(8) 

 ( m " n '" m'"n" ) x -f ( m'"n' w V" ) jr + ( m V /"' ) z 



v* 



Si conferentur coefficientes x, y, z qui occurrunt in aequationibus 

 (g) et (n), novem aequationes prodibunt, scilicet: 

 n " p '"^p"n'" = hn'i n'" P 'p'"n' == fln",- n'p"n"p' = lm'" 1 

 m "'p"m"p'"=ln'; m!p M 'Tn"'p'=ln"; m"p'm'p"=lri" [ > . . (12) 



= l"; m'n"m"n' = 



si addantUF quadrata aequationvun cjuae primam seriem constituunt, in- 

 venietur, ope requatioMim (8), 



form sinistrum membrw<m hanc potest irvd.ere focmam 



(.. + //. 4. ') (/ +X" +/'") ('X + '>" + '"/>'" ) a 



quaj , Eequationum (8) causa , tinitati fit aeqiualis : prodit ergo /* = i , unde 

 / =: -+ i ; attamen facile protatur quantitatem / necessario esse affir- 

 mativam ; nam si concipiamus coordinatas novas x' , y' , z' cadere in 

 prioress, y, z, id est, si x'= x, y''=:y } z' z, fiunt ml ' =, i, n" = i, 

 p'"= i et alii coefficientes annil<iil v aiibur ; wide concluditur quantitatem 

 / fieri aequalem -\- i : itaque aequationes (8) et seqnentes 



m" +n'* +p" = i 

 ////' + " + /j" 1 = i 



r p'-~ m'p"Y= i 



TO'"!*")* 4 (ro /7 V ''?')* + (TO'n' f ra,'V)=: i k ' ^ 

 m 'n"p'"m"n'p"'+ m"'n'p"m'n'"p"+m"n'"p'm"n'"p' , 

 siniul locuni habent, 



Quo similitudo formularum (4)et(8); (6) et (10) melius perspiciatur , 

 determinandi veniunt coefficientes indeterminati m', n' , p' f m!' ..... etc. 

 ope cosinuuni angulorum inter novos et primitivo&axes: pon-o contemplando 

 sequationes (7) et ponendo in his vicissim y' = o et z' = o, prodeunt 



' 



x *y z 



m' = -, ; m" = , : m'" = ' 



