436 _A Demonstration of : 
to the square of a tangent from R to the 
circle, and through F any line be drawn 
meeting the circle in q and N’, and Kq, 
KN be drawn meeting the circle again in 
s and 'T’, then the points s, T’, R, are in 
35 a right line. Which is the thirty-fifth 
Proposition. 
Diacram IV. 
In the preceding Diagrams it is shewn | 
that 3H. 2h which is the square of a tan- 
gent from 3 to the circle is = F2> + FD. 
FH (Prop. 11.) = F8* + F3. Fy (Prop. 
23.) == Ba. ay 3 also yo. yE = yh * yD (be- 
cause in the preceding Diagrams, F, 3, h, 
D are in a circle) = the square of a tan- 
gent from , to the circle; therefore 24 x 
(F3 + Fy) = 37? = the sum of their squares. 
rectangle ACB be equal to the square of the semidiameter ; 
bisect ABin D, and raise the perpendicular DM; from the 
point A draw AF to any point F in the circumference, 
and FE perpendicular to DM; then I say that the square 
of AF is equal to twice the rectangle contained by AC+ 
and FE, ; 
Prop. XXXVIJI. If any regular figure be circum- 
scribed about a circle, and from any point within the figure 
there be drawn perpendiculars to all the sides of the figure 5 
the sum of the perpendiculars will be equal to the mul- 
