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Life of Archimedes
Archimedes was born in the Greek colony of Syracuse, on the
island of Sicily, in the year 287 B.C. When he visited Alexandria
he probably found Apollonius of Perga, the pupil of Euclid, at
the head of the mathematical school there. Just how long
Archimedes remained at Alexandria is not known. When he had
satisfied his curiosity or completed his studies, he returned to
Syracuse and spent his life there, chiefly under the patronage of
King Hiero, who seems fully to have appreciated his abilities.
Archimedes was primarily a mathematician. Left to his own
devices, he would probably have devoted his entire time to the
study of geometrical problems. But King Hiero had discovered that
his protege had wonderful mechanical ingenuity, and he made good
use of this discovery. Under stress of the king's urgings, the
philosopher was led to invent a great variety of mechanical
contrivances, some of them most curious ones. Antiquity credited
him with the invention of more than forty machines, and it is
these, rather than his purely mathematical discoveries, that gave
his name popular vogue both among his contemporaries and with
posterity. Every one has heard of the screw of Archimedes,
through which the paradoxical effect was produced of making water
seem to flow up hill. The best idea of this curious mechanism is
obtained if one will take in hand an ordinary corkscrew, and
imagine this instrument to be changed into a hollow tube,
retaining precisely the same shape but increased to some feet in
length and to a proportionate diameter. If one will hold the
corkscrew in a slanting direction and turn it slowly to the
right, supposing that the point dips up a portion of water each
time it revolves, one can in imagination follow the flow of that
portion of water from spiral to spiral, the water always running
downward, of course, yet paradoxically being lifted higher and
higher towards the base of the corkscrew, until finally it pours
out (in the actual Archimedes' tube) at the top. There is another
form of the screw in which a revolving spiral blade operates
within a cylinder, but the principle is precisely the same. With
either form water may be lifted, by the mere turning of the
screw, to any desired height. The ingenious mechanism excited the
wonder of the contemporaries of Archimedes, as well it might.
More efficient devices have superseded it in modern times, but it
still excites the admiration of all who examine it, and its
effects seem as paradoxical as ever.
Some other of the mechanisms of Archimedes have been made known
to successive generations of readers through the pages of
Polybius and Plutarch. These are the devices through which
Archimedes aided King Hiero to ward off the attacks of the Roman
general Marcellus, who in the course of the second Punic war laid
siege to Syracuse.
Plutarch, in his life of Marcellus, describes the Roman's attack
and Archimedes' defence in much detail. Incidentally he tells us
also how Archimedes came to make the devices that rendered the
siege so famous:
"Marcellus himself, with threescore galleys of five rowers at
every bank, well armed and full 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 device in execution, and to make him see
by experience, some great or heavy weight removed, by little
force. So Archimedes caught hold with a book of one of the
greatest carects, or hulks of the king (that to draw it to the
shore out of the water required a marvellous number of people to
go about it, and was hardly to be done so) and put a great number
of men more into her, than her ordinary burden: and he himself
sitting alone at his ease far off, without any straining at all,
drawing the end of an engine with many wheels and pulleys, fair
and softly with his hand, made it come as gently and smoothly to
him, as it had floated in the sea. The king wondering to see the
sight, and knowing by proof the greatness of his art; be prayed
him to make him some engines, both to assault and defend, in all
manner of sieges and assaults. So Archimedes made him many
engines, but King Hiero never occupied any of them, because he
reigned the most part of his time in peace without any wars. But
this provision and munition of engines, served the Syracusan's
turn marvellously at that time: and not only the provision of the
engines ready made, but also the engineer and work-master
himself, that had invented them.
"Now the Syracusans, seeing themselves assaulted by the Romans,
both by sea and by land, were marvellously perplexed, and could
not tell what to say, they were so afraid: imagining it was
impossible for them to withstand so great an army. But when
Archimedes fell to handling his engines, and to set them at
liberty, there flew in the air infinite kinds of shot, and
marvellous great stones, with an incredible noise and force on
the sudden, upon the footmen that came to assault the city by
land, bearing down, and tearing in pieces all those which came
against them, or in what place soever they lighted, no earthly
body being able to resist the violence of so heavy a weight: so
that all their ranks were marvellously disordered. And as for the
galleys that gave assault by sea, some were sunk with long pieces
of timber like unto the yards of ships, whereto they fasten their
sails, which were suddenly blown over the walls with force of
their engines into their galleys, and so sunk them by their over
great weight."
Polybius describes what was perhaps the most important of these
contrivances, which was, he tells us, "a band of iron, hanging by
a chain from the beak of a machine, which was used in the
following manner. The person who, like a pilot, guided the beak,
having let fall the hand, and catched hold of the prow of any
vessel, drew down the opposite end of the machine that was on the
inside of the walls. And when the vessel was thus raised erect
upon its stem, the machine itself was held immovable; but, the
chain being suddenly loosened from the beak by the means of
pulleys, some of the vessels were thrown upon their sides, others
turned with the bottom upwards; and the greatest part, as the
prows were plunged from a considerable height into the sea, were
filled with water, and all that were on board thrown into tumult
and disorder.
"Marcellus was in no small degree embarrassed," Polybius
continues, "when he found himself encountered in every attempt by
such resistance. He perceived that all his efforts were defeated
with loss; and were even derided by the enemy. But, amidst all
the anxiety that he suffered, he could not help jesting upon the
inventions of Archimedes. This man, said he, employs our ships as
buckets to draw water: and boxing about our sackbuts, as if they
were unworthy to be associated with him, drives them from his
company with disgrace. Such was the success of the siege on the
side of the sea."
Subsequently, however, Marcellus took the city by strategy, and
Archimedes was killed, contrary, it is said, to the express
orders of Marcellus. "Syracuse being taken," says Plutarch,
"nothing grieved Marcellus more than the loss of Archimedes. Who,
being in his study when the city was taken, busily seeking out by
himself the demonstration of some geometrical proposition which
he had drawn in figure, and so earnestly occupied therein, as he
neither saw nor heard any noise of enemies that ran up and down
the city, and much less knew it was taken: he wondered when he
saw a soldier by him, that bade him go with him to Marcellus.
Notwithstanding, he spake to the soldier, and bade him tarry
until he had done his conclusion, and brought it to
demonstration: but the soldier being angry with his answer, drew
out his sword and killed him. Others say, that the Roman soldier
when he came, offered the sword's point to him, to kill him: and
that Archimedes when he saw him, prayed him to hold his hand a
little, that he might not leave the matter he looked for
imperfect, without demonstration. But the soldier making no
reckoning of his speculation, killed him presently. It is
reported a third way also, saying that certain soldiers met him
in the streets going to Marcellus, carrying certain mathematical
instruments in a little pretty coffer, as dials for the sun,
spheres, and angles, wherewith they measure the greatness of the
body of the sun by view: and they supposing he had carried some
gold or silver, or other precious jewels in that little coffer,
slew him for it. But it is most certain that Marcellus was
marvellously sorry for his death, and ever after hated the
villain that slew him, as a cursed and execrable person: and how
he had made also marvellous much afterwards of Archimedes'
kinsmen for his sake."
We are further indebted to Plutarch for a summary of the
character and influence of Archimedes, and for an interesting
suggestion as to the estimate which the great philosopher put
upon the relative importance of his own discoveries.
"Notwithstanding Archimedes had such a great mind, and was so
profoundly learned, having hidden in him the only treasure and
secrets of geometrical inventions: as be would never set forth
any book how to make all these warlike engines, which won him at
that time the fame and glory, not of man's knowledge, but rather
of divine wisdom. But he esteeming all kind of handicraft and
invention to make engines, and generally all manner of sciences
bringing common commodity by the use of them, to be but vile,
beggarly, and mercenary dross: employed his wit and study only to
write things, the beauty and subtlety whereof were not mingled
anything at all with necessity. For all that he hath written, are
geometrical propositions, which are without comparison of any
other writings whatsoever: because the subject where of they
treat, doth appear by demonstration, the maker gives them the
grace and the greatness, and the demonstration proving it so
exquisitely, with wonderful reason and facility, as it is not
repugnable. For in all geometry are not to be found more profound
and difficult matters written, in more plain and simple terms,
and by more easy principles, than those which he hath invented.
Now some do impute this, to the sharpness of his wit and
understanding, which was a natural gift in him: others do refer
it to the extreme pains he took, which made these things come so
easily from him, that they seemed as if they had been no trouble
to him at all. For no man living of himself can devise the
demonstration of his propositions, what pains soever he take to
seek it: and yet straight so soon as he cometh to declare and
open it, every man then imagineth with himself he could have
found it out well enough, he can then so plainly make
demonstration of the thing he meaneth to show. And therefore that
methinks is likely to be true, which they write of him: that he
was so ravished and drunk with the sweet enticements of this
siren, which as it were lay continually with him, as he forgot
his meat and drink, and was careless otherwise of himself, that
oftentimes his servants got him against his will to the baths to
wash and anoint him: and yet being there, he would ever be
drawing out of the geometrical figures, even in the very imbers
of the chimney. And while they were anointing of him with oils
and sweet savours, with his finger he did draw lines upon his
naked body: so far was he taken from himself, and brought into an
ecstasy or trance, with the delight he had in the study of
geometry, and truly ravished with the love of the Muses. But
amongst many notable things he devised, it appeareth, that he
most esteemed the demonstration of the proportion between the
cylinder (to wit, the round column) and the sphere or globe
contained in the same: for he prayed his kinsmen and friends,
that after his death they would put a cylinder upon his tomb,
containing a massy sphere, with an inscription of the proportion,
whereof the continent exceedeth the thing contained."
It should be observed that neither Polybius nor Plutarch mentions
the use of burning-glasses in connection with the siege of
Syracuse, nor indeed are these referred to by any other ancient
writer of authority. Nevertheless, a story gained credence down
to a late day to the effect that Archimedes had set fire to the
fleet of the enemy with the aid of concave mirrors. An experiment
was made by Sir Isaac Newton to show the possibility of a
phenomenon so well in accord with the genius of Archimedes, but
the silence of all the early authorities makes it more than
doubtful whether any such expedient was really adopted.
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