For let the two planes < A B >, < B C > be at right angles to the plane of reference, and let / B D / be their common section; I say that / B D / is at right angles to the plane of reference.
For suppose it is not, and from the pointD let / D E / be drawn in the plane < A B > at right angles to the straight line/ A D /, and / D F / in the plane < B C > at right angles to / C D /.
Now, since the plane < A B > is at right angles to the plane of reference, and / D E / has been drawn in the plane < A B > at right angles to / A D /, their common section,
[G.521]therefore / D E / is at right angles to the plane of reference.
Similarly we can prove that / D F / is also at right angles to the plane of reference.
Therefore from the same point D two straight lines have been set up at right angles to the plane of reference on the same side: which is impossible. [G.515]
Therefore no straight line except the common section / D B / of the planes < A B >, < B C > can be set up from the point D at right angles to the plane of reference.
