Among his mathematical works were two books on the Sphere and Cylinder, in which he gave the demonstration that the solid content of a sphere is two-thirds that of its circumscribing cylinder.

So highly did he esteem this, that he directed the diagram to be engraved on his tombstone.

He also treated of the quadrature of the circle and of the parabola; he wrote on Conoids and Spheroids, and on the spiral that bears his name, the genesis of which was suggested to him by his friend Conon the Alexandrian.

As a mathematician, Europe produced no equal to him for nearly two thousand years.

In physical science he laid the foundation of hydrostatics; invented a method for the determination of specific gravities; discussed the equilibrium of floating bodies; discovered the true theory of the lever, and invented a screw, which still bears his name, for raising the water of the Nile.