[ssener2001]

I agree.Obtaining this formula by observing is more difficult than obtaining it by proving it. Besides, it is an issue that is already needed in field work. If you have pen, paper and a good number system, it shouldn't be too difficult to find the formula with shapes.

[loa_in_]

I imagine back then things like number systems and methods of proving were just made up as they go.

[lazide]

Clay tablets and a stylus also less convenient than pen and paper.