3. The plaine of the ray, and of halfe the periphery is the content of the circle.
For here 7, the ray, of halfe the diameter 14, Multiplying 22, the halfe of the periphery 44, maketh the oblong 154, for the content of the circle. In the diameter two opposite sides, and likewise in the perimeter the two other opposite sides of the rectangle are conteined. Therefore the halfes of those two are taken, of the which the rectangle is comprehended.
And
4. As 14 is unto 11, so is the quadrate of the diameter unto the Circle.
For here 3 bounds of the proportion are given in potentia: The fourth is found by the multiplication of the third by the second, and by the Division of the product by the first: As here the Quadrate of the diameter 14, is 196. The product of 196 by 11 is 2156. Lastly 2156 divided by 14, the first bound, giveth in the Quotient 154, for the content of the circle sought. This ariseth by an analysis out of the quadrate and Circle measured. For the reason of 196, unto a 154; is the reason of 14 unto 11, as will appeare by the reduction of the bounds.
This is the second manner of squaring of a circle taught by Euclide as Hero telleth us, but otherwise layd downe, namely after this manner. If from the quadrate of the diameter you shall take away 3/14 parts of the same, the remainder shall be the content of the Circle. As if 196, the quadrate be divided by 14, the quotient likewise shall be 14. Now thrise 14, are 42: And 196 - 42, are 154, the quadrate equall to the circle.
Out of that same reason or rate of the pheriphery and
diameter ariseth the manner of measuring of the Parts of a circle, as of a Semicircle, a Sector, a Section, both greater and lesser.
And