Laplace's theorem, &c. 405 



lytique, page 227, where Lagrange has enu- 

 merated the principal steps in the science of 

 mechanics, and by whom they were made. 



I may here state that besides the relations 

 above given we have 



Cos.^a + Cos.2/3 + Cos.^7 = 1 

 R = A Cos. a + B Cos. iS + C Cos. y 



Let a.\ , j/i , 2^1 be the rectangular co-ordinates of 

 the point P, , origin at O. 



ix^i y2i ^2 do. do. P2 do. 



&c. &c. &c. 



And a, b, c be the rectangular co-ordinates of 

 the point P 



Put Pi P = m;, and P2 P = m;2 &c. &c. 



X y z 



Let 2 ; 2 ; 2 refer to all the material points 

 situated in the lines parallel to axis .v, i/, z re- 

 spectively, and each passing through the point P. 



X y X z y z 



And let 2, S, 2 refer to points placed in 

 planes parallel to the co-ordinate planes xy, ,rz, 

 yz respectively passing through the point P, 



