[ 9 2 3 J 
diately to depend, was introduced by Regiomontanus, 
and is dill retained, as the foundation of the prefent 
methods of computing logarithmically an angle from 
the three fides of a fpherical triangle given, though 
they may be demonftrated more diredtly by the fol- 
lowing lemma. 
In the circle ABC, the chord A C being drawn, 
and the arch ABC bifedted in B, if D be taken in 
the circle at pleafure, and the lines B E, D F drawn 
alfo at pleafure parallel to each other, one terminated 
by the circle in E, and the other by the chord A C 
in F > then AD, DC being drawn, BE x DFis = 
A D x D C. 
Draw D H perpendicular to A C, and alfo the 
diameter BG, joining EG. Then the angles FDH, 
E B G are equal, and the angles D HF, BEG right. 
Therefore BE is to BG as DH to DF, and BE x DF 
= BG x DH = AD x DC. 
Vol. LI. 
6 C 
Now, 
