PROPERTIES of the CIRCLE. 67 
the chord to the tangent to the circle at the other extremity, or 
a fourth proportional to the diameter, the chord and verfed fine 
of the arc AC. 
For, the angle CAF = the angle ABC = the angle CAD. 
Therefore CD ='CF, and AD = AF. But CD = Confe- 
BC 
| AcscoD:! AC* Ho": a 
quently = = 8@ which has to BC the ratio of AG’ 
to BC: Q.E.D. 
Cor. 1. BD = perpendicular BG ; GF = the chord AE of 
double the arc AC = twice the fine of the arc AC. 
ABXBG _ABXBD 
Cor. 2. Ba or—3q? has to BC, the ratio of AB 
to BC. 
6 
Cor. 3 CF = a BG = CF =2 si “ 
BC = AC aor XE ack BG ah Pte BG = 
BG BC 
AB 2 Bi x BC ; and the lines, which have to BC the ratios of 
Paka dal, Ears 9 ed | 
AC: BC ; and AB: BG are to each other as ACXGD to 
AB x BD, or as ACx CF : ABx BG. 
T2 ‘ SEE 
