70 SCIENCE IN GRECO-ROMAN ANTIQUITY 



can only suppose it to have been modelled after the 

 type of the ■' Sophistical arguments" of Aristotle, 

 and to have contained historical comments of great 

 interest. Another dissertation, of which only the 

 Arabic version has come down to us, entitled the 

 Division of Figures, shows how triangles, quadrilaterals, 

 and circles can be divided into equal parts, or according 

 to a certain ratio. 1 



Finally Euclid composed books on optics (or per- 

 spective), astronomy and mathematical acoustics, all 

 with a view to teaching. By his didactic methods, 

 Euclid differs essentially from Archimedes, whose 

 creative genius ranks him amongst the greatest mathe- 

 maticians of all times. 



Archimedes (257-212 b.c.) was born at Syracuse, 2 

 and was on intimate terms with, if not related to, 

 King Hiero. It was to Gelo, the son of Hiero, that he 

 addressed the curious problem of the Arenarius, relat- 

 ing to the number of grains of sand which could be 

 contained in the universe. In spite of the advantages 

 offered by Alexandria, he preferred to live in his own 

 country, to which he was much attached. In his 

 writings, for instance, he uses the local dialect rather 

 than the common speech, thus showing his patriotism 

 and independence of character. It was especially 

 during the siege of Syracuse that he applied his talents 

 to the service of his country. By his wonderful 

 inventions, he held in check the Roman armies and 

 fleet, commanded by Marcellus. Polybius (bk. VIII, 

 fgmt. iv), Livy (bk. XXIV, ch. 34), and Plutarch have 

 left us an account of these inventions, but they pass 

 over in silence the burning of the ships by means of 



1 15 Heiberg, Naturwiss., p. 50. 



2 For a critical study of the life and works of Archimedes, 

 consult P. ver Eecke, Les CEuvves completes d'Archimede, 

 Paris, 192 1 ; T. L. Heath, The Works of Archimedes, Cam- 

 bridge, 1897. 



