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53. 1. Of the trees in an cr-jhalf in the waler, one third in the charu, bear apples plums and mud aol 6 feet above the water, 20 bear cherries; how many trees what is its lenz(!? are there?

in lu a school 5 sevenths of the 2. Of the trees in a garden one p pils are learnin intellectual ahall bear apples one fourth peac.-rith:vetic, 3 fourtcentis are learnes, one sixth pluis, 4 bear pearsing geography and the rest, 3 in and I cheries, how many trees arejaumber are learning latin, what there?

is the amber of pupils? ***+1=htt 1 ; 8 Which is most 6 thirds of 20 then 4+ = the remains 1 apples, or 40 apples?

12 9. Woat is the difference beand if

Tz0,12i-no-Dutween 5 oranges, and i third and

b=5,13=12X5==60. .Ansicer.

I half of i third of 12 oranges? 3. A boy having spent šanci d 10. is there any difference beof his money had 10 cents left, how tween I third of 1 half and i ball much had he at first? Ans. 24 cts.of 1 thiru? Explain the operation

11. John lad I third of : melon 4. In a school 1 fifth of the pu-laod cave 1 of what he had to pils study gcography, 2 filths are lfames, what part of the melou did learning to write, and the rest, be - James havc: what part had John ing 20 in number, are learning in-heli? tellectual arithmetic, what is the 12. A boy being asked hot mawhole number of scholars ? invanpies lie bad, said, if I had as 25. Triple, one half, and I fourthly

arenany more as faow have, apci half of a certain number is 30; wizal is many more, I should hare an is that number?

Jhundred; how many had he? 6. There is a pole which is one ****

59. 1. A cistern has 2 cocks; would last him 3 and one thirt the tirst will fill it in three hours, weeks. the second in six hours: how muehl 3. If one man could build a of it would each fill in an hour?ipiece of wall in 4 days, and 20: how long would it take them both other man could do it in 6 days, together to fill it?

how much of it would each do in 2. A man and his wife found bylone day? How many days would experiment, that when they were it take them both to do it? Ans. together a bushel of wheat would2 and two fifths. laet nly 2 weeks, but when thej 4. A cis:crn has 3 cocks, the man was gone, it would laat his first will fill it in 2 hours, the secwile 5 weeks; how much of it did ond in 3 hours, and the third in 4 both together consume in one hours, what part of the wiole will week? what part did the map each fill in 1 hour? how long consume in one week? how long would it take to fill it is all were would it last the man alone? Aos. running at once ? : Both together would consume 5 5. A man being asked the price tenths of a bushel in a week, the of his livrze, said, his horse anci woman alone tenths in a week, saddle were worth $00, but the the man alone 3 tenths, and a bus, house was worth & times as much

as the saddle, what was the worth second one fourth ; in the third of each?

Jone sixth, and in the fourth 20 6. A man, having a cow, a hog, bushels ; how much graiu had he? and a sheep, and being asked the 9.1f $ 10 worth of provisions value of each, said, that the hoz will serve 24 men 20 days, how was worth twice as much as the long will $20 worth serves2 men? shcep, and the cow twice as much $60 worth 36 men? $10 worth us the hor, and that all together 18 men ? were worth $56; what was the 10. What number is tbat to Value of each?

which if its hall be added the 7. A boy bought an apple, alsum will be 45? If to a number pear and a nelon for 18 ceats; for half itself be added the sum is the pear lie gave twice as much and its are 45. £is 30. Ans. as for the apple, and for the mel- 11. 'What number is that to on 3 times as niuch as for the pear; which is its third part be added what was the price of each? the sun will be 36?

8. A farmer being asked how 12. A man being asked his age, i much grain he had, replied, that replied, that if its 1 fifth part be it was in 4 bins; in the first bejadùed to it the sum would be 54; had one third of his grain, in the what was his age.? .

60. 1. III mix a quart of be melted with 21b. 23 carats fine, cherries, worth 8 cents, with a gt. what will be the freness of the of currants worth 6 cents, what mixture? is a quart of the mixture worth? 7. I have currants worth 5 cents Ans. 7 cents.


la pint, others worth 3 cepts a pint, 2. If a pound of raisins, worth in what proportion must they be 12 cents, be mixed with a poundmixed lu make the mixture worth of figs, worth 16 cents, what is 14 ceats a pint? Ans. in equal quanpound of the mixture worth? Ilities.'

3. If 2 quarts of rum, worth 141 8. I have berries worth 5 cents cents a quart, be mixed with la pint, and others worth cents a quart of rum, worth 18 cents a pint, in whai proportion must I guart, what is a quart of the mix-imix them that the con

con pound may ture worth ? 2 quarts at 14 cts. be worth 7 cents a piat? Each pint . are 28 cents, and 1 quart at 18 is at 8 cents will be worth 1 cent -18 cents, and 18plus28-46 cts. more than the mean, and each ati 3qts. then cost 46 cts, and 46-;-3=5 cents will be worth two cents 15} cents. Ans.

lless than the mean, they must 4. If 3lb. of sugar, worth 10cts. therefore be inixed in proportion a pound, be mixed with 21b. worth as 2 pts. at 8 cents to. I pint at 5 13 cents a pound, what is a pound cents, to make the mean worth 7 of the mixture worth?. .. cents a piot.

5. If 4 bushels of oats, worth - 9. lf 2 lb. of silver 20 carals 25 cente a bushel, be mixed with fine, be mixed with 4ib. of pure

bushels of rye, worth 40 cents a silver, what will be the fineness of lushel, what is a bushel of thelthe mixture? A carat is the 24th mixture worth? Ans. 32 cents. Ipart of any thing, or quantity, and

6. If 3 lb. of gold, 20 carats.fine,'when gold or silver is said to be so

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many carats fine, it is understood 12. What fineness is the standthat if the whole mass be divided ind for our corus? into 24 equal parts, so many oil 13. What is generally used for them would be pure gold, or silviloy? ver, and the rest alloy. Pure gold 14. For what purpose is alloy would be said to be 2 carats fine. used ? The standard for our gold and sil-i 15. What are the gold coins of ver coins, is 11 parts fine, to 1 part the United States? (33) the silalloy, or in other words, 22 carats ver coins? the copper coins? five. Copper is commonly used as Uncoined gold, 22 carats fine, is alloy in gold and silver, and is em-worth, at the mint of the United ployed to render coins more hard States, $209.77 per lb. Troy, and and durable.

Jancorned silver, of the same fine. 10. What is meant by a carat? ness, is worth $9.92 per pound. . 11. How many carats fine is pure gold?

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61, 1. What is a square?. Ans. root of a number?-by the second A square is a A

B power of a number?--hy the figure having 4

square of a number? equal sides, and

Ti 7. What is the square root of 9 ? 4 equal aisgles

I loi 4? 16? 25? of 10? of 100? or corners, as A

il 8. What is the square of 1?. B C D

Aos, 1.

| 9. Why? Because if the length

D of the side of a square be only 1 2. How many square feet in a foot, the content of the square can square measuring 3 ft, on each be only 1 square foot, i side?

10. What is a cube? Ans. A 3. How many eqiiare feet in alcube is a square measunng 4 feet on each solid body, side? 5 feet? 6 feet? 8 feet? which has -4. What is the square of ing ft. six equal FM The square of 7 is the area, or sides, ali of content, of a square, which meas which are Dies 7 fl. ou cach side, and is found square:, 05 by multiplying 7 by =49 sq. fi. A B C D The product of a number multi-lE F. plied by itself is also called its


D second power; thus 19 j3 the 11. How many solid feet in a square or second power of 7, and cubic block, which measures 3 ft. 7 is ealled ine square root of' 49. on every side? . The square root of a number, then 12. How many feet in a block is the length of the side of a square which measures 2 feet on every of which the number expresses the side? 4 feet on every side? If the area. The length A B is the rooi square of a riven number he mulof the square ABCD. . ltiplied by the given number, the

5. What is the second power of given number is said to be cubed, 52 of 3 ? of 10?..

as 3 times 3 art. 9, ani 3 times 9 6. What is meant by the square are 27. The 27 is called the cuba

or third power of 3, and 3 is called a foot on each side. 2X=1 the cube root vf 27.

sq. ft. Ans. (121.) 13. What is the cube root of 8?! 16. What would be the content

14. How would you proceed fofof a square which measures a find the cube of a given number?-- quarter of a foot on each sida how to find the cube root of a giv-la boy 1=iso. it. Ans. (121.) en number?

17. What is the square root of 15. What would be the content one-fourth? of one-sixteenth of of a square, which measures ballliwo-iwentyfifths ?

62. 1. What is the differencel 11. What is the difference behelween 2 feet square and 2 square iween a cube 2 inches in heiglit, feet?

Jone 3 inches ? 2. What is the difference be. 12. How many feet in a cubical {ween 3 feet square and 3 square pile of wood which measures 5 feet feet? A surface 3 feet square on every side? Is there a cord ? measures 3 feet on every side and how many feet does it lack? contains 9 square feet. (36, fig.) All similar solids are to one ano3 square feet are 3 squares, each her as the cubes of three similar of which measures a foot on every diameters, or sides. side.

| 13. What proportion have simi- . 3. What is the difference he-lar solids to une another? tween 4 miles square and 4 square 14. I have two lead balls, the di. miles? 5 miles square und 5 square ameter of one is one inch, of the miles ?

lother 2 inches, what proportiondo 4. How many square miles in a they bear to each other? Ans. as township, which is 6 miles square? 1 to 8..

5. What is meant by a solid 15 If the weight of tho smallest foot?

ibe 2 lbs. what will be the weight 6. What is the difference be- of the other? tween half a sulid foot and a solid 16. If a bullet 2 inches diameter half foot? Ans. Haif a solid footjweigh 4 lbs. what will be the is a block a foot Square and half a weight of a bullet 3 inches diamefoot high. A solid half fout is alter? Hock a ball foot square and half a 17.' There are 2 giobes, one is 1 fout high-ther half a solid foot is foot diameter and the other 4 feet equal 104 solid half feet and the diameter, how many of the smaller difference is 3 solid hall feel, (36 globes would be required to make

one of the larger? 7. Which is most, a solid fout, ori 18. There is a cubical box one 2 solid half feet? what is the dif- side of which is 1 foot, what is the ference?

side of a box which will holl 3 8. What part of a foot is a solid times as much? 27 tiines as much? half foot? 2 solid half feet? 4?.164 times as much?

9. What part of a solid fool are 19. ln a certain company, the half a solid foot and a solid halfdumber of mep in raok and file is foot?

the same, being 20 in each, what is 10. I bave two cubes, one is antie whole number of men? inch high and the other 2 inches. 20. How many square rods in a high. how many solid inches in piece of land 6 rods square?' 60 one more than in the other? . Trods square?



What is a point out magnitude. Ii is sometimes

How is it represent. represented by a dot.

ed? Why is not a A line is length, without

dot a point ? breadth, or thickness. Some

What is a line ? times represented by a mark, as A

How represented ! A. B. fig. 2.

Wby is not a mark Marks are of great use in rea

a line? What is soning, of the properties of

their use? lines and figures, and when us

What is a straight ed for that purpose are called

line ? a curve line ! lines.

Make a straight line Lines are either straight orc

-a curve line? curved. A Straight (or right)

Is A B a straight line is the shortest distance be

or curve line?. tween two points. A curve line

What are paralcontinually changes its direc. a

Jel lines ? Will partion, as C. D.

allels meet if proParallel lines are always at

duced ? Draw two the same perpendicular dis

parallels. lance; and they never meet

What are oblique though continued ever so far.

lines ? Will oblique E. F. Oblique lines change

lines meet if protheir distance, and, if produc.

duced ? on which ed, would meet on the side of


side? Draw two the least distance, fig. 4. An

lines oblique to each angle is the opening between

otber. two lines having different di.

A: What is an angle? rections and meeting at a point

What is the point called tbe apex, fig 4.


comb of meeting called ? When an angle is read by

Make an angle. three letters, the letter which

How is au angle stands at the apex of the angle

read ? Give an es. is always placed between the

ample, other two, as A B C, or CBA,

When is a line fig. 4.

perpendicular toanOne line is perpendicular to 4

other? another when the angles on

A What is a right both sides of it are equal, fig 5.

angle ? Make one. The angles made by one line

What is an olm falling perpendicular upon an

lique angle? other are called right angles as

What is an acute A B C, or A B D, fig. 5.

angle? What is an Angles either greater or less A.

obiuse apgle? Make than a right angle are called ob.

an acute angle ? lique angles.

an obtuse one ? If an oblique angle be less!

What is a surface! than a right angle it is called an

What is the mean. accute angle, if greater, an ob

g ing of the word a. tuse angle, fig 6.

.A, BA B cute? 64. A surface, or superficies is

What is the mean. a figure having length & breadth

ing of the word op: without thickness.

· tuse!


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