of the earth.
Archimedes founds his whole theory on two postulates, one of which comes at the beginning and the other after Prop. 7 of Book I. Postulate 1 is as follows:—
“Let us assume that a fluid has the property that, if its parts lie evenly and are continuous, the part which is less compressed is expelled by that which is more compressed, and each of its parts is compressed by the fluid above it perpendicularly, unless the fluid is shut up in something and compressed by something else.”
Postulate 2 is: “Let us assume that any body which is borne upwards in water is carried along the perpendicular [to the surface] which passes through the centre of gravity of the body”.
In Prop. 2 Archimedes proves that the surface of any fluid at rest is the surface of a sphere the centre of which is the centre of the earth. Props. 3-7 deal with the behaviour, when placed in fluids, of solids (1) just as heavy as the