I think it is safe to say that 14'th century mathematicians were not reading "sources dating to Babylonian times"--certainly not cuneiform tablets. Independent discovery.On the other hand, the Babylonians are known to have had procedures for solving certain classes of binomial equation, and it wouldn't surprise me to find that they were using this kind of estimate for area estimation. Without more details I can't tell if they understood about taking the limit--that would surprise me, and would be a grim reminder of how much can be lost and how easily. See Lucio Russo
What I am given to understand is that ancient Babylonian math was better than ancient Greek math, just because the Babylonians were only interested in accuracy of calculation and not in understanding why it worked. The Greeks would reject things that didn't make sense, and try to find methods that both worked and were comprehensible. The Babylonians were happy with a method that produced accurate results, and thus were better at the tasks of the day -- navigation and astronomy, say. A lot has been lost, though, and even scholars of ancient knowledge are putting together a picture from pictures of pictures. As James says, nobody was reading cuneiform again until quite recently.
I didn't even notice that someone in the article suggested the 14th-century Europeans were influenced by this old Babylonian art--I assumed it was an independent discovery. I was just amazed that it had been figured out so long ago and then forgotten.
The Babylonians were happy with a method that produced accurate results, and thus were better at the tasks of the day -- navigation and astronomy, say. Sounds like my method. It also reminds me of the Chinese room problem.If you know the rules to a cipher, you can decipher it, and pass it on, for someone else to understand. Even if you do not understand the language the cipher was used on.
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