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.
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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"