The GRA wrote a sefer on geometry called Ayil Meshulash available to download at https://hebrewbooks dot org/20713. He has an interesting algebraic proof on the Pythagorean Theorem.
See also the Shut Chavas Yair at Siman 172.
Sometimes we can understand a mishna with a secular theorem, הזהב קונה את הכסף. There is a law in economics called Gresham’s Law. The bad coin drives out the good coin from circulation. Gold would be a good coin so people don’t use it as a currency but hoard it and it becomes a commodity. So silver is the currency. When meshicha is koneh, through acquiring the commodity we acquire the currency. The more valuable acquires the less valuable.
Menu