Why can't ptolemaic Venus be fully lit? In wikipedia's article on the phases of Venus it says:

The Ptolemaic system would never allow Venus to be fully lit from the perspective of the Earth, as this would require it to be on the far side of the Sun, which is impossible if Venus's orbit in its entirety is between the Earth and the Sun,

But the moon's orbit &quot;in its entirety is between the Earth and Sun&quot;, and is &quot;fully lit from the perspective of the Earth&quot; once a month, so how can we conclude that Venus revolves around the Sun?
The Moon orbits the Earth in such a way that it sometimes can be on the opposite side of the Earth as seen from the Sun. In other words, it’s possible to have Sun-Earth-Moon along an imaginary straight line, in that order.
However, by Ptolemy’s time, it had already been noticed that Venus is always seen close to the Sun (maximum angular distance about 47°). So it can never get opposite to the Sun as seen from Earth.
Ptolemy didn’t know why (the reason is that Venus orbits the Sun, not the Earth, which was inconceivable to Ptolemy), but his system made it so that Venus (and Mercury, for that matter) were orbiting the Earth closer to it than the Sun, and in such a way as to always be near it.
So imagine moving your two hands at arm’s length, but one closer to your face than the other. Imagine the distant one is the Sun. Then your closest hand would never get completely lit. Unless you put it behind your back, where Venus (and Mercury) never go.
So that’s why in the Ptolemaic system, Venus (or Mercury) would never get fully lit.