n m, a b c, o p

If from equal things an equal part is taken, the remainder will be equal. I have here two semicircles, from each of which I take away the portion b. And then I take from each the 2 portions n m and o p, which are equal to one another.

M, c, a, p o, b, d

n

m

a b

another way

p, another way

c d

I can give you whatever part you know how to ask me of a circle between 2 parallel lines. Suppose you ask me for 1/9 of a circle between 2 equidistant lines. I will divide a circle into 18 triangles of 2 straight sides and the third curved [fig.]. And then I will divide it in half [fig.] and divide the cut apex into 2 equal parts, from the base to the apex [fig.]. And these two parts I will fit to the sides of the remainder of the said triangle, that is a square, and it will stand in this form [fig.]. This done, I will place, or add to it, a similar and equal figure. Its end will stand in this way [fig.], that is [fig.], which will come to be composed of 2 eighteenths, and so it will be the ninth part of a circle placed between 2 parallel lines, as I promised to do.

b, a, c

With the figure M above we have drawn from the circle the parallel part a b c d, equal to the sixteenth part of the whole circle [fig.], and set it in the diameter; and if you want it in the semicircle, do as below in figure p. [fig.] a b is similar to a c, being with their bases and apexes between parallel lines.