Squaring of the Circle

Second
b 2

...of such parts as the 28 that complete the given line K.3. It will be necessary that the orb original: "orbis"; here referring to the circle formed from the given line of 28 parts be equal to the square formed from the same line of 28 parts, which was to be demonstrated.

A horizontal line segment labeled K at the left and 3 at the right, divided into 28 small equal units by vertical tick marks.

And since we have demonstrated that the circle exceeds three times the diameter, as was said The author is referencing the common approximation that the circumference of a circle is roughly three times its diameter (Pi ≈ 3).. Thus, the diameter of the circle B.C. consists of nine such parts as those we placed upon the line K.3, which when tripled makes 27. And since both the circle and the square exceed the diameter original: "dimentiente" by exactly one part, add this one part to the diameter: and thus there will be just as many parts for both the circle and the square; hence from three times the diameter plus a ninth part The author is calculating the circumference as (3 × 9) + 1 = 28 units. This implies a value for Pi of 28/9, or approximately 3.11., that entire circular line will be completed.

A geometric diagram consisting of a circle inscribed within a square. A vertical diameter line is drawn through the center, labeled B at the top and C at the bottom. The square's left side is labeled D and the right side E. The vertical diameter is marked with nine small horizontal tick marks indicating units of measurement.

Another demonstration concerning the diameter.

Many have stated fully that the proportion of the diameter to the circle is in a smaller number and proportion than 14, and in a larger one than 7 This likely refers to the bounds of the ratio of circumference to diameter; in this specific example where the circumference is 28, the diameter (approx. 8.9) is indeed between 7 and 14.. For example, let the diameter of the circle be f.g. Since it was established above that the entire circumference original: "circūcurrens linea" is 28 parts, of which f.g. is the diameter and f.h.g. is the arc...