13. As may be seen, the instrument composed of three firmly united
rulers is the simplest of all and easy to use. Any one can construct it
for himself with a piece of cardboard, and give the angle 2 [alpha] the
value that he thinks most suitable for each application. The greater
2 [alpha] is, the shorter is the distance at which we should put the
needles for a given point of meeting.
14 The jointed instrument may be constructed as shown in Figs 8, 9, and
10. The three pieces, A. B, and C, united by a pivot, O, in which there
is a small hole, are of brass or other metal. Rulers may be easily
procured of any length whatever. The instrument is Y-shaped. In the
particular case in which [alpha] = 180° it becomes T-shaped, and serves
to draw parallel lines.
[Illustration: Fig. 8, Fig. 9, Fig. 10]
15. The instrument may be used likewise, as we have seen, to draw arcs
of circles of the diameter C I or of the radius A O = r, whose center o
falls outside the paper. The pencil will be rested on C. We may operate
as follows (Fig. 2): Being given the direction of the radii A O and B
O, or, what amounts to the same thing, the tangents to the curve at the
given points, A and B to be united, we draw the line A D and raise at
its center the perpendicular D C, which, prolonged, passes necessarily
through the center. It is necessary to calculate the length C D.