SOLIDS OS -I «B \('ES. 12] 



philosophical writings pointed out the influence which words 

 have upon our thoughts should have studied so little the ad- 

 vantages of symmetrica] and well selected symhols. It se< ms 

 reasonable to suppose too, that as the general speculations of 

 mechanical science refer equally to the thine dimensions ol 

 space, the formulas would naturally arrange themselves in 

 three sets similar in their form and in the process of their 

 derivation: an arrangement which would he favoured by the 

 method taught Ion-- since by Daniel Bernoulli and Euler 1 of 

 separating the motion of a body into the progression of its 

 centre of gravity and the rotation round that centre, those 

 two constituents of the motion being absolutely independent 

 of each other. There were however good reasons for not 

 adopting at that time this threefold division of algebraic sym- 

 bols. The most interesting application of the calculus was 

 the investigation of the celestial motions, and analysts there- 

 fore employed the astronomical elements of position, which 

 have not the same reference to the three parts of space. Ne- 

 vertheless th e preparations for a more symmetrical analysis 

 had been made by John Bernoulli in ] 7 1 ">. Euler in 1736, 

 and Maclaurin in 17 1-2. The first of these three authors 

 had employed, in defining the position of the points of a curve 

 surface, three rectangular coordinates 1 ", the second had adopt- 

 ed this method for the purpose of following the motion of a 



16 Comment.i r. Acad. PetropoL I7S7, 



Leib. el B i .;. Com. Epis. Tom. II. p. 345. The inventi »n Df this method 



cribed by Euler and b Maclaurin. The following extr 



from John Bernoulli'- letter and Leibnitz's reply, while tb . bai all claims in favour 



Df the former two, maki i bat doubtful to which of the httur the meril 



lobe ascribed. "Intel uperficiem curvam datam, cujus singula puncta 



rminantur sic tri lini e curvae data puncta) per on rum 



nihil iliud 

 p indicul u in 



Ntia. Sil 

 mtor roor.lii. ipli gratia, Ii.tc xy: = a*. Feb. 6, 1715." To which 



Leibnitz replies, "Doctrinam de cquationibus localibua trium co urn, 



I- solidis, olim aggredi ccspi, eorumque intei ■• 

 i nor planas ; mi nun racavil I pretium facerel qui stud 



impenden I Ipr. ,J . 1 715." 



