Kitap 11
2
For, if part of the triangle ECB, either FHC or GBK, is in the plane of reference, and the rest in another, a part also of one of the straight lines EC, EB will be in the plane of reference, and a part in another.
2
But, if the part FCBG of the triangle ECB be in the plane of reference, and the rest in another, a part also of both the straight lines EC, EB will be in the plane of reference and a part in another: which was proved absurd. [XI. 1]
2
Therefore the triangle ECB is in one plane.
2
But, in whatever plane the triangle ECB is, in that plane also is each of the straight lines EC, EB, and, in whatever plane each of the straight lines EC, EB is, in that plane are AB, CD also. [XI. 1]
2
Therefore the straight lines AB, CD are in one plane, and every triangle is in one plane. Q. E. D.
PROPOSITION 3.
3
If two planes cut one another, their common section is a straight line.
3
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.
3
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.
3
Then the two straight lines DEB, DFB will have the same extremities, and will clearly enclose an area: which is absurd.
3
Therefore DEB, DFB are not straight lines.
3
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.
3
Therefore etc. Q. E. D.
PROPOSITION 4.
