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It was Galileo who discovered Venus's phases. What more resolution do you need?

The Ptolemaic explanation worked just as well once the planets were treated as spheres. It was the detailed observation of all the planets' movements that finally settled the issue.

But, just for fun.

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What would have settled the issue for anyone who wasn't a slave to Church dogma was seeing the phases of Venus show that at times it was closer to us than the sun, at other times farther away. That's at variance with the diagram you posted, which shows Venus always being closer.