Engineers and Architects of Rome.]


1. LET A and B be two fixed points and A C and C B two straight lines
converging at C and moving in their plane so as to always remain based
on this point (Fig. 1). The geometrical place of the positions occupied
by C is the circumference of the circle which passes through the three
points A, B, and C. Now let C F be a straight line passing through C. On
prolonging it, it will meet the circumference A C B I at a point I. If
the system of three converging--lines takes a new position A C' F B,
it is evident F' B' prolonged will pass through I, because the angles
[alpha] and [beta] are invariable for any position whatever of the
system.

[Illustration: Fig. 1.]

2. In the particular case in which [alpha] = [beta] (Fig. 2), the point
I is found at the extremity of the diameter, and, consequently, for a
given distance A B, or for a given length C D, such point will be at its
maximum distance from C.

[Illustration: Fig. 2.]

3. This granted, it is easy to construct an instrument suitable for
drawing converging lines which shall prove useful to all those who have
to do with practical perspective. For this purpose it is only necessary
to take three rulers united at C (Fig. 3), to rest the two A C and C B
against two points or needles A and B, and to draw the lines with the
ruler C F, in placing the system (Sec. 1) in all positions possible. The
three rulers may be inclined in any way whatever toward each other, but