第11卷命题 1 · 直线不能部分在参考平面部分在更高平面

For, if possible, let a part AB of the straight line ABC be in the plane of reference, and a part BC in a plane more elevated.

假设可能，设直线ABC的一部分AB在参考平面内，另一部分BC在更高平面内。

There will then be in the plane of reference some straight line continuous with AB in a straight line.

则在参考平面内存在与AB成一直线的直线，设其为BD。

Let it be BD; therefore AB is a common segment of the two straight lines ABC, ABD: which is impossible, inasmuch as, if we describe a circle with centre B and distance AB, the diameters will cut off unequal circumferences of the circle.

因此AB是两条直线ABC和ABD的公共线段，这是不可能的。

因为以B为圆心、AB为半径画圆，直径会截出不相等的圆弧。