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. To
him also are to be attributed the endless screw, and a peculiar
form of burning-mirror, by which, at the siege of Syracuse, it is
said that he set the Roman fleet on fire.

ERATOSTHENES--APOLLONIUS--HIPPARCHUS. Eratosthenes, who at one
time had charge of the library, was the author of many important
works. Among them may be mentioned his determination of the
interval between the tropics, and an attempt to ascertain the
size of the earth. He considered the articulation and expansion
of continents, the position of mountain-chains, the action of
clouds, the geological submersion of lands, the elevation of
ancient sea-beds, the opening of the Dardanelles and the straits
of Gibraltar, and the relations of the Euxine Sea. He composed a
complete system of the earth, in three books--physical,
mathematical, historical--accompanied by a map of all the parts
then known. It is only of late years that the fragments remaining
of his "Chronicles of the Theban Kings" have been justly