Proof: By Euclid

∎

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 straight-on 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.

fig01e

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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The proofs of the first three propositions in this book are not at all rigorous. Hence, these three propositions should properly be regarded as additional axioms (translator's note) ↩
This assumption essentially presupposes the validity of the proposition under discussion (translator's note). ↩