s
work entitled "Psammites" he alludes to the astronomical system
subsequently established by Copernicus, whose name has been given to it.
He also mentions the attempts which had been made to measure the size of
the earth; the chief object of the work being, however, to prove not
only that the sands upon the sea-shore can be numbered, but even those
required to fill the entire space within the sphere of the fixed stars;
the result being, according to our system of arithmetic, a less number
than is expressed by unity followed by 63 ciphers. Such a book is the
sport of a geometrical giant wantonly amusing himself with his strength.
Among his mathematical investigations must not be omitted the quadrature
of the parabola. His fame depends, however, not so much on his
mathematical triumphs as upon his brilliant discoveries in physics and
his mechanical inventions. How he laid the foundation of Hydrostatics is
familiar to everyone, through the story of Hiero's crown. A certain
artisan having adulterated the gold given him by King Hiero to form a
crown, Archimedes discovered while he was accidentally stepping into a
bath, that the falsification might be detected, and thereby invented the
method for the determination of specific gravity. From these
investigations he was naturally led to the consideration of the
equilibrium of floating bodies; but his grand achievement in the
mechanical direction was his discovery of the true theory of the lever:
his surprising merit in these respects is demonstrated by the fact that
no advance was made in theoretical mechanics during the eighteen
centuries intervening between him and Leonardo da Vinci. Of minor
matters not fewer than forty mechanical inventions have been attributed
to him. Among these are the endless screw, the screw pump, a hydraulic
organ, and burning mirrors. His genius is well indicated by the saying
popularly attributed to him, "Give me whereon to stand, and I will move
the earth," and by the anecdotes told of his exertions against Marcellus
during the siege of Syracuse; his invention of catapults and other
engines for throwing projectiles, as darts and heavy stones, claws
which, reaching over the walls, lifted up into the air ships and their
crews, and then suddenly dropped them into the sea; burning mirrors, by
which, at a great distance, the Roman fleet was set on fire. It is
related that Marcellus, honouring his intellect, gave the strictest
orders that no harm should b