S oa P R I K C 1 P I A 



duas , vel tres , rel quatuor habent dimenfiones , erunt 

 iequentes. 



I. S — A 



II S~Ax-\-By-\-Cz 



III. S :== Ax x-\-Byy-\-Czz-\- aD^-l-2 JLxz-{- ifyx 



exiftente A-4~B-|-C — o 



IV. $~Ax* tBy z +Cz 3 +3Dxxy+3Fxxz-\-3Hjyz+6Kxyz 



-\- 3 Exvy+3Gxzz-\-^lyzz 

 exiftente A-f-E+Grro; B-hD-t-Imo; C-hFH-Hizio 

 -\-Ax*-\-6Dxxyy-\-+Gx 3 y-\-^Hxy 3 -f 1 2?*xxyz 



V. S — -\-By*-\-6Exxzz-\-+ 1 x 3 z-\- $Kxz % + i zOxyyz 



-\-Cz*-\-6vyy zz-+-q r Ly*z-\-$.N{yz s ^-,i aP^sz 

 exiftente ; A.+;D+-E = o G-FH-f-Pizro 

 B-f-D-h-Fzno l-\-K-\-Ozzo 

 C-t-.EH-Fzro £-KM + N=z:o 



71. Hinc perfpienum eft , quoroodo hae fbr- 

 mulae pro quolibet ordine fe fint habiturae : fingulis 

 fcilicet terminis primo iidem dentur coefficienteb nu- 

 merici, qui iisdem terminis ex lege permutationum con- 

 \eniunt, feu, qui oriuntur, fi trinomium _x-\-y-\-z ad 

 poteftatem eiusdem ordinis eleuetur. Numericis autem 

 coefficientibus adiunganturlitterales indefiniti A, B, C, etc. 

 Tum reiectis numericis difpiciatur , quoties eiusmodi 

 terni termini occurruot LZxx-\- Dt\2,yy-\-NZzz , 

 qui fcilicet fadlorem communem Z ex variabilibus for- 

 matum habeant , totiesque fumma coeffiVjentium litte- 

 ralium L-f-M-j-N ftatuatur nihilo aequalis. Ita 

 cum pro poteftate quinta hubeatur. 



S: — -+-B> 5 -4- s E^ *-^j(£y+?--+-ioHx 2 y i ~h\cf}y :l zk-i-2nLxy 3 z-4-ioOxxyzii 

 -i-Cz 5 ri-sVxz4--i-5$yz+-i-iolxxz 3 -i-io%yyz i *i-2c'M.xyz :! ~hiO?x.y2Z 



iequen- 



