From the same point two straight lines cannot be set up at right angles to the same plane on the same side.

For, if possible, from the same point *A* let the two straight lines *AB* and *AC* be set up at right angles to the plane of reference and on the same side.

Draw a plane through *BA* and *AC.* It intersects the plane of reference in a straight line through *A.* Let the line be *DAE.*

Therefore the straight lines *AB, AC,* and *DAE* lie in one plane. And, since *CA* is at right angles to the plane of reference, it also makes right angles with all the straight lines which meet it and lie in the plane of reference.

But *DAE* meets it and lies in the plane of reference, therefore the angle *CAE* is right. For the same reason the angle *BAE* is also right. Therefore the angle *CAE* equals the angle *BAE.*

And they lie in one plane, which is impossible.

Therefore, *from the same point two straight lines cannot be set up at right angles to the same plane on the same side.*

Q.E.D.