1. Parallel planes intercept equal segments on parallel lines.
2. Parallel lines intersecting the same plane make equal angles with it.
3. A right line intersecting parallel planes makes equal angles with them.
PROP. XVII.—Theorem.
If two parallel lines (AB, CD) be cut by three parallel planes (GH, KL, MN) in two triads of points (A, E, B; C, F, D), their segments between those points are proportional.
Dem.—Join AC, BD, AD. Let AD meet the plane KL in X. Join EX, XF. Then because the parallel planes KL, MN are cut by the plane ABD in the lines EX, BD, these lines are parallel [XI. xvi.]. Hence
In like manner,
