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University. The Reader who wishes for farther infor-
mation, is referred to Professor Woodhouse's treatise, or
that of Cagnoli, to the latter of which are appended
extensive Tables of trigonometrical formulæ.

From this performance the only credit expected is
that of having endeavoured to place principles in a clear
light, and to render a service to the younger

students by
setting before them a series of Problems, on the solution
of which they are recommended to exercise their own
ingenuity; for which purpose a table of Contents has
been prefixed.

a

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.

16. To trisect a right angle.

17. To trisect a given finite straight line.

18. To divide a given straight line into any number of equal

parts.

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

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in any point, so that those from the extremities of the second pro-

portional may be perpendicular to each other; the line drawn from

the extremity of this proportional will bisect the angle formed by the

lines drawn from the extremities of the other two.

21. If a straight line be drawn through any point in the line

bisecting a given angle, and produced to cut the sides containing

that angle, as also a line drawn from the angle perpendicular to the

bisecting line; it will be harmonically divided.

22. If from a given point there be drawn three straight lines

forming angles less than right angles, and from another given point

without them a line be drawn intersecting the others, so as to be

barmonically divided; then will all lines drawn from that point

meeting the three lines be harmonically divided.

23. If a straight line be divided into two equal and also into

two unequal parts, and be produced, so that the part produced may

have to the whole line so produced, the same ratio that the unequal

segments of the line have to each other; then shall the distances of

the point of unequal section from one extremity of the given live,

from its middle point, from the extremity of the part produced, and

from the other extremity of the given line, be proportionals.

24. Three points being given; to determine another, through

which if any straight line be drawn, perpendiculars upon it from two

of the former shall together be equal to the perpendicular from the

third.

25. From a given point in one of two straight lines given in

position, to draw a line to cut the other, so that if from the point

of intersectiou a perpendicular be let fall upon the former, the seg-

ment intercepted between it and the given point together with the

first drawn line may be equal to a given line.

26. One of the lines which contain a given angle is also given.

To determine a point in it such that if from thence to the indefinite

line there be drawn a line having a given ratio to that segment of it

which is adjacent to the given angle; the line so drawn and the

other segment of the given line may together be equal to another

given line.

27. Two straight lines and a point in each are given in position;
to determine the position of another point in each, so that the straight

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