Proposition 19 . If two planes which cut one another are at right angles to any plane, then their intersection is also at right angles to the same plane. Proposition 20 . If a solid angle is contained by three plane angles, then the sum of any two is greater than the remaining one. Proposition 21 .
Any solid angle is contained by plane angles whose sum is less than four right angles.
If there are three plane angles such that the sum of any two is greater than the remaining one, and they are contained by equal straight lines, then it is possible to construct a triangle out of the straight lines joining the ends of the equal straight lines. Proposition 23 . Lemma for XI.23. Proposition 24 . If a solid is contained by parallel planes, then the opposite planes in it are equal and parallelogrammic.