Explanation: How a line is different from a solid and a surface?

(related to Definition: 1.02: Line, Curve)

A line is a space of one dimension. If it had any breadth, no matter how small, it would be space of two dimensions, i.e. a surface; and if in addition, it had any thickness it would be space of three dimensions, i.e. a solid; hence a line has neither breadth nor thickness.

The modern definition of a line is a combined set-theoretic and topologic one. A line has been defined as a subset of another set fulfilling the topological property that if we take away a point from it, it will be disconnected. Connectivity is a topological property.

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Adapted from CC BY-SA 3.0 Sources:

  1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

  1. Casey, John: "The First Six Books of the Elements of Euclid"