GREEK SCIENCE IN ALEXANDRIA 103 



(2) Magnitudes of equal weight acting at unequal distances 

 from their point of support are not in equilibrium, but the one 

 acting at the greater distance sinks. 



From these he deduces : 



(3) Commensurable magnitudes are in equilibrium when they 

 are inversely proportional to their distances from the point of 

 support. 



In a work on Floating Bodies, extant in a Latin version by 

 Tartaglia, Archimedes defines a fluid as follows : " Let it be 

 assumed that the nature of a fluid is such that, all its parts lying 

 evenly and continuous with one another, the part subject to less 

 pressure is expelled by the part subject to greater pressure. But 

 each part is pressed perpendicularly by the fluid above it, if the 

 fluid is falling or under any pressure." "Every solid body lighter 

 than a liquid in which it floats sinks so deep that the mass of liquid 

 which has the same volume with the submerged part weighs just 

 as much as the floating body." The specific gravity of heavier 

 bodies was of course employed in his solution of the crown problem, 

 which with his achievements as a military engineer gave him a 

 great reputation among his contemporaries. Vitruvius in his 

 De Architectures says: 



Though Archimedes discovered many curious matters that 

 evinced great intelligence, that which I am about to mention is the 

 most extraordinary. Hiero, when he obtained the regal power in 

 Syracuse, having, on the fortunate turn of his affairs, decreed a votive 

 crown of gold to be placed in a certain temple to the immortal gods, 

 commanded it to be made of great value, and assigned for this purpose 

 an appropriate weight of the metal to the manufacturer. The latter, 

 in due time, presented the work to the king, beautifully wrought; 

 and the weight appeared to correspond with that of the gold which 

 had been assigned for it. 



But a report having been circulated, that some of the gold had 

 been abstracted, and that the deficiency thus caused had been sup- 

 plied by silver, Hiero was indignant at the fraud, and, unacquainted 

 with the method by which the theft might be detected, requested 

 Archimedes would undertake to give it his attention. Charged with 



