Page:Squaring the circle.djvu

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Squaring the circle

(Journal of the Indian Mathematical Society, v, 1913, 138)

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.

For ,
where is the diameter of the circle.
Therefore .

But and are equal to and respectively.

Therefore , and .
Hence ,
and .
Approximately squaring the circle.svg
But ,
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.