PROPERTIES of the CIRCLE. 6y 



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 SS the angle CAD. 



t. 

 AC 

 Therefore CD = CF, and AD = AF. But CD = ^r. Confe- 



quently gp = f^s, which has to BC the ratio of AG 



toBC 3 . Q;.E. D. 



Cor. i. BD = perpendicular BG; GF == the chord AE of 

 double the arc AC = twice the fine of the arc AC 



AB X BG AB X BD , - Br , . . c ^=% 

 Cor. 2. — ^ — , or gr; — , has to BC, the ratio of AB 



toBC 3 . 



3 __ AC 6 -^3 _ AB 6 —3 AC* X CD* r 

 Cor. j. CF - w , BG _ — CF = ^^ X 



BC m ACWXIC and = ABW x Bc = 

 BC BC 



AB X BG x BC j and the lines, which have to BC the ratios of 

 BC 





AC : BC ; and AB : BC are to each other as AC X CD to 

 AB x BD, or as AC xCF : AB X BG. 



1 2 See 



