If two planes cut one another
, their common section is a straight line.
For let the two planes AB
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
let the straight line DEB
be joined in the plane AB
, and in the plane BC
the straight line DFB
Then the two straight lines DEB
will have the same extremities, and will clearly enclose an area: which is absurd.
are not straight lines.
Similarly we can prove that neither will there be any other straight line joined from D
the common section of the planes AB
Therefore etc. Q. E. D.