ARCHIMEDES. 
contrived to set fire to them with the rays 
of the sun reflected from burning glasses. 
However, notwithstanding all his art, 
Syracuse was at length taken by storm, and 
Archimedes was so very intent upon some 
geometrical problem, that he neither heard 
tile noise, nor regarded any thing else, till a 
soldier that found him tracing lines, asked 
his name, and upon his request to be- 
gone, and not disorder his figures, slew 
him. “ What gave Marcellus the greatest 
concern, says Plutarch, was the unhappy 
fate of Archimedes, who was at that time in 
his museum ; hud his mind, as well as his 
eyes, so fixed and intent upon some geome- 
trical figures, that he neither heard the noise 
and hurry of the Romans, nor perceived the 
city to be taken. In this depth of study 
and contemplation, a soldier came suddenly 
upon him, and commanded him to follow 
him to Marceiius ; which lie refusing to do, 
till he had finished Iris problem, the soldier, 
in a rage, drew his sword, and ran him 
through.” Livy says he was slain by a sol- 
dier, not knowing who he was, while lie was 
drawing schemes in the dust; that Marcel- 
los vt as grieved at his death, and took care of 
his funeral ; and made his name a protection 
and honour to those who could claim a rela- 
tionship to him. His death it seems hap- 
pened about the 142d or 143d Olympiad, or 
210 years before the birth of Christ. 
When Cicero was quaestor for Sicily, he 
discovered the tomb of Archimedes, all 
overgrown with bushes and brambles ; which 
he caused to be cleared, and the plac&set in 
order. There were a sphere and cylinder 
cut upon it, with an inscription, hut the lat- 
ter part of the verses were quite worn out. 
Many of the works of this great man are 
still extant, though tiro greatest parts of 
them are lost. The pieces remaining are as 
follow : 1. Two books on the Sphere and 
Cylinder. — 2. The Dimension of tiie Circle, 
or Proportion between the Diameter and 
the Circumference. — 3. Of Spiral tines. — 4. 
Of Conoids and Spheroids. — 5. Of Equipon- 
derants, or Centres of Gravity. — 6. The 
Quadrature of the Parabola. — 7 . Of Bodies 
floating on Fluids. — 8. Lemmata. — 9. Of 
the N umber of the Sand. 
Among the works of Archimedes which 
are lost, may be reckoned the descriptions 
of the following inventions, which may be 
gathered from himself and other ancient au- 
thors. 1. His Account of the Method which 
he employed to discover the Mixture of Gold 
and Silver in the Crown, mentioned by Vi- 
truvius. — 2. His Description of the Coch- 
leon, or engine to draw water out of places 
where it is stagnated, still in use under the 
name of Archimedes’s Screw. Athemeus, 
speaking of the prodigious ship built by the 
order of Hiero, says, that Archimedes in- 
vented tiie cochleon, by means of which the 
hold, notwithstanding its depth, could be 
drained by one man. And Diodorus Sicu- 
lus says, that he contrived this machine to 
drain Egypt, and that by a wonderful me- 
chanism it would exhaust the water from 
any depth. — 3. The Helix, by means of 
which, A tiienseus. informs us, he launched 
Hiero’s great ship. — 4. The Trispaston, 
which , according to Tzetzes and Qribasius, 
could draw the most stupendous weights. — 
5. The Machines, Which, according to Po- 
lybius, Livy, and Plutarch, he used in the 
defence of Syracuse against Marcellus, con- 
sisting of Tormenta, Balistae, Catapults, Sa- 
gittarii, Scorpions, Cranes, ixc. — 6. His 
Burning Glasses, with which he set fire to 
the Roman gallies. — 7. His Pneumatic 
and Hydrostatic Engines, concerning which 
subjects he wrote some books, according to 
Tzetzes, Pappus, and Tertullian. — 8. His 
Sphere, which exhibited the celestial mo- 
tions. And probably many others. 
A considerable volume might be written 
upon the curious methods and inventions “of 
Archimedes, that appear in iiis mathematical 
writings now extant only. He was the first 
who squared a curvilineal space ; unless 
Hypocrates be excepted on account of 
his limes. In his time the conic sections 
were admitted into geometry, and he ap- 
plied himself closely to the measuring of 
them, as well as other figures. Accordingly 
he determined the relations of spheles, 
spheroids, and conoids to cylinders and 
cones ; and the relations of parabolas to 
rectilineal pianes whose quadratures had 
long before been determined by Euclid. He 
has left us also his attempts upon the circle : 
he proved that a circle is equal to a right- 
angled triangle, whose base is equal to the 
circumference, and its altitude equal to the 
radius ; and consequently, that its area is 
equal to the rectangle of half the diameter 
qnd half the circumference ; finis reducing 
tiie quadrature of the circle to the determi- 
nation of the ratio between the diameter 
and circumference ; which determination 
however has never yet been done. Being 
disappoint ed of the exact quadrature of the 
circle, for want of the rectification of its 
circumference, which all his methods would 
not effect, he proceeded to assign an useful 
approximation to it : this he effected by the 
