more from Euclid

Single Idea 22278

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry]

Full Idea

Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms.

Gist of Idea

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


comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim'

Book Reference

Potter,Michael: 'The Rise of Anaytic Philosophy 1879-1930' [Routledge 2020], p.21

A Reaction

I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone!