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15. A line of 100 feet in length extends from the top of a wall to a point 80 feet from its base— What is the height of the wall ?


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3600 square of BC. ✓ 3600 = 60= BC. Answer. 16. A line of 365 yards in length, will exactly reach from the top of a fort, known to be 27 yards high, to the opposite bank of a river—The breadth of the river is required.

Ans. 364 yards. 17. Suppose a ladder 68 feet long be so placed as to reach a window 32 feet from the ground, on one side of the street, and without moving it at the foot, will reach a window 60 feet high on the other side— What is the breadth of the street, and what is the distance from one window to the other ? D


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3600 square of EB.

✓3600 60 = BE.

32 + 60 92 breadth of the street. Ans.
DF = AB = 92, and BF = AD, consequently
CF = AD-BC 28.

square of DF.
28x28= 784 square of CF.


square of DC.
and ✓9248 96.167 DC, as required.
18. A castle wall there was, whose height was found,

To be an hundred feet from the top to the ground;
Against the wall a ladder stood upright,
Of the same length the castle was in height;
A waggish youth did the ladder slide,
The bottom of it ten feet from the side;
Now I would know how far the top did fall,
By pulling out the ladder from the wall.

Ans. 6 inches +

EFFECTS OF LIGHT AND HEAT. The effects or degrees of light, heat and attraction are reciprocally proportional to the square of their distance from the centre whence they propagated.

19. In a room where two men, A. and B. are sitting, there is a fire, from which A. is two feet and B, is four feet distant; it is required to find how much hotter it is at A's feet than at B's.

Ans. A's is 4 times as hot as B's. 20. The distance between the earth and sun is accounted 95 millions of miles ; I wish to know what distance from the sun another body must be placed, so as to receive light and heat double to that of the earth. Ans. 67175144 miles,



VELOCITIES OF HEAVY BODIES FALLING. The velocity of heavy bodies falling near the surface of the earth, is 16 feet in the first second; and, As 16 feet are to the given distance, So is the square of one second, or 1, To the square of the seconds required.

21. In what time will a bullet, dropped from the top of a steeple 324 feet high, come to the ground ?

ft. ft. As 16 : 324 :: 1 : 204 and 7204 41 Ans. 22. A bullet dropped from the top of a building, was found to come to the ground in 21 seconds-Required its height.

ft. ft. As 1 : 22 x 23 16 100 Answer. 23. Ascending bodies are retarded in the same ratio that descending bodies are accelerated; therefore, if a ball discharged from a gun, returns to the earth in 10 seconds—How high did it ascend?

Ans. 400 feet.





To extract the cube root, is to find out a number which being multiplied into itself, and then into that product, produceth the given number.

RULE. 1. Point every third figure of the cube number given, beginning at the units place or decimal point, seek the greatest cube of the left hand period or to the first point, and subtract it therefrom; put the root in the quotient, and bring down the figures in the next point to the remainder for a dividend.

2. Square the root and multiply it by 3 for a defective divisor; see how often the said defective divisor is contained in the said number, (the units and tens excepted) which place in the quotient, and its square to the right of the said divisor, supplying the place of tens with a cypher, if the square be less than ten.

3. Complete the divisor, by adding thereto the product of the last figure of the root by the rest, and by 30. Multiply and subtract as in Division; bring down the next period, for which find a divisor as before, and so proceed with every period.

Note. After the first, the defective divisors may be found more concisely, thus : To the last complete divisor add the number which completed it, with twice the square of the last figure in the root: the sum will be the next defective divisor.

Examples. 1. What is the cube root of 676836152?

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Defective divisor and square of 8=19249)164836

+1680= complete divisor 20929) 146503 Defective divisor and square of 7=2270764) 18333152 +20880-complete divisor 2291644)18333152

2. What is the cube root of 926859375 ? Ans. 975. 3. What is the cube root of 2077552.576 ? Ans. 1276. 4. What is the cube root of .015252992? Ans. .248. 5. What is the cube root of 1371.74211248? Anş.11.111.+. 6. What is the cube root of 794022984? Ans. 926+ 7. What is the cube root of 15.926972504? Ans. 2.516+ 8. What is the cube root of 27054.036008? Ans. 30.02. 9. What is the cube root of 36155.027576? Ans. 33.06+ 10. What is the cube root of .001906624? Ans. .124. 11. What is the cube root of 33.230979637? Ans. 3.215+ 12. What is the cube root of 53157376? Ans. 376. To extract the Cube Root of a Vulgar Fraction.

Rule. Reduce the fraction to its lowest terms, then extract the cube root of its numerator and denominator for a new numerator and denominator; bnt if the fraction be a surd, reduce it to a decimal, and then extract the root from it.

Examples. 13. What is the cube root of 2000

Ans. 14. What is the cube root of

Ans. 15. What is the cube root of 16

Ans. 26. What is the cube root of




who not con


17. What is the cube root of 7? 18. What is the cube root of 4? 19. What is the cube root of į? 20. What is the cube root of ?

Ans. .822+
Ans. .829+
Ans. .873+
Ans. .736+

DUODECIMALS. Duodecimals is a rule by which workmen and artificers take the dimensions, and cast up the content of their work. It is also used for finding the tonnage of ships, and the content of bales,"cases, &c. The denominations are:

12 fourths "'I make 1 third,
12 thirds

1 second,"
12 seconds

1 inch, in. 12 inches

1 foot.

Rule. Set the feet of the multiplier under the lowest name of the multiplicand, and in multiplying carry 1 for every 12; placing the results of the lowest name in the product, under its multiplier, or,

Multiply by the feet and take parts for the inches, &c.
Note.Feet multiplied by feet give feet.

Feet multiplied by inches give inches.
Feet multiplied by seconds give seconds.
Inches multiplied by inches give seconds.
Inches multiplied by seconds give thirds.
Seconds multiplied by seconds give fourths.

Examples. 1. How many square feet in a board 14 feet 7 inches long, and 1 foot 5 inches broad? ft. in.

Or thus : 14 7

14 1 5


x1 6

4 in. }

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