Rs=the radius of the sun

Re=radius of the earth

Rm=radius of the moon

Dm=distance of moon from earth

Ds=distance of sun from earth

Triangles ABC and DCF are similar, and DS=AC, and DM=DF.

Also, AB=Rs-SA=Rs-EC=Rs-Re and DC=Re-ED=Re-MF=Re-2Rm (the 2RM is based on the lunar observation)

By similar triangles, Dm/Ds=(Re-2Rm)/(Rs-Re)

Using the result from proposition 1that Ds=19Dm, and the result from proposition 2that Rs=19Rm, by substitution onto the above equation, we get 1/19=(Re-2Rm)/(19Rm-Re).

Solving this equation for Rm/Re gives Rm/Re=20/57, which shows that the earth is approximately three times larger than the moon. From this and the equation Rs=19Rm, it follows that the radius of the sun is more than 6 times larger than the radius of the earth.