Archimedes Cubic Quadrature
Triangle GHC is 1/4 Triangle AEC
Trapezium GHKJ equals Triangle AEC.
Paralelogram MHKF equals CEK / GLFJ equals CAJ
GHKJ equals MHKF plus GLFJ equals CEK plus CAJ equals 1/4 AEC
By induction, area of segment is therefore:
AEC ( 1 + 1/4 + 1/16 + 1/64 ... equals '4/3' AEC
See video: https://www.youtube.com/watch?v=3n3PLk19DR0