and, consequently,
C I = n.C i (8)
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 α the value that he thinks most suitable for each application. The greater 2 α 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 α = 180° it becomes T-shaped, and serves to draw parallel lines.
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.
We shall have
