The elements of non-Euclidean plane geometry and trigonometry, by H. S. Carslaw.

54, 55] CONCENTRIC LIMITING-CURVES

93

Then we know from (2) that the arc BB'=m times the arc
BQ, and that the arc BB"=n times the arc BQ.
A
B
A 1
B"
A"l
FIG. 64.
Thus the proportion follows.
Secondly, if the arcs are incommensurable, we reach the
same conclusion by proceeding to the limit.
A
Al
2
B
FIG. 65.
~ 55., Let us start with a Limiting-Curve whose centre is ~,
and take any two points A and B upon the curve (Fig. 65).