LIST OF EXTANT WORKS 
23 
at the area of any 
e. a parabola) is 
he same base and 
ds theorem in the 
rom that in the 
ument is clinched 
ion. 
it. 
der in which they 
g the order of the 
ses are concerned, 
Books. 
somposition ; and, 
3 own prefaces to 
n certain treatises 
;e out an approxi 
mated in the above 
)n Floating Bodies 
station by William 
now been in great 
tinople manuscript 
i fragment of the 
on of propositions 
1 us through the 
lation by Thâbit b. 
Qurra the book is attributed to Archimedes, the propositions 
cannot be his in their present form, since his name is several 
times mentioned in them; but it is quite likely that some 
of them are of Archimedean origin, notably those about the 
geometrical figures called ap/377X09 (‘shoemaker’s knife’) and 
ad\Lvou (probably ‘ salt-cellar ’) respectively and Prop. 8 bear 
ing on the trisection of an angle. 
There is also the Cattle-Problem in epigrammatic form, 
which purports by its heading to have been communicated by 
Archimedes to the mathematicians at Alexandria in a letter 
to Eratosthenes. Whether the epigrammatic form is due to 
Archimedes himself or not, there is no sufficient reason for 
doubting the possibility that the substance of it was set as a 
problem by Archimedes. 
Traces of lost works. 
Of works which are lost we have the following traces. 
1. Investigations relating to polyhedra are referred to by 
Pappus who, after alluding to the five regular polyhedra, 
describes thirteen others discovered by Archimedes which are 
semi-regular, being contained by polygons equilateral and 
equiangular but not all similar. 1 
2. There was a book of arithmetical content dedicated to 
Zeuxippus. We learn from Archimedes himself that it dealt 
with the naming of numbers [xarovoya^Ls ran> dpi.dp.cop) 2 and 
expounded the system, which we find in the Band-reckoner, of 
expressing numbers higher than those which^ould be written 
in the ordinary Greek notation, numbers in fact (as we have 
said) up to the enormous figure represented by 1 followed by 
80,000 million million ciphers. 
3. One or more works on mechanics are alluded to contain 
ing propositions not included in the extant treatise On Plane 
Equilibriums. Pappus mentions a work On Balances or Levers 
{nepl £vya>v) in which it was proved (as it also was in Pinion’s 
and Heron’s Mechanics) ,that ‘ greater circles overpower lesser 
circles when they revolve about the same centre ’. 3 Heron, too, 
speaks of writings of Archimedes ‘which bear the title of 
1 Pappus, v, pp. 352-8. 
2 Archimedes, vol. ii, pp. 216. 18, 236. 17-22 ; cf. p. 220. 4. 
3 Pappus, viii, p. 1068.