I'm having a hard time gathering my thoughts about this. I'm trying to find a connection or some sort of relation between the first 3 axioms (postulates) of Euclidean geometry (though around Aristotle's time it wasn't called Euclidean geometry yet, but the concepts were there) and Aristotle's theory of elements and motion.
I know that Aristotle believed that elements move on a straight line according to their 'weight' (heavy to light), and that objects have 2 natural movements, towards the center of the earth (downwards) or further from the center of the earth (upwards). So that I think kind of covers the first geometrical axiom, of a straight line between 2 points. What about the other two?
I'm aware of his adoption of Eudoxus geometrical planetary movements model and his uniform circular motion of the planets, but I can't seem to think of a way to connect them in any way to the geometrical axioms.
Any ideas, guys?