1 The Birth of Science - MSRI

3.4 Hydrostatics 65
ers more intuitive. Archimedes’ exposition is of great interest for several
reasons: the great intellectual honesty of a man who tries to communicate
not only the proof of his results but also the mental route through which
they were identified; the importance he gives to what we might call physical
intuition; the illustration of how important it is, even for a genius such
as Archimedes, to use familiar methods in finding new scientific results
(though the “objective” connection between these methods and the initial
problem seems tenuous later).
Many widespread ideas about the relationship between mathematics
and physics should perhaps be revised in the light of the realization that
the original proof of the now familiar formula for the volume of a sphere
was in fact one of the first results of mechanics.
3.4 Hydrostatics
As far as we know, scientific hydrostatics was born with the work On floating
bodies, by Archimedes. And it was born already with much the same
form it has today. Indeed, Archimedes makes it a scientific theory by laying
its foundation in the form of a postulate:
If contiguous portions of liquid lie at the same level, the portion that
is more compressed pushes away the portion that is less compressed.
Each portion is compressed by the weight of liquid that lies vertically
above it, as long as the liquid is not enclosed in something and compressed
by something else. 69
The second half of the postulate has generally been misunderstood, both
because a key word was twisted in the Latin translation that was until
1906 the only accessible version, and because Archimedes never uses the
statement in this one surviving work, which deals with bodies that float
on an open liquid. But note that the so-called principle of communicating
vessels (though also not deduced explicitly in this work) clearly follows
from the postulate, and may even have suggested its formulation. 70
As a theorem arising from this postulate, Archimedes derives the famous
principle that bears his name and that we all learn in school: Any
69 Archimedes, On floating bodies, I, 6 (ed. Mugler, vol. III).
70 If two open vessels joined by a horizontal tube are in equilibrium, portions of liquid lying at
the same level are under the same pressure, whether they be contiguous (by the first part of the
postulate and the assumption of equilibrium) or not (by transitivity). Now consider a portion of
liquid in each container, both portions being at the same level and not compressed by anything else,
only by the liquid above them: the equality of pressures just derived implies (by the second part of
the postulate) that the columns of liquid above these two portions are equal. Therefore the surface
of the liquid is at the same level in both containers.
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