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:

Explanations: 1

Definitions: 1 2 3 4 5 6 7
Explanations: 8

Thank you to the contributors under CC BY-SA 4.0!



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"

Adapted from (subject to copyright, with kind permission)

  1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"