18 
ARCHIMEDES 
the making of spheres and produce a model of the heavens by 
means of the circular motion of water’, it is possible that 
Archimedes’s sphere was moved by water. In any case Archi 
medes was much occupied with astronomy, Livy calls him 
‘ unicus spectator caeli siderumque ’} Hipparchus says, ‘ From 
these observations it is clear that the differences in the years 
are altogether small, hut, as to the solstices, I almost think 
that Archimedes and I have both erred to the extent of a 
quarter of a day both in the observation and in the deduction 
therefrom ’. 2 Archimedes then had evidently considered the 
length of the year. Macrobius says he discovered the dis 
tances of the planets, 3 and he himself describes in his Sand- 
reckoner the apparatus by which he measured the apparent 
angular diameter of the sun. 
(/3) Mechanics. 
Archimedes wrote, as we shall see, on theoretical mechanics, 
and it was by theory that he solved the problem To move a 
given weight by a given force, for it was in reliance ‘ on the 
irresistible cogency of his proof ’ that he declared to Hieron 
that any given weight could be moved by any given force 
(however small), and boasted that, ‘ if he were given a place to 
stand on, he could move the earth ’ (nd (3d>, Kkl kluco rdv ydv, 
as he said in his Doric dialect). The story, told by Plutarch, 
is that, ‘ when Hieron was struck with amazement and asked 
Archimedes to reduce the problem to practice and to give an 
illustration of some great weight moved by a small force, he 
fixed upon a ship of burden with three masts from the king’s 
arsenal which had only been drawn up with great labour by 
many men, and loading her with many passengers and a full 
freight, himself the while sitting far off, with no great effort 
but only holding the end of a compound pulley (noXva-Traa-Tos) 
quietly in his hand and pulling at it, he drew the ship along 
smoothly and safely as if she were moving through the sea.’ 4 
The story that Archimedes set the Roman ships on fire by 
an arrangement of burning-glasses or concave mirrors is not 
found in any authority earlier than Lucian; but it is quite 
1 Livy xxiv. 84. 2. 2 Ptolemy, Syntaxis, III. 1, vol. i, p. 194. 28. 
3 Macrobius, In Somn. Scip. ii. 3; cf. the figures in Hippolytus, Refut., 
p. 66. 52 sq., ed. Duncker. 
4 Plutarch, Marcellus, c. 14. 
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Book XII lef' 
1 Cicero, Tusc. 
Vitruvius, D, 
4 Tzetzes, Chil