SEQUEL OF THE GENERALIZATION. 95 



of Motion analytically expounded ; in the may of a 

 Supplement to the Transactions of the Imperial 

 Academy of Sciences. In the preface to this work, 

 he says, that though the solutions of problems by 

 Newton and Hermann were quite satisfactory, yet 

 he found that he had a difficulty in applying them 

 to new problems, differing little from theirs; and 

 that, therefore, he thought it would be useful to 

 extract an analysis out of their synthesis. 



3. Mechanical Problems. In reality, however, 

 Euler has done much more than merely give analy- 

 tical methods, which may be applied to mechanical 

 problems : he has himself applied such methods to 

 an immense number of cases. His transcendent 

 mathematical powers, his long and studious life, 

 and the interest with which he pursued the subject, 

 led him to solve an almost inconceivable number 

 and variety of mechanical problems. Such problems 

 suggested themselves to him on all occasions. One 

 of his memoirs begins, by stating that, happening to 

 think of the line of Virgil, 



Anchora de prora jacitur stant Htore puppes ; 

 The anchor drops, the rushing keel is staid ; 



he could not help inquiring what would be the 

 nature of the ship's motion under the circumstances 

 here described. And in the last few days of his 

 life, after his mortal illness had begun, having seen 

 in the newspapers some statements respecting bal- 

 loons, he proceeded to calculate their motions ; and 



