... sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare'

There are some, King Gelo (Gelo II, son of Hiero II), who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited.

Magnitudes are in equilibrium at distances reciprocally proportional to their weights.

A sphere has 2/3 the volume and surface area of its circumscribing cylinder including its bases.

In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. Archimedes' principle of buoyancy is given in the work, stated as follows:

Any body wholly or partially immersed in fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.

In 1906, the Archimedes Palimpsest revealed works by Archimedes thought to have been lost.

Historians of science and mathematics almost universally agree that Archimedes was the finest mathematician from antiquity. Eric Temple Bell, for instance, wrote: