the points a, b, c, d are coplanar.
12. If in the last exercise the intersecting plane be parallel to any two sides of the quadrilateral, it cuts the two remaining sides proportionally.
Def. x.—If at the vertex O of a trihedral angle O—ABC we draw normals OA′, OB′, OC′ to the faces OBC, OCA, OAB, respectively, in such a manner that OA′ will be on the same side of the plane OBC as OA, &c., the trihedral angle O—A′B′C′ is called the supplementary of the trihedral angle O—ABC.
13. If O—A′B′C′ be the supplementary of O—ABC, prove that O—ABC is the supplementary of O—A′B′C′.
14. If two trihedral angles be supplementary, each dihedral angle of one is the supplement of the corresponding face angle of the other.
15. Through a given point draw a right line which will meet two non-coplanar lines.
16. Draw a right line parallel to a given line, which will meet two non-coplanar lines.
17. Being given an angle AOB, the locus of all the points P of space, such that the sum of the projections of the line OP on OA and OB may be constant, is a plane.
APPENDIX.
PRISM, PYRAMID, CYLINDER, SPHERE, AND CONE
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DEFINITIONS.