Lawson's Geometrical Theorems. 435 
(The 32d is evident from the printed 32 
figure, because FA. AG = DA. AC, F, 
D, G, C are in acircle ; therefore 2FCA 
= DGA = DKH, and KH parallel to 
BG.) If R be taken so that RK . Kl — the 
square of a tangent to the circle from K, 
then R, I’, T’, N’ are ina circle; through 
K draw Kq cutting the circle again in s, 
then R, Il’, q,s are ina circle, and Z’IqK 
= l’Rs, but ’qK — sqT = T'T’s, therefore 
YRs = TT's and R, s, TF’ are in a right 
line. Hence if from the extremes of FK 
two lines be drawn to touch a circle, and 
in FK let a point I’ be taken on the same 
side of F with K such that the rectangle 
KEV may be equal to the square of FT 
the tangent from F, and also in FK ano- 
ther point R on the same side of K with I, 
such that the rectangle KR may be equal 
circle in G and H, and BG, BH be drawn meeting the 
circle again in K and L; thenthe points L, K, F, are ina 
right line. 
Prop. XXXVI. If from A the vertex of a triangle 
_ ABC be drawn AD to any point D in the base, and DE 
be drawn parallel to AC, and DF to AB; I say the sum 
of the rectangles BAE, CAF will be equal to the square of 
AD together with the rectangle BDC. 
Prop, XXXVII. Let A and B be two points in the 
diameter of a circle whose centre is C, and let the 
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