Lawson's Geometrical Theorems. 489 
circle, and the angles FIE — FSE. Also 
DG .GN + FG? ~ (TG. GT’) G1. 
F@’ +. FG =F@’. FlI= FD’. FN =Fh 
. FE, therefore h, G’, 1, E are in a circle, 
consequently the angle HhR = ESR, and 
the sum of the angles EhR. FIE is equal 
to two right ones, therefore the sum of 
their equals ESR, ESF must be equal to 
two right, and F, S, R ina right line. 
Which is the thirty-fourth Proposition. 
Dracram V. 
' To any point g” in TT’ from the center 
ndrawn g’n, perpendicular to which thro’ 
g’ draw ba cutting the two tangents in a 
and b ; then the angles at 'T and g’ being 
right, the points g’, a, 'T’, n are in a circle, 
and the angle nag’ = nT'g’ =nI’g’; again 
34 
of contact, and another line to be intercepted between the 
tangents cut the foregoing which joins the point of contact, 
so as to be bisected in the point of intersection; then I say 
that the part of that line which is a chord of the circle will 
also be bisected by the same point. 
And, conversely, if the chord cutting the Jine joining 
the points of contact be bisected by the point of intersec- 
tion; then the continuation of the same to meet the tan- 
gents will also be bisected by the same point. 
Prop. XLII. If from one of the equal angles of an 
