Ideas from 'fragments/reports' by Archimedes [240 BCE], by Theme Structure

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6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Archimedes defined a straight line as the shortest distance between two points
                        Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.
                        From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13
                        A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry.