Source edition
Aristotle. Aristotelis Opera, Volume 6. Bekker, Immanuel, editor. Oxford: Oxford University Press, 1837.
Source data
Open Greek and Latin · CC BY-SA 4.0
Cloned and adapted by Humanitext, with ongoing edits.
Summary
This treatise addresses the ancient geometrical and philosophical debate surrounding the infinite divisibility of space and lines, critically examining the theory that 'indivisible lines' exist. In the opening, the author presents the primary physical and metaphysical arguments used to defend indivisible lines, but immediately launches into a systematic refutation. In the middle section, the work demonstrates how such indivisible units contradict established geometrical principles, including Zeno's paradoxes, proportions, and the Pythagorean theorem. The critique then shifts to the view that lines are composed of points, exposing the geometrical absurdities that arise from the contact and overlapping of points. Finally, the author demonstrates the impossibility of extracting points from lines, concluding that a point can be neither a minimal constituent nor a joint of a line, thereby defending the continuous nature of geometrical magnitudes.