Of all lines which have the same extremities the straight line is the…

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Of all lines which have the same extremities the straight line is the… — Archimedes · Smartyfair

Of all lines which have the same extremities the straight line is the least.

Source foundScience

In plain words

Between two points, the straight path is always the shortest one. Every bend makes the trip longer.

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How sure this is: 95% sureThese words were traced back to where they first appeared. That source is listed below.
What turned up: On the Sphere and Cylinder, Book I, Assumption 1, c. 225 BC; trans. T. L. Heath, The Works of Archimedes (1897), p. 3.
Work: On the Sphere and Cylinder, Book I, Assumption 1; trans. T. L. Heath, 1897
Occasion: c. 225 BC · Syracuse, Sicily · the first assumption of his book on spheres and cylinders — the ancestor of 'a straight line is the shortest path'
Sources checked: archive.orgChecked using claude-fable-5, 22 August 2026Full djvu text read this pass; Assumption 1 verbatim in the treatise's own ASSUMPTIONS list (not Heath's commentary — his footnote calls it 'this well-known Archimedean assumption', citing Proclus). Complete standalone postulate; ancestor of the proverb 'a straight line is the shortest distance'.