If two planes cut one another, their common section is a straight line.
如果两个平面彼此相交，则它们的公共交线是一条直线。
For let the two planes AB, BC cut one another, and let the line DB be their common section; I say that the line DB is a straight line. For, if not, from D to B let the straight line DEB be joined in the plane AB, and in the plane BC the straight line DFB.
设两平面AB和BC相交，其公共交线为DB。
Then the two straight lines DEB, DFB will have the same extremities, and will clearly enclose an area: which is absurd.
假设DB不是直线，则在平面AB内连接D到B的直线DEB，在平面BC内连接D到B的直线DFB。
Therefore DEB, DFB are not straight lines.
于是两条直线DEB和DFB有相同的端点，并围成一个区域，这是不可能的。
Similarly we can prove that neither will there be any other straight line joined from D to B except DB the common section of the planes AB, BC.
因此DEB和DFB不是直线，同理可证除DB外没有其他直线连接D和B，故DB是直线。