Is there any way of obtaining the area of an ellipse without using calculus?

AI Thread Summary
The discussion centers on finding the area of an ellipse without using calculus. Participants express curiosity about alternative methods and seek hints for non-calculus approaches. There is a reference to Apollonius's work, questioning whether the area of an ellipse could be determined prior to calculus. The mention of Newton suggests that earlier mathematicians may not have had the tools to derive the area without calculus. Overall, the conversation highlights the historical context and challenges of deriving the area of an ellipse.
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If so, can I get a hint on how to do it?

I did a text search for a proof in "Conics" by Apollonius, but couldn't find one. If they couldn't prove it without calculus it means they had to wait until at least Newton's time to find the area of an ellipse?
 
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