Supplement TO THE Square Hoot,

QUESTIONS.

Į. WHAT is to be understood by a root? A power? The second, third, and fourth powers?

2. WHAT is the Index, or Exponent?

3. WHAT is it to extract the Square Root ?

4. War is the given sum pointed off into periods of two figures each?

5. In the operation, having found the first figure in the root, why do we subtract the square number, that is, the square of that figure, from the period in which it was taken ?

6. WHr do we double the root of a divisor ?

7. In dividing, why do we except the right hand figure of the dividend ?

8. War do we place the quotient figure in the root and also to the right hand of the divisor?

9. Ir there be decimals in the given number, how must it be pointed? 10. How is the operation of extracting the Square Root proved?

EXERCISES IN THE SQUARE ROOT.

1. A CLERGYMAN'S glebe consists of three fields; the first contains 5 Acr. 2 r. 12 p. the second, 2 ac. 2 r. 15 p. the third 1 ac. 1 r. 14. in exchange for which the heritors agree to give him a square field, equal to all the three. Sought the side of the square? Answer 39 Poles.

2. A GENERAL has an army of 4096 men; how many must he place in rank and file to form them into a square? Answer 64.

3. There is a circle whose diameter is 4 inches, what is the diameter of a ircle 4 times as large? Answer, 8 inches.

NOTE. SQUARE the given diameter, multiply this square by the given proportion, and the square root of the product will be the diameter required. Do the same in all similar cases.

Ir the circle of the required diameter were to be less than the circle of the given diameter, by a certain proportion, then the square of the giv en diameter must have been divided by that proportion.

4. THERE are two circular ponds in a gentleman's pleasure ground: the diameter of the less is 100 feet, and the greater is three times as large. What is its diameter. Answer, 173,2+

5. In the diameter of a circle be 12 inches, what will be the diameter of a nother circle, half so large?

Answer, 8,48 inches.

6. A wall is 36 feet high, and a ditch before it is 27 feet wide; what is the length of a ladder, that will reach to the top of the wall from the opposite side of the ditch? Answer, 45 feet.

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NOTE. A FIGURE of three sides, like that formed by the wall, the ditch and the ladder, is called right angled triangle, of which, the square of the hypotenuse, or slanting side, (the ladder) is equal to the sum of the squares of the two other sides,that is, the heighth of the wall and the width of the ditch.

7. A LINE of 36 yards will exactly reach from the top of a fort to the opposite bank of a river, known to be 24 yards broad; the height of the wall is required? Answer, 26,83+yards.

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8. GLASGOW is 44 miles west from Edinburgh: Peebles is exactly south from Edinburgh, and 49 miles in a straight line from GLASGOW; what is the distance between Edinburgh and Peebles?

Answer, 21,5+miles.

§ 4. Extraction of the Cube Hoot.

To extract the Cube Root of any number is to find another number, which multiplied into its square shall produce the given number.

RULE.

1. "SEPARATE the given number into periods of three figures each, by putting a point over the unit figure, and every third figure beyond the place of units.

2. "FIND the greatest cube in the left hand period, and put its root in the quotient.

3. "SUBTRACT the cube thus found, from the said period, and to the remainder bring down the next period, and call this the dividend.

4. " MULTIPLY the square of the quotient by 300, calling it the triple square, and the quotient by 30, calling it the triple quotient, and the sum of these call the divisor.

5. "SEEK how often the divisor may be had in the dividend, and place the result in the quotient.

6. " MULTIPLY the triple square by the last quotient-figure and write the product under the dividend; multiply the square of the last quotient figure by the triple quotient, and place this product under the last; under all, set the cube of the last quotient figure, and call their sum the subtrahend.

7. "SUBTRACT the subtrahend from the dividend, and to the remainder bring down the next period for a new dividend, with which proceed as before, and so on till the whole be finished.

NOTE. THE same rule must be observed for continuing the operation, and pointing for decimals, as in the square root."

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