Definition: 1.03: Intersections of Lines

And the extremities of a line are points.

Modern Definition

Given two lines \(g\) and \(h\) with \(g\cap h=A\), where \(A\) is a point, we say that \(g\) and \(h\) intersect at the point \(A\).

If \(g\cap h=\{A_1,A_2,\ldots\}\), where \(A_1,A_2,\ldots\) are all points, we say that \(g\) and \(h\) intersect at the points \(A_1,A_2,\ldots\).

If \(g\cap h=\emptyset\), we say that \(g\) and \(h\) do not intersect.

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"