XIII 
ARCHIMEDES 
The siege and capture of Syracuse by Marcellus during the 
second Punic war furnished the occasion for the appearance of 
Archimedes as a personage in history; it is with this histori 
cal event that most of the detailed stories of him are con 
nected ; and the fact that he was killed in the sack of the city 
in 212 B.C., when he is supposed to have been 75 years of age, 
enables us to fix his date at about 287-212 B.c. He was the 
son of Phidias, the astronomer, and was on intimate terms 
with, if not related to, King Hieron and his son Gelon. It 
appears from a passage of Diodorus that he spent some time 
in Egypt, which visit was the occasion of his discovery of the 
so-called Archimedean screw as a means of pumping water. 1 
It may be inferred that he studied at Alexandria with the 
successors of Euclid. It was probably at Alexandria that he 
made the acquaintance of Conkm of Samos (for whom he had 
the highest regard both as a mathematician and a friend) and 
of Eratosthenes of Gyrene. To the former he was in the habit 
of communicating his discourses before their publication; 
while it was to Eratosthenes that he sent The Method, with an 
introductory letter which is of the highest interest, as well as 
(if we may judge by its heading) the famous Cattle-Problem. 
Traditions. 
It is natural that history or legend should say more of his 
mechanical inventions than of his mathematical achievements, 
which would appeal less to the average mind. His machines 
were used with great effect against the Romans in the siege 
of Syracuse. Thus he contrived (so we are told) catapults so 
ingeniously constructed as to be equally serviceable at long or 
1 Diodorus, v. 37, 3. 
short range, 
through hob 
long movabL 
dropped hea 
their prows 
a crane, then 
Marcellus is 
words, ‘ Shal] 
geometrical ! 
water from 
with cudgel-1 
hurls at us a 
mythology ? ’ 
such abject t 
or wood proj 
is ”, declaring 
motion again 
away ’. 2 The 
of geometry 
importance to 
‘ though these 
more than hi 
leave behind 
regarding as i 
every sort of t 
his whole an 
subtlety of w] 
mon needs of 
Archimedes 
Sphere-makini 
of a sphere 1 
planets. 5 Cic( 
of it; he sayf 
and the appar 
it would even 
sun and moon. 
1 Polybius, His 
2 lb., c. 17. 
Carpus in Pa 
6 Cicero, Be rej 
1823.2