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Feet.

8000 Contents of Fig. I.

4800 addition to the faces or fquares a, c, and b, Fig. II.

960 addition to fill the deficiencies n, n, n, Fig III.

64 addition at the corner e, e, e, Fig. IV. where the additions which fill the deficiencies n, n, n, approach together.

13824 Number of blocks or folid feet, all which are now disposed in Fig. IV. forming a pile, or folid body of timber, 24 feet, on a fide.

Such is the demonstration of the reason and nature of the various fteps in the operation of extracting the cube root. Proper views of the figures, and of those steps in the operation illuftrated by them, will not generally be acquired without fome diligence or attention. Scholars, more especially will meet with difficulty. For their affistance, small blocks might be formed of wood in imitation of the Figures, with their parts in different pieces. By the help of these, Masters, in most inftances, would be able to lead their pupils into right conceptions of thofe views, which are here given of the nature of this operation.

3. What is the cube root of 21024576 ?

Ans. 276.

4. What is the cube root of 253395799552 ?

Anfwer, 6328.

5. What is the cube root of 84,604519 ?

Anfwer, 4,39.

6. What is the cube root of 2?

Anfwer, 1,25+

Supplement to the Cube Host.

1. WHAT is a cube?

QUESTIONS.

2. What is understood by the cube root ?

3. What is it to extract the cube root?

4. In the operation having found the first figure of the root, why is the cube

of it fubtracted from the period in which it was taken ?

5. Why is the fquare of the quotient multiplied by 300 ?

6. Why is the quotient multiplied by 30?

7. Why do we add the triple square and the triple quotient together, and the fum of them call the divifor?

8. To find a fubtrahend, why do we multiply the triple fquare by the last quotient figure? The square of the last quotient figure by the triple quotient? Why do we cube the quotient figure? Why do these fums added, make the fubtrahend?

9. How is the operation proved?

EXERCISES IN THE CUBE ROOT.

1. If a bullet 6 inches diameter weigh 32lb. what will a bullet of the fame metal weigh, whofe diameter is 3 inches?

Ans. 4lb. NOTE. "The folid contents of fimilar figures are in proportion to each other, as the cubes of their fimilar fides, or dis ameters."

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2. What is the fide of a cubical mound equal to one 288 feet long, 216 broad, and 48 high?

Ans. 144 feet.

3. There is a cubical vessel, whofe fide is 2 feet: I demand the fide of a veffel, which fhall contain three times as much?

7

Ans. 2 feet 10 inches and 3 nearly.

NOTE. Cube the given fide, multiply it by the given proportion, and the cube root of the product will be the fide fought

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