104 A SHORT HISTORY OF SCIENCE 



this commission, he by chance went to a bath, and on jumping into 

 the tub, perceived that, just in the proportion that his body became 

 immersed, in the same proportion the water ran out of the vessel. 

 Whence, catching at the method to be adopted for the solution of the 

 proposition, he immediately followed it up, leapt out of the vessel in 

 joy, and returning home naked, cried out with a loud voice that he 

 had found that of which he was in search, for he continued exclaiming, 

 * I have found it, I have found it ! ' Vitruvius. 



Archimedes, who combined a genius for mathematics with a physical 

 insight, must rank with Newton, who lived nearly two thousand 

 years later, as one of the founders of mathematical physics. . . . The 

 day (when having discovered his famous principle of hydrostatics 

 he ran through the streets shouting Eureka ! Eureka !) ought to be 

 celebrated as the birthday of mathematical physics ; the science came 

 of age when Newton sat in his orchard. Whitehead. 



The recently discovered New Manuscript 1 of Archimedes 

 throws a very interesting light on his methods of attacking prob- 

 lems in mechanics, as well as on his use of mechanical methods 

 for geometrical problems. Naturally his mathematical methods 

 are highly developed in comparison with the relatively simple 

 problems of mechanics with which he deals. 



' Certain things first became clear to me by a mechanical method, 

 although they had to be demonstrated by geometry afterwards because 

 their investigation by the said method did not furnish an actual 

 demonstration. But it is of course easier, when we have previously 

 acquired, by the method, some knowledge of the questions, to supply 

 the proof than it is to find it without any previous knowledge. I 

 apprehend that some, either of my contemporaries or of my succes- 

 sors, will, by means of the method when once established, be able to 

 discover other theorems . . . which have not yet occurred to me.' 



Our admiration of the genius of the greatest mathematician of 

 antiquity must surely be increased, if that were possible, by a perusal 

 of the work before us. Heath. 



ARCHIMEDES AS AN ENGINEER. - - His engineering skill, which 

 has gained from an eminent German historian the appellation of 



1 See Reviews by C. S. Slichter and D. E. Smith. Bulletin, American Mathe- 

 matical Society, May, 1908, Feb. 1913. 



