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.