Squaring of the Circle

Second conclusion.

¶ To provide a straight line equal to a line drawn circularly.

original: "Lineæ orbiculariter ductæ lineã rectã eq̃líter dare." This refers to the "rectification of the circle," or finding a straight line that has the same length as a circle's circumference.

[One might] add that it is possible: according to mathematical science and physical truth, a circle is divided into 22 equal parts; if one part is removed—namely the twenty-second part—the remaining third that is, the remaining seven parts is the diameter of the circle. This describes the Archimedean approximation of Pi as 22/7. If the circumference is 22 units, the diameter is 7 units. Therefore, let the diameter be tripled and a seventh [of the diameter] be added: and let these parts be arranged in a straight line, and a straight line equal to the circular one will be obtained.

Before we come to explaining the text of Campanus Campanus of Novara, a 13th-century mathematician famous for his commentary on Euclid., it must be noted that some geometersoriginal: "geometræ"; practitioners of geometry. imagine that a circle is divided into 22 equal parts in this way: first, let two circles of the same size be drawn separately. Then, with a compassoriginal: "circinus"; the primary tool for drawing circles and measuring distances in geometry. set, let one of them be divided into three equal portions. Afterward, let one of those three parts be cut again into seven equal small portions. Then, without changing the compass setting, place one of these seven small parts into the other circle. Finally, take the entire remainder of the circle (after removing the small part marked in it, starting from the points of that part already marked there) and cut it into three equal portions. Then divide each of those three parts again into seven equal small portions. And in this way, you will have the circle divided into almost 22 equal small portions, namely in this manner.