MATHEMATICS. 315 



long and peaceful reign of that prudent monarch. Though the Sicilian 

 prince reigned at the time when the contests of the Romans and Car- 

 thaginians were becoming a struggle for existence, and in the situation 

 where the rival nations most naturally came in contact, he kept him- 

 self pretty well out of the vortex of wars and calamities, into which 

 the violence of his neighbours might have drawn him ; and the warlike 

 machines which the great mathematician constructed, to prove to the 

 king the resources of his art, found no employment during his reign. 

 Archimedes appears to have been born B. c. 287, a little before Hiero's Archimedes 

 accession to the crown. His youth corresponded with the time of bo c< 287> 

 Ptolemy Philadelphus, under whom Alexandria, then the principal 

 seat of science, contained several of the mathematicians whom we have 

 already mentioned. To this school he travelled, but at what precise 

 time does not appear. He was probably too late to be a personal 

 scholar of Euclid ; but, among the other mathematicians with whom 

 he became acquainted, he frequently in his works mentions CONON, 

 with particular expressions of attachment. Conon is known to have 

 resided in Egypt, under Ptolemy Euergetes, in honour of whose queen 

 he formed the constellation of Berenice's Hair. It is said to have 

 been for the purpose of raising water out of the canals of Egypt that 

 Archimedes invented the machine, which yet has the name of his 

 screw ; and the Arabian historian attributes to him the mounds and 

 bridges, which are rendered necessary by the inundations of the Nile. 



The greater part of his life, however, appears to have been spent at 

 Syracuse ; and his mathematical researches are given in " his beloved 

 Doric dialect," as one of his ancient commentators calls it ; the form 

 of Greek which was spoken in Sicily, and with which the pastoral 

 poets have made us associate something of picturesque simplicity. It 

 was there that he pursued his investigations, and carried forwards the 

 mathematical knowledge of his time by those wide advances, which 

 we shall shortly mention. 



It would appear that then, as in later times, mathematicians used to 

 announce their discoveries in part, in such a manner as to challenge 

 the ingenuity of their contemporaries by what they kept concealed. 

 Archimedes had sent to Conon a long list of propositions on various 

 subjects, of which he required the demonstrations; and, it would 

 appear, that he employed the artifice of stating some false theorems 

 along with the true ones: "In order," he says, " that if any assert 

 themselves to have discovered the whole, and produce no demon- 

 strations, they may be convicted, as pretending to have done what is 

 impossible." These discoveries refer to the area of the parabola, the 

 surface and solidity of the sphere and cylinder, the properties of 

 spheroids, and of that spiral, which is called indifferently the spiral 

 of Conon or of Archimedes. Conon, however, died before he had 

 obtained the demonstration of these propositions, to the great grief of 

 Archimedes. " If he had lived," he says, " he would have found out 

 these, and invented more, and would have done much for the advance- 



