Let be a circle with centre , of which a diameter is . Bisect at and let be the point of trisection of nearer . Draw perpendicular to and place the chord .
Join , and draw and parallel to . Place a chord , and draw the tangent . Join , and . Cut off . Draw parallel to , meeting at .
Then the square on will be equal to the circle approximately.
But and are equal to and respectively.
|Therefore||, and .|
|Therefore||, very nearly.|
Note.—If the area of the circle be square miles, then is greater than the true length by about an inch.