Proof: By Euclid
(related to Proposition: Prop. 11.01: Straight Line cannot be in Two Planes)
∎
^{1}
 For, if possible, let some part, $AB$, of the straight line $ABC$ be in a reference plane, and some part, $BC$, in a more elevated (plane).
 In the reference plane, there will be some straight line continuous with, and straighton to, $AB$.^{2}
 Let it be $BD$.
 Thus, $AB$ is a common segment of the two (different) straight lines $ABC$ and $ABD$.
 The very thing is impossible, inasmuch as if we draw a circle with center $B$ and radius $AB$ then the diameters ($ABD$ and $ABC$) will cut off unequal circumferences of the circle.
 Thus, some part of a straight line cannot be in a reference plane, and (some part) in a more elevated (plane).
 (Which is) the very thing it was required to show.
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References
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"
Footnotes