Aristotle, On Indivisible Lines

LCL 307: 414-415

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This is a most interesting and extremely difficult treatise, written by some author of the Peripatetic School. It refers directly to Euclid’s Elementa, Book X., and is unintelligible without some understanding of Euclid’s definitions. Unfortunately the condition of the manuscripts is most unsatisfactory. By kind permission of Messrs. Teubner, Apelt’s text has been used for this volume. This together with his comments in the Introduction has elucidated a number of difficulties, but, even so, the thought as well as the terminology is involved. The treatise is mainly concerned with a refutation of the theory that every line contains a unit which is an indivisible line. Without the modern view of infinity, there is much which is mathematically brilliant, and on his own terms the author seems to prove his case. The main argument is a syllogism:

All lines consist of indivisible lines (Zeno). All indivisible lines are points. ∴ all lines consist of points.

Aristotle then demonstrates the absurdity of this conclusion, thus demolishing the major premiss.

DOI: 10.4159/DLCL.aristotle-divisible_lines.1936