particular case in which [alpha] = 180 deg. 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.

We shall have

___ ___ ___
CD (2r - CD) = AD squared.CD squared - 2r.CD + AD squared = o.

[TEX: CD (2r - CD) = \overline{AD^2}.\overline{CD^2} - 2r.CD +
\overline{AD^2} = o.]

_________
/ ___
CD = r +- \ / r squared - AD squared .
\/

[TEX: CD = r +- \sqrt{r^2 - \overline{AD^2}}.]

It is evident that the lower sign alone suits our case, for d < r;