78 SCIENCE IN GRECO-ROMAN ANTIQUITY 



preserved in an Arabic translation. In one disserta- 

 tion, unfortunately also lost, Apollonius examines the 

 Foundations of Mathematics, and the fragments which 

 have come down to us witness to his desire to connect 

 mathematical concepts with reality, to reduce the 

 number of fundamental propositions, and to justify 

 their scope in the Elements of Euclid. Probably the 

 other works published by Apollonius likewise had the 

 aim of taking up again and investigating questions 

 already studied by Euclid and Archimedes. For ex- 

 ample a short work on Unclassified Incommensurables , 

 and another on The Dodecahedron and Icosahedron 

 are clearly inspired by Euclid, whilst the investigations 

 of the Helicoidal Line, the Contracted Method of Calcu- 

 lation, and The Burning Mirrors were suggested 

 by Archimedes. A treatise on Contacts of which 

 many attempts at reconstruction have been made, 

 must also be mentioned. Finally must be noted an 

 astronomical treatise on the positions and retro- 

 gradations of the planets, which reveals Apollonius 

 as the author of the ingenious theory of epicycles. 1 



As mathematicians belonging to the Alexandrian 

 period, we must mention Nicomedes, the inventor of 

 the conchoid (r = a sec 6 ± d), and Diocles, the 

 inventor of the cissoid (y 2 (2a — %) = x 2 ) — these curves 

 being used to solve the trisection of the angle and the 

 duplication of the cube ; and also Gemixus, who wrote 

 a valuable history of mathematics. 



Whilst mathematics were advancing, practical me- 

 chanics also made remarkable progress as more 

 and more importance was attached to engines of war 

 used in besieging and defending fortified towns. The 

 honour of having created the technics of this practical 

 mechanics belongs to Ctesibius, a contemporary of 

 Archimedes, who lived at Alexandria about the middle 

 of the third century B.C. He constructed heavy 

 1 15 Heiberg, Naturwiss., p. 58. 



