Proof that the diameter of the sun is greater than 18 times, but less than 20 times, the diameter of the moon:

Let our eye be at A, let B be the center of the sun, and C the center of the moon when the cone comprehending both the sun and the moon has its vertex at our eye, that is, when the points A, C, B are in a straight line.

Let a plane be carried through ACB; this plane will cut the spheres in great circles and the cone in straight lines.

Let the plane cut the spheres in great circles FG, KLH, and the cone in the straight lines AFH, AGK, and let CG, BK be joined.

Then, as BA is to AC, so will BK be to CG.

But it was proved in proposition 7 (link to prop 7) that BA is greater than 18 times, but less than 20 times, AC.

Therefore BK is also greater than 18 times, but less than 20 times, CG.