INTRODUCTION. 29 



mer he treats in his work entitled " Isorropica," or " De Equiponderan- 

 tibus." His statics are founded on the ingenious idea of the centre of 

 gravity, which he first conceived, and which has been so advantageously 

 employed by modern writers on statics. By means of this principle, 

 and a few simple axioms, he demonstrates the reciprocity of the weight, 

 and the distance in the lever and in balances, with unequal arms. He 

 determined the centre of gravity of various figures, particularly of the 

 parabola, with great ingenuity. 



His discoveries in hydrostatics were the consequence of a query put 

 to him by King Hiero. This monarch had given a certain quantity of 

 gold to a jeweller, to fabricate a crowh, and he suspected that the artist 

 had purloined a portion of the gold, and substituted silver in its place. 

 Archimedes was requested to point out a method of determining how 

 much gold had been purloined, and how much silver substituted. The 

 method, it is said, occurred to him all at once, while in the bath ; and he 

 was so transported with joy, that he ran naked through the streets of 

 Syracuse, crying out, tvpnxa, ev^a, "I have found it! I have found 

 it !" The discovery with which he was so deservedly delighted was 

 this : " Every body plunged into a fluid loses as much of its weight as 

 is equal to the weight of a quantity of the fluid equal in bulk to the body 

 plunged in." This discovery furnished him with the method of deter- 

 mining the specific gravity of pure gold and pure silver. These being 

 known, he had only to take the specific gravity of the crown, which 

 (supposing no alteration in volume when the two metals are melted to- 

 gether) would enable him to discover how much gold and how much 

 silver it contained. 



The first principle being known, Archimedes deducted from it various 

 other well-known hydrostatical principles, which he consigned in the 

 first book of his treatise " de Incidentibus in Fluido." The second 

 book of that treatise is occupied with various difficult questions respect- 

 ing the situation and stability of certain bodies immersed in a fluid. 



The ancients ascribe to him the invention of forty remarkable me- 

 chanical contrivances ; but nothing more than some obscure notices of 

 two or three of them have come down to us. His sphere, a machine 

 by which he represented the movements of the stars and planets, is one 



