Fig. 7.
In other terms, Ci is the reduction to the scale of CI.
I describe the circumference C b i a, and arrange the instrument as seen in the figure, and measure the length C b.
It is visible that
C i 1 C b C d
----- = --- = ----- = ------; then C B = n.C b (5)
C I n C B C D
CD = n.C d; (6)
and, consequently, the position of the needles which are found at A and B are determined.
12. The question treated in § 10, then, is simply solved. In fact, on describing the circumference C b i a with any radius whatever, I shall have
C B
n = -----; (7)
c b