Euclid's first common notion is this: Things which are equal to the same things are equal to each other. That's a rule of mathematical reasoning and its true because it works - has done and always will do. In his book Euclid says this is self evident. You see there it is even in that 2000 year old book of mechanical law it is the self evident truth that things which are equal to the same things are equal to each other.
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