The Laplace equation has applications in several fields of physics, and problems involving this equation serve as paradigms for boundary value problems. In the case of the Laplace equation in a disc there is a well-known explicit formula for the solution: Poisson's integral. We show how one can derive this formula, and in addition two equivalent but less well-known expressions of a more geometrical character, using little more than elementary geometry. (Contains 6 figures and 3 footnotes.)