21. The area of a circle is 240 square feet, what is its radius or diameter ? *

22. The area of a circle is 14 square feet 13 square inches, its radius is 5 feet 3 inches, what is its circumference?

23. What is the length of an arc of 14 degrees 29 minutes 24 seconds, in a circle whose radius is 14 inches?

24. What, that of an arc of 6 degrees 9 seconds, in a circle whose radius is 1 foot?

25. What, that of an arc of 9 seconds, in a circle whose radius is 1 inch?

26. What is the area of a sector of 15 degrees, in a circle whose radius is 3 feet?

27. What, that of a sector of 19 degrees 45 minutes, in a circle whose radius is 1 foot 3 inches?

The teacher may now vary and multiply these questions.

*

*

END.

* Divide the area by the circumference, and extract the square root of the quotient, the answer is the radius of the circle.

22

NOTE to Principle 5th of Geometrical Proportions, page 74.

For the same reason, that the second term of a geometrical proportion may be added once or any number of times to the first term, and the fourth term, the same number of times to the third term, without destroying the proportion, the second term may also be subtracted once or any number of times from the first term, provided the fourth term be the same number of times subtracted from the third term, and the result will still be a geometrical proportion.

If, in the geometrical proportion

3

the first term (AB) is twice as great as a b, and AC twice as great as a c, we shall, by subtracting ab from AB, and ac from AC, make the two terms in each ratio equal; that is, we shall have a new proportion

AB-ab: a b = AC -ac: ac.

If AB were three times as great as a b, AC would, of course, be three times as great as ac; and therefore, by subtracting a b from AB, and ac from AC, the first term (AB — ab) in the last proportion would still be twice as great as a b; and for the same If AB were reason would AC a c, be twice as great as a c. four times as great as a b, AC would be four times as great as a c, and therefore by subtracting a b from AB, and a c from AC, the first term (AB - ab) in the last proportion would be three times as great as the second term a b, and for the same reason would AC ac be three times as great as a c. In the same manner this principle may be applied to every other geometrical proportion; and it may also be proved that the first term of a geometrical proportion may be once or any number of times subtracted from the second term, provided the third term is the same number of times subtracted from the fourth term, without destroying the proportion.

ibid. 66

ERRATA.

'

Page 9, in the figure read quadrant' instead of ' quadrat.'

ibid. line 15, omit it.'

66

27, read 'parallel' instead of equal.'

8, read' vertices' instead of 'verteces.' 13, read sometimes' instead of something.' 2, read 'vertices' instead of 'verteces.' 1, read learned' instead of learnt.' "13, read' diagonals' instead of diagonal.'

66

.

19' instead of 18.'

cr 132

"176

"186

" 190

<< 204

<< 214

<< 223

"225

22, read' instead of '6.'

3, read or the areas of the squares upon, &c.' instead of are to the areas of, &c.' exteriorly' instead of 'interiorly.'

12, read

3, read

of tangent,' instead of ' of a tangent.'

66 22, read a' instead of A.'

66 15, omit 'a d.'

It is hoped that all the errors are carefully enumerated here.'