Single Idea 13007

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

Full Idea

Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points.

Gist of Idea

Archimedes defined a straight line as the shortest distance between two points

Source

report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13

Book Reference

Leibniz,Gottfried: 'New Essays on Human Understanding', ed/tr. Remnant/Bennett [CUP 1996], p.451


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.