Definition: 1.02: Line, Curve
And a line is a length without breadth.
Modern Definition
A curve (or a curved line) \(g\) is a connected subset of a Euclidean metric space \(A\in\mathbb R^n\) such that taking away a point \(A\in g\) disconnects \(g\).
Example of two curves in a plane:
Table of Contents
Explanations: 1
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclidâ€™s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"