i'm a physicist and i'm enjoying studying geometry. What i dont understand is why the euclidean geometry system doesn't respect the modern formulation of a deductive system. Can you explain this completely ?
2026-03-27 13:46:09.1774619169
Why Euclidean Geometry is not a modern deductive system?
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Euclid fails to account for all assumptions he makes. Take, for instance, the first theorem of the elements, that you can erect an equilateral triangle on any segment. In the proof he assumes that two circles which look like they ought to intersect actually intersect in a point. This is not started anywhere, neither as an axiom nor as a theorem.