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NOTE TO PROBLEM VIII. PAGE 50.

C

The area of a circle is to the area of the circumscribed square as .7954 is to 1, and to that of the inscribed square as.7854 is to. Consequently the square described within a circle is precisely half of the square described without it. To illustrate this proposition let abcd in the annexed figure be the inscribed square, and ABCD the circumscribed square of the circle abcd.

a

The area of the circle is equal to acx.7854 (Art. 19.) But the area A

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of the circumscribed square (Art. 4.) is equal to AB; or the side ABX BC. And we see that the inscribed square contains only 4 equal right angled triangles, while the circumscribed square contains 8.

Ex. 1. The circumference of a circle is 715, what is the side of the inscribed square? (Consult Art. 20 and 24.) Ans. 160.9465.

NOTE TO PROBLEM XIX. PAGE 59.
A much shorter method for finding the
area of a Hyperbola is the following:

To find the area of a Hyperbola.
Rule.-Multiply the base by of the

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height and subtract of the product; the remainder will be the area, very nearly.

Ex. 1. If the base of a hyperbola be 24 feet, the height 10 feet, and the transverse axis 30; what is the area?

OPERATION.

24×63-160. Then, 160-8.33-151.67 Ans.

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