ALEXANDRIAN OR HELLENISTIC PERIOD 



on the island of Sicily, in the year 287 B.C. When he 

 visited Alexandria he probably found Apollonius of 

 Perga, the pupil of Euclid, at the head of the mathe- 

 matical school there. Just how long Archimedes re- 

 mained at Alexandria is not known. When he had 

 satisfied his curiosity or completed his studies, he re- 

 turned to Syracuse and spent his life there, chiefly 

 under the patronage of King Hiero, who seems fully 

 to have appreciated his abilities. 



Archimedes was primarily a mathematician. Left 

 to his own devices, he would probably have devoted 

 his entire time to the study of geometrical problems. 

 But King Hiero had discovered that his protege" had 

 wonderful mechanical ingenuity, and he made good use 

 of this discovery. Under stress of the king's urgings, 

 the philosopher was led to invent a great variety of 

 mechanical contrivances, some of them most curious 

 ones. Antiquity credited him with the invention of 

 more than forty machines, and it is these, rather than 

 his purely mathematical discoveries, that gave his 

 name popular vogue both among his contemporaries 

 and with posterity. Every one has heard of the screw 

 of Archimedes, through which the paradoxical effect 

 was produced of making water seem to flow up hill. 

 The best idea of this curious mechanism is obtained if 

 one will take in hand an ordinary corkscrew, and im- 

 agine this instrument to be changed into a hollow tube, 

 retaining precisely the same shape but increased to 

 some feet in length and to a proportionate diameter. 

 If one will hold the corkscrew in a slanting direction 

 and turn it slowly to the right, supposing that the 

 point dips up a portion of water each time it revolves, 



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