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Ideas for 'Physics', 'Phaedrus' and 'Elements of Geometry'

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6 ideas

6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry

22278

Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]

8673	Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]

10250

Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]

10302

Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]

14157

Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic

1600	Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]