(7) 



priori casu, = *' -f j 1 -f z 1 , et, in posteriore, = x'* + /' + z" : et 

 ponendo loco x, y, z valores (7), hanc habebinius ecquationem, 

 (m'x 1 + ny +p'z')* + (m"x' + n"y' +/>"*') + (m'"x' + 



= *"+/' + *", ...... (/) 



Evolvendo et conferendo (7) et (7'), prodibunt sequationes 



m'ri 



(8). 



' 4- " -|- B"" = I 

 P" + P"* + P"" = I 



+ m"p" + m'"/>"' = o 

 rip' 4- /i"/>" + '"/'" = o 

 Si multiplicentur respective expressiones (7) quantitatum x , y , z, i per 

 m', m", m'"} a per ri, n" , n'"; 3 per p', p", p"' } et addanttir 

 tria priora producta , dein tria posteriora , tandem tria idlima , habebimus , 

 repectu babito ad squationes (8) , 



x' = m'x -f- m"y -\- m" z } 



y' = n'x + n"y + ri" z ( (9) 



_' _ if_ i_ '/ i /;/_ \ 

 z := p x -f- p y -\~ p z ) 



substituendo illos valores in relatione (7') , et aequando productum inde 

 i mi u in expressioni ** -\- y* + z* , invenientur sex sequentes aequationes 



771' 



rri' 



+ p'* = i 



1 = i 



(.0) 



m'm" +n'n" + p'p" = o 



m'm'" + n'n'" + p'p"' = o 

 m"m r "+n"n'"+p"p'" = o 



Eliciamus jam ex formulis(7) valores x' ,y' , z' , ponendo, brevitatis causa, 



m'n"p'"-.m"n r p"' + m'"n'p" m'n'"p" + m"n"'p' m'"n"p' = /,- 

 habebiinus 



./_. (n"p"'-n'" P "}x + (n"'p'-n'p'") r 



x' = 



(n'p"-n"p') z 



( m 'p"< _ m '"p' )p + ( m"p' m'p")z. 



