[ 437 T 
tile fine of the arc GI to the line of the arc I K, 
that is, as the fine of the angle GAI to the fine 
of the angle I A K. Therefore, the fine of the 
angle I A K (—2 IAC -}- GAI) is equal to three 
times the fine of the angle GAIj but GAI is the 
complement of AGB, and IAC the complement of 
ABG. 
COROL. 3, 
If (Fig. 3.) any line BN be drawn to divide the’ 
angle ABG, and AN be joined,. alfo AO be drawn, 
perpendicular to BN, and continued to the circle: 
in P, the fine of the angle compofed of NAP 
and 2PAC will be lefs than three times the fine of 
the angle N A P. Draw N QR perpendicular to 
AB, cutting A P in S .; join AR, and draw Q_T 
perpendicular to BN, and parallel to AO; then 
BQ^= NBT. But BQ^is greater than the recN 
angle ESC, that is, greater than the redtangle 
NBV, under the two fegments of the line BN 
drawn from B, to cut the circle in N and V : 
therefore, TB is greater than YB, and NO greater 
than O T. Conlequently NS is greater than S Q ? 
Hence RS is lefs than three times NS j. and there- 
fore, the fine of the angle PAR (zr NAP4-2PAC) 
is left than three times the fine of NAP. 
Erobls >1 
