Definition: 1.06: Intersections of Surfaces

And the extremities of a surface are lines.

Modern Definition

Given two surfaces \(s\) and \(t\) with \(s\cap t=g\), where \(g\) is a line, we say that \(s\) and \(t\) intersect at the line \(g\).

If \(s\cap t=\{g_1,g_2,\ldots\}\), where \(g_1,g_2,\ldots\) are all lines, we say that \(s\) and \(t\) intersect at the lines \(g_1,g_2,\ldots\).

If \(s\cap t=\emptyset\), we say that \(s\) and \(t\) 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"