On Indivisible Lines
The treatise criticizes the existence of minimal lines that could not be divided. It examines geometrical and philosophical arguments about magnitudes, points and the composition of the continuum.
Understanding the text
Its author is uncertain; the setting is Academic and Peripatetic debate concerning mathematical entities.
Transmitted under Aristotle’s name; personal authorship is disputed or rejected.
Key points
- 01
Continuity
A continuous magnitude cannot simply be understood as an assembly of units without extension.
- 02
Points and lines
Confusing a line’s limit with its smallest constituent part produces conceptual difficulties.
- 03
Refutation
The inquiry proceeds by examining opponents’ arguments rather than presenting a complete mathematical system.
How to read it
Distinguish point, segment and measure before reconstructing objections, then compare the Physics on infinity.
Editions & sources
- Consult the reference 1loebclassics.comnew tab
- Consult the reference 2plato.stanford.edunew tab
- Consult the reference 3classics.mit.edunew tab
Summaries and key points are original editorial interpretations. They accompany reading the work and do not replace an edition of the text. Editorial method ↗