Ancient civilizations may not have had higher mathematics; so stumbling across an accurate solution is very possible...
At the same time, some at least had tremendous grasp of concepts, functions and proofs to recognize calculations that work correctly.
Over time, lots of supposed calculations have been proven incorrect.
Later yes, but my favorite is still Eratosthenes; calculating diameter of earth within ~100 to 800 miles, practically from his own backyard! That to me is monumental beyond calculation alone, with science, observation, reasoning, mathematics working in concert. Likely, any deviation mostly due to the limited accuracy of instruments.
And one more thing; he wasn't first but KNEW earth was spherical.

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