Bifurcations at the dawn of Modern Science

In this article we review two classical bifurcation problems: the instability of an axisymmetric floating body studied by Archimedes, 2300 years ago and the multiplicity of images observed in curved mirrors, a problem which has been solved by Alhazen in the 11th century. We will first introduce these problems in trying to keep some of the flavor of the original analysis and then, we will show how they can be reduced to a question of extremal distances studied by Apollonius.