of all sorts of artillery and fireworks, did
assault by sea, and rowed hard to the wall, having made a great engine
and device of battery, upon eight galleys chained together, to batter
the wall: trusting in the great multitude of his engines of battery, and
to all such other necessary provision as he had for wars, as also in his
own reputation. But Archimedes made light account of all his devices, as
indeed they were nothing comparable to the engines himself had invented.
This inventive art to frame instruments and engines (which are called
mechanical, or organical, so highly commended and esteemed of all sorts
of people) was first set forth by Architas, and by Eudoxus: partly to
beautify a little the science of geometry by this fineness, and partly
to prove and confirm by material examples and sensible instruments,
certain geometrical conclusions, where of a man cannot find out the
conceivable demonstrations by enforced reasons and proofs. As
that conclusion which instructeth one to search out two lines mean
proportional, which cannot be proved by reason demonstrative, and yet
notwithstanding is a principle and an accepted ground for many things
which are contained in the art of portraiture. Both of them have
fashioned it to the workmanship of certain instruments, called mesolabes
or mesographs, which serve to find these mean lines proportional, by
drawing certain curve lines, and overthwart and oblique sections. But
after that Plato was offended with them, and maintained against
them, that they did utterly corrupt and disgrace, the worthiness
and excellence of geometry, making it to descend from things not
comprehensible and without body, unto things sensible and material, and
to bring it to a palpable substance, where the vile and base handiwork
of man is to be employed: since that time, I say, handicraft, or the
art of engines, came to be separated from geometry, and being long time
despised by the philosophers, it came to be one of the warlike arts.

"But Archimedes having told King Hiero, his kinsman and friend, that
it was possible to remove as great a weight as he would, with as little
strength as he listed to put to it: and boasting himself thus (as they
report of him) and trusting to the force of his reasons, wherewith he
proved this conclusion, that if there were another globe of earth, he
was able to remove this of ours, and pass it over to the other:
King Hiero wondering to hear him, required him to put his