ita formulae (i), (2) et (3) Hunt 



x = x'cos(x' } x] -\-y' cos (y' , x} -\- z' 



', x} 



z = x r cos (x'j, z ) -\-y' cos (y' } z ) + &' cos ( z' } z ) 

 simul sex sequentes aequationes habemus 

 cos a (x'j x) + cos'C^'jJK) 



..... (4) 



cos' ( z' } x} + cos* (s'jjp ) + cos' (2% z) = i 



s^',^) cos(.z ; , j) -f co 



(5) 



cos (a?'^' ) := cos(a;', x) cos(y f > x} + cos (x r , y] cos (y '^) + cos ( x ' > - s ) c os (y ', zj) 

 aequationes (4) et (5) conveniunt cum sequationibus (i), (2), (3) et (4) 

 inventis ( probl. II. ) 



-dnnotatio. Ut formulae (4) facilius ad usum accomodentur , sint 

 asquationes axium x' , y' , z' relatorum ad axes x,y, z, sequenti modo : 



axis x 



x = az 

 y b-z 



axis y 



x = a' z . . \ x a z 



axis z' 



y b" z 



porro 



>)=K^fw;' ^^^v^W^ cosCr>)== ^^Tr 

 *Hx a ^^ co <^ 



cosz x= 



ergo ponendo 



h = 



formulae (4) fiunt 



x = ahx' + a'h'f + a"h"z' 

 y = bhx' + b'h'y' + b"h"z' 

 z = hx' + hy + h"z' 



(6). 



