"Archimedes... work... The following is a fair specimen of the questions considered. A solid in the shape of a paraboloid of revolution of height h and latus rectum 4a floats in water, with its vertex immersed and its base wholly above the surface. If equilibrium be possible when the axis is not vertical, then the density of the body must be less than (h - 3a)^2/h^2 (book II. prop. 4). When it is recollected that Archimedes was unacquainted with trigonometry or analytical geometry, the fact that he could discover and prove a proposition such as that... will serve as an illustration of his powers of analysis."