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

144

144 NON-EUCLIDEAN GEOMETRY [O.VI

[CH. VIL

From ~ 81 (III.), applied to the acute angles den and
bern, we have eb < cd, cm:cb < cC:co, and en e d < cC:cO.
From the second of these relations we have
Cm Cc<Cc cb,
Ss Ss Ss co
/Bb Bbr\Cc Cc cb
Ss Cm Ss Ss co
Then, by ~83, if Ss, and thus Bb and Cm tend to zero,
we have
Bb
Lt = (x - )
LtBb=
Lt ~-= Wk()
Further, Ltcb=CB=y and Ltco=CO=V-x.
Therefore, from (CL), we have
q$(x- y) y 0(
ite. /)(x - Y) - 0(x) (y _ (pW0 x.>...y).. (3)
cn cC
Again, from the inequality -d< -, we have in the same way
Adding (/3) and (y), we have
since k5 (x), 0/ (y) are each less than unity. It follows that
k5 (x) is a continuous function of x.