two given lines. Draw through _P_ a line parallel to this line. This is
the required line.

*3.* Given a parallelogram in the same plane with a given segment _AC_,
to construct linearly the middle point of _AC_.

*4.* Given four harmonic lines, of which one pair are at right angles to
each other, show that the other pair make equal angles with them. This is
a theorem of which frequent use will be made.

*5.* Given the middle point of a line segment, to draw a line parallel to
the segment and passing through a given point.

*6.* A line is drawn cutting the sides of a triangle _ABC_ in the points
_A’_, _B’_, _C’_ the point _A’_ lying on the side _BC_, etc. The harmonic
conjugate of _A’_ with respect to _B_ and _C_ is then constructed and
called _A"_. Similarly, _B"_ and _C"_ are constructed. Show that _A"B"C"_
lie on a straight line. Find other sets of three points on a line in the
figure. Find also sets of three lines through a point.





CHAPTER III - COMBINATION OF TWO PROJECTIVELY RELATED FUNDAMENTAL FORMS




[Figure 9]