9. From a given point between two indefinite straight lines given
in position, to draw a line which shall be terminated by the given
lines, and bisected in the given point.
10. From a given point without two indefinite straight lines
given in position, to draw a line such that the parts intercepted by
the point and the lines may have a given ratio.
11. From a given point to draw a straight line which shall cut
off from lines containing a given angle, segments that shall have a
given ratio.
12. If from a given point any number of straight lines be drawn
to a straight line given in position; to determine the locus of the
points of section, which divide them in a given ratio.
13. A straight line being drawn parallel to one of the lines con-
taining a given angle, and produced to meet the other; through a
given point within the angle to draw a line cutting the other three,
so that the part intercepted between the two parallel lines may have
a given ratio to the part intercepted between the given point and
the other line.
14. Two parallel lines being given in position; to draw a third
such, that if from any point in it lines be drawn at given angles to
the parallel lines, the intercepted parts may have a given ratio.
15. If three straight lines drawn from the same point and in the
same direction be in continued proportion, and from that point also
a line equal to the mean proportional be inclined at any angle; the
lines joining the extremity of this line and of the proportionals will
contain equal angles.