Illustration of Proposition 3 of the book On Sizes. The circle in the moon which divides the dark and the bright portions is least when the cone comprehending both the sun and the moon has its vertex at our eye (Heath 1913:361).
Prop. 3 proves that the greatest difference between the dividing circle and a great circle occurs when the visual cone which contains both the sun and the moon has its vertex at our eye (Berggren and Sidoli 2007:228). Blue points can be dragged around with the mouse.