MECHANICS 
19 
of the heavens by 
b is possible that 
In any case Archi- 
. Livy calls him 
rchus says, ‘ From 
ences in the years 
is, I almost think 
o the extent of a 
d in the deduction 
tly considered the 
iscovered the dis- 
iribes in his Sand- 
ured the apparent 
oretical mechanics, 
)rohlera To move a 
in reliance £ on the 
declared to Hieron 
>y any given force 
ire given a place to 
/C*£ KLVCO TOLV ydv, 
y, told by Plutarch, 
azement and asked 
tice and to give an 
by a small force, he 
ists from the king’s 
ith great labour by 
issengers and a full 
vith no great effort 
ulley (noXvcnr guttos) 
Irew the ship along 
; through the sea.’ 4 
lan ships on fire by 
icave mirrors is not 
dan; but it is quite 
, III. 1, vol. i, p. 194. 23. 
ss in Hippolytus, Refut., 
likely that he discovered some form of burning-mirror, e.g. a 
paraboloid of revolution, which would reflect to one point all 
rays falling on its concave surface in a direction parallel to 
its axis. 
Archimedes’s own view of the relative importance of his 
many discoveries is well shown by his request to his friends 
and relatives that they should place upon his tomb a represen 
tation of a cylinder circumscribing a sphere, with an inscrip 
tion giving the ratio which the cylinder bears to the sphere; 
from which we may infer that he regarded the discovery of 
this ratio as his greatest achievement. Cicero, when quaestor 
in Sicily, found the tomb in a neglected state and repaired it 1 ; 
but it has now disappeared, and no one knows where ho was 
buried. 
Archimedes’s entire preoccupation by his abstract studies is 
illustrated by a number of stories. We are told that he would 
forget all about his food and such necessities of life, and would 
be drawing geometrical figures in the ashes of the fire or, when 
anointing himself, in the oil on his body. 2 Of the same sort 
is the tale that, when he discovered in a bath the solution of 
the question referred to him by Hieron, as to whether a certain 
crown supposed to have been made of gold did not in fact con 
tain a certain proportion of silver, he ran naked through the 
street to his home shouting evprjKa, evprjKa. 3 He was killed 
in the sack of Syracuse by a Roman soldier. The story is 
told in various forms; the most picturesque is that found in 
Tzetzes, which represents him as saying to a Roman soldier 
who found him intent on some diagrams which he had drawn 
in the dust and came too close, ‘ Stand away, fellow, from my 
diagram’, whereat the man was so enraged that he killed 
him. 4 
Summary of main achievements. 
In geometry Archimedes’s work consists in the main of 
original investigations into the quadrature of curvilinear 
plane figures and the quadrature and cubature of curved 
surfaces. These investigations, beginning where Euclid’s 
Book XII left off, actually (in the words of Chasles) ‘ gave 
1 Cicero, Tusc. v. 64 sq. ’ 2 Plutarch, Marcellus, c. 17. 
3 Vitruvius, De architecture!,, ix. 1. 9, 10. 
4 Tzetzes, Chiliad, ii. 35. 135. 
c 2