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versity. The Reader who wishes for farther information,
From this performance the only credit expected is
ingenuity; for which purpose a table of Contents has
To the Syndics of the University Press, who from
9. From a given point between two indefinite straight lines given
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.
16. To trisect a right angle. K4.
17. To trisect a given finite straight line
18. To divide a given straight line into any number of equal
Cor. To divide a straight line into any number of parts having
a given ratio.
19. To divide a given finite straight line harmonically:
20. If a given finite straight line be harmonically divided, and
from its extremities and the points of division lines be drawn to meet
21. If a straight line be drawu through any point in the line
to determine the position of another point in each, so that the straight
30. The length of one of two lines, which contain a given angle