110 HISTORY OF MECHANICS. 



former branch, it mainly owed its cultivation to the 

 problems suggested by the solar system. Newton, 

 as we have seen, endeavoured to calculate the effect 

 of the attraction of the sun and moon in producing 

 the precession of the equinoxes; but in doing this he 

 made some mistakes. In 1747, D'Alembert solved 

 this problem by the aid of his " Principle ;" and it 

 was not difficult for him to show, as he did in his 

 Opuscules, in 1761, that the same method enabled 

 him to determine the motion of a body of any figure 

 acted upon by any forces. But, as the reader will 

 have observed in the course of this narrative, the 

 great mathematicians of this period were always 

 nearly abreast of each other in their advances. 

 Euler 8 , in the mean time, had published, in 1751, a 

 solution of the problem of the precession ; and in 

 1752, a memoir which he entitled, Discovery of a 

 New Principle of Mechanics, and which contains a 

 solution of the general problem of the alteration of 

 rotary motion by forces. D'Alembert noticed with 

 disapprobation the assumption of priority which this 

 title implied, though allowing the merit of the 

 memoir. Various improvements were made in these 

 solutions; but the final form was given them by 

 Euler ; and they were applied to a great variety of 

 problems in his Theory of the Motion of Solid and 

 Rigid Bodies, which was written 9 about 1760, and 

 published in 1765. The formulae in this work were 

 much simplified by the use of a discovery of Segner, 

 8 Ac. Berl. 1745. 1750. fl See the Preface to the book. 



