two or more numbers in one sum.

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2 o'clock, twice; will these make?

14. When it is 1 o'clock, a regular clock strikes once; when it is when it is 3 o'clock, thrice. How many strokes A. 6 strokes: because 1 and 2 are 3, and 3 are 6. 15. Add together all the strokes that a clock strikes in 12 hours, as in the above picture of a clock. [Thus 1 and 2 are 3, and 3 are 6, and 4 are 10, and so on up to 12.]

In the following table the single figures are combined' by pairs in every possible manner; so that, if it be committed to memory, the learner can add with facility' any two numbers whatever.

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16. Repeat the above table beginning at the top on the left. What are all the different pairs of single figures that together make 7? make 9? 10? 12 13 14 15 16 17? 18?

17. How many are 8 and 4? 18 and 4? 28 and 4? 48 and 4? 7 and 6? 17 and 6? 26 and 7? 57 and 6? 86 and 7? 96 and 7?

18. How many are 9 and 5? 19 and 5? 55 and 9? 8 and 8? 38 and 8? 98 and 8? 5 and 7? 65 and 7? 9 and 8? 49 and 8? 99 and 8? 19. Add together audibly3 10 twos: 10 threes: 10 fours: 10 fives: 10 sixes: 10 sevens: 10 eights: 10 nines: 10 tens.

20. How many are 78 and 10 and 3? 78 and 13? 91 and 14 [10 and 4]? 105 and 15 [10 and 5]? 120 and 16? 136 and 17? 153 and 18? 171 and 19?

21. Add together audibly' all the different numbers under 20, beginning with the lowest.

1 COMBINED, United closely; associated; leagued; confederated.

2 FACILITY, [L. facilitas.] Easiness to be performed; readiness; affability.

3 AUDIBLY, In a manner so as to be heard; in an audible manner.

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