From the same point two straight lines cannot be set up at right angles to the same plane on the same side.
从同一点在同一平面的同侧不能作两条直线垂直于该平面。
For, if possible, from the same point A let the two straight lines AB, AC be set up at right angles to the plane of reference and on the same side, and let a plane be drawn through BA, AC; it will then make, as section through A in the plane of reference, a straight line. [XI. 3] Let it make DAE; therefore the straight lines AB, AC, DAE are in one plane.
假设可能，从同一点A作两条直线AB、AC垂直于参考平面且在同侧。
And, since CA is at right angles to the plane of reference, it will also make right angles with all the straight lines which meet it and are in the plane of reference.
过BA、AC作平面，该平面与参考平面交于过A的直线DAE。
[XI. Def. 3] But DAE meets it and is 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 is equal to the angle BAE.
因为CA垂直于参考平面，所以CA与参考平面内所有过A的直线成直角，故角CAE为直角；同理角BAE也为直角。
And they are in one plane: which is impossible.
因此角CAE等于角BAE，且它们在同一平面内，矛盾。