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

67, 68] LIMITING-CURVE COORDINATES 117
cut off an arc of length r (OA) on the Limiting-Curve through
o. (Fig. 79.)
(i, 7) are called the Limiting-Curve Coordinates of the
point P.
Now take another point Q with coordinates
(6+ e8, +e).
Let the Limiting-Curve through Q cut the axis of x (the
axis through O) at Q0.
Let the Limiting-Curve through P be cut by the axis through
Q at S, and the Limiting-Curve through Q by the axis through
P in R.
Also, let A and B be the points where the Limiting-Curve
through O is cut by the axes through P and Q.
B
O P Q --
FIG. 80.
Then we have
arc OA =, arc OB = I + 6i,OP0 =, OQ = +-
It follows from the properties of Concentric LimitingCurves [~ 55], that
arc QR = 86 e k.'. arc QR = di e k, to the first order.