Geometric Bayesian Update

Today, I present to you Bayes theorem like you have never seen it before.
Take a moment to think about the equation in the Bayes theorem. How would you calculate it using only basic geometry?
Or, to state it more precisely: you are given the unit segment, as well as line segments of lengths equal to P(H), P(E | H) and P(E | ~H) (or the ratio of the last two, if you prefer). How do you get P(H | E) only by drawing straight lines on paper? Can you think of a way that would be possible to implement using a simple mechanical instrument?