Van Ceulen's book De Circulo

 

This is a case of  "right angled triangle in a  semi-circle" or Thales' theorem. 

and a case of Ptolemy's theorem , pentagon in a circle

 

 b x b = a x a + a x b

 

a x d = 2 x b x c

 

Van Ceulen goes on the doubling the sides from pentagon, to decagon(10 sides) and so on

ptolemy's theorem

edwardworth

maa