What claims are just not backed by historical facts?
To me, it's: That ancient people thought the Earth was flat.
We have records from around 430BC where Greek philosophers spoke of the Earth being a sphere. In 240BC the Greek astronomer Eratosthenes calculated the circumference of the Earth and was only about 2% out.
The idea that historically people were somehow less, or more intelligent than people today.
Saying things like "ancient people knew over 300 plants and what they do" as if this is somehow amazing. Kids can name 300 Pokemon, and their movesets and how they relate to eachother. Your sportsfan cowoker can name their top 100 players and all their stats. This is not amazing, we just focus on other things nowadays.
Nor were ancient people stupid. Obviously they noticed things like certain events happening at fixed times of the year. They just didn't have encyclopedias, but they did have centuries of passed-down knowledge.
To me, it's: That ancient people thought the Earth was flat.
Ancient peoples DID think the Earth was flat.
The conception of a spherical earth was only widely accepted in academic traditions derived from late Greek philosophy and even in those cultures, had a mixed reception in popular conceptions of the earth's shape until the 16th century.
Yes. It was backed by the oldest book of events at that time.
There were mathematicians that wrote against Galileo, and a notable one, a Dominican I think.
Everything in the past moves to the category of belief.
It depends which ancient people. That may be what thought in Greece, but what about elsewhere? Also a lot of Greek and Roman knowledge was lost by the dark ages or ever made it to Europe at all.
Sun dial proves flat earth.
Just imagine a sun dial on a ball earth.
You need a very strong belief to believe in ball earth.
Check out 4 Kings 20:11 (Go and read it).
We always believed rightly until people started believing imaginations and fancies.
So few years before Christ, we had few fanciful school of thoughts.
Speaking to all:
How did Eratosthenes get the circumference of the earth?
The length of shadows.
Now for those who believe such a science:
Let us pretend the earth is a ball.
In 24 hours, let us take the distance between the earth and the sun to be constant (not changing) (change negligible).
But in that same 24 hours, no shadow, short shadow, long shadow, very long shadow could be obtained.
So, constant distance, changing shadows.
Inference:
You cannot obtain the distance of the sun from shadows.
Conclusion:
If the distance of the sun cannot be obtained, Eratosthenes is finished!
You're forgetting one crucial detail about Eratosthenes' experiment: the measurements were taken at the same time, noon on the summer solstice, the time of minimum shadow length in both locations.