Full Idea
A line is a continuous quantity. For it is possible to find a common boundary at which its parts join together, a point.
Gist of Idea
Parts of a line join at a point, so it is continuous
Source
Aristotle (Categories [c.331 BCE], 04b33)
Book Reference
Aristotle: 'Categories and De Interpretatione', ed/tr. Ackrill,J.R. [OUP 1963], p.13
A Reaction
This appears to be the essential concept of a Dedekind cut. It seems to be an open question whether a cut defines a unique number, but a boundary seems to be intrinsically unique. Aristotle wins again.