QUARTA PARS , 



SEU APPLICATIO THEOFxI^E SUPRA EXPOSIT^. 



Oi in sequatione maxime general! super ficierum , quae hanc formam 

 induit 



ax 1 -{- by* -f cz* + dxy + eyz -\-fxz -\- gx -\- hy + iz + i = o . (i) 

 substituantur loco x, y, z valores (24, part. i"), prodibit transformata 

 semper secundi gradus inter x' , y' , z', in qua coefficientes erunt func- 

 tiones angulorum 4/ et 9 et quantitatum a, b, c, etc. 



Pon-6 indeterminata? ^ et Q ita assumi poterunt ut rectanguli x'z' } y'z' 

 evanescant et emerget sequens transformata 



oV + b'y'* + c'z" + d'y'x' + g'x'+ h'y' + i'z' = 1 . (2). 



Ut rectangulum x'y 1 annihiletur, sufficit mutare directionem axitim rec- 

 tangularhmi x' ,y' in eodem piano, qnod fit ope formularum notarum: 



vmde 



a"x"* + b"y" + c"z' f * + g"x" + hy"+i"z"= i .... (3) 



tandem mutando coordinatarum ini'linm, juvantibus formulis 



x" = a + *'"., y" = |8 W, z"*= y + z'", 

 ultima prodibit transformata 



P* 4 4- Mj 1 + N^ i *= o (4) 



Jam calculos peragamus: si prioribus sabstitutionibus factis, coefficienles 



rectangn-lorum x'z' et y'z' 'acquales 'cypbi'se ponawbur , orientur aequationes 



2(0 6) sin^sin^cos^/ + cos ^ (fc 05 ^ <?sinv{/ ) 



c/sind (sin*vf/ tos'xp) = o . . (5) 



2 sinflcos9.(osin'4/ + ^cos*^.) + rf(sin4/cosvp (?) 



(sin'fl cos'6) (/sin4/ + ecos4/) =o (6) 



Jam angulorum 4/ et d reales 'esse valores profeandum est: in hunc finem 

 dhidatur (5) per cos^ et (6) per sinflcosfl, t prodibunt 



