PROBLEMS
1. Given four lines in the plane, to construct another which shall meet them in four harmonic points.
2. Where are all such lines found?
3. Given any five lines in the plane, construct on each the point of contact with the conic tangent to them all.
4. Given four lines and the point of contact on one, to construct the conic. ("To construct the conic" means here to draw as many other tangents as may be desired.)
5. Given three lines and the point of contact on two of them, to construct the conic.
6. Given four lines and the line at infinity, to construct the conic.
7. Given three lines and the line at infinity, together with the point of contact at infinity, to construct the conic.
8. Given three lines, two of which are asymptotes, to construct the conic.
9. Given five tangents to a conic, to draw a tangent which shall be parallel to any one of them.
10. The lines a, b, c are drawn parallel to each other. The lines a', b', c' are also drawn parallel to each other. Show why the lines (ab', a'b), (bc', b'c), (ca', c'a) meet in a point. (In problems 6 to 10 inclusive, parallel lines are to be drawn.)