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Euclid's Elements
In Our Time: Science
The Four Axioms of Geometry
Without the definitions and postulates, you can't go anywhere. A lot of mathematicians thought the fifth postulate could be proved from the previous four. And this was to cause a lot of problems later on. We then also have some common notions - these are the sort of logical axioms if you like. They're things to do with magnitude. If you have equals and you add equal parts to them, the holes are equals.
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