Indicates that venus orbits closer to the sun than the earth.
There are several assumptions that Galileo had to make. They are
1. The smaller the visible arc, the further away the object is.
2. When Venus is nearly full, he sees almost all of the surface of Venus that's exposed to the sun.
3. When Venus is half full, he sees half of the surface of Venus that's exposed to the sun.
4. When Venus is just a crescent, he sees almost none of Venus that's exposed to the sun.
So Crescent, 61 arc seconds
Large, so it's close to Earth
Crescent, so can not see most of the surface that's exposed to the sun.
Implies that Venus is between Earth and Sun
Nearly full, 10 arc seconds.
Small, so it's far from Earth
Nearly full, so can see most of surface exposed to sun
Implies that Venus is nearly opposite from sun as Earth (e.g. Sun is almost between Venus and the Earth)
Half full, 59 arc seconds
Almost as large as full, so it's a little further away, but not a whole lot
Half full, so from the point of view of venus, there's a 90 degree angle between the Sun and Earth.
Those observations indicate that Venus is closer to the sun than the earth is. To show why, assume Venus is farther away from the sun than the earth. If that were the case, then you would never see Venus as a Crescent. The least you would see would be half.
