Further, we want to prove with this pentagonal figure that the circle can be squared with line x.y. divided into four equal parts which make up the square, or tetragon with which the circle is squared, and we prove it as follows: from the 5 circumferential lines contained in the pentagon plus a sixth line, let us make one straight line worth as much as line x.y., not more and not less, and we can clearly sense this when measuring it with a compass, and thus we must know that the square made from line x.y. has the same value in containing capacity as circle e.f.g.h., for if it did not amount to this, but to something more or less, it would not be equivalent to the straight line made from the pentagon and from the sixth line.

The pentagon was used to prove that its 5 lines plus one line are worth line x.y., and the same method of proof can be applied to the six angled figure, and to figures with seven or eight angles, as this can be proved to the senses with a compass by adding a line to each successive figure, as we exemplified with the pentagonal figure in long geometry, and we call this 'long geometry' because in it we multiply the principles of other sciences.