22 
ARCHIMEDES 
on the Quadrature of the parabola, namely that the area of any 
segment of a section of a right-angled cone (i. e. a parabola) is 
four-thirds of that of the triangle which has the same base and 
height. The mechanical proof, however, of this theorem in the 
Quadrature of the Parabola is different from that in the 
Method, and is more complete in that the argument is clinched 
by formally applying the method of exhaustion. 
List of works still extant. 
The extant works of Archimedes in the order in which they 
appear in Heiberg’s second edition, following the order of the 
manuscripts so far as the first seven treatises are concerned, 
are as follows: 
* 
(5) On the Sphere and Cylinder : two Books. 
(9) Measurement of a Circle. 
(7) On Conoids and Spheroids. 
(6) On Spirals. 
(1) On Plane Equilibriums, Book I. 
(3) „ „ „ Book II. 
(10) The Sand-reckoner (Psammites). 
(2) Quadrature of the Parabola. 
(8) On Floating Bodies: two Books. 
? Stomachion (a fragment). 
(4) The Method. 
This, however, was not the order of composition; and, 
judging (a) by statements in Archimedes’s own prefaces to 
certain of the treatises and (6) by the use in certain treatises 
of results obtained in others, w r e can make out an approxi 
mate chronological order, which I have indicated in the above 
list by figures in brackets. The treatise On Floating Bodies 
was formerly only known in the Latin translation by William 
of Moerbeke, but the Greek text of it has now been in great 
part restored by Heiberg from the Constantinople manuscript 
which also contains The Method and the fragment of the 
Stomachion. 
Besides these works we have a collection of propositions 
{Liber assumptorum) which has reached us through the 
Arabic. Although in the title of the translation by Thabit b. 
Qurra the b 
cannot be hi 
times menth 
of them are 
geometrical i 
craKivov (pro 
ing on the tr 
There is 
which purpo: 
Archimedes i 
to Eratosthe 
Archimedes 
doubting the 
problem by i 
Of works 
1. Investig 
Pappus who 
describes thi 
semi-regular, 
equiangular 
2. There m 
Zeuxippus. 
witli the na r i 
expounded t] 
expressing m 
in the ordim 
said) up to t 
80,000 millio 
3. One or 
ing propositi 
Equilibrium 
(irepi £vy5>v) 
and Heron’s 
circles when 
speaks of w 
) Pappus, v, 
2 Archimedei 
3 Pappus, vii