30AN>IS FRANCTSCI SERVOIS. aSS 



61* piinctorum niimerus sit iuGnitus uti in corpore rigi- 

 do niolis finifae , jam habeiitur acquai iones systemafis 

 infinitae numero ac proinde difTerentialium eliminatio 

 prat'scripfa (lillicilliina salfem sinon prorsus impossi- 

 ImIìs. Evudit: verum levi attentione deprehenditur go- 

 neralissime fieri omnibus atquationibus (8) satis, ponendo 

 dx:^p-*-tz — uy; d)'^=q-^ux — sz; dz=r+sy — tx ì 

 djc=p-^tz — uy; dy=q-*-ux'—^z' ; dz'=r+sy' — Ix > w^ 

 etc. etc. etc. etc. etc. etc. ' 



ubi sex quanKtates p, q , r, s, t, u sunt prorsus arbi- 

 trariae : etenim si reponantur in (8) praedicti valores 

 {ij) diffeientialium dx , dy , etc. colligitur 



(x-x .{dx-dx')+(y-y' )-{dy-dy' ■*-(z-z').(dz-dz') = 

 2/(x x').(z-z')-'2u (x-x).(y-yì-^-2u(x-x)(y-y')-2s(y-y'). 



(z-z')-ir-2s{y-y'.(z-z')-:if(x-x')[z-z'). 

 Porro quaecunque simultanea fiat accentuum immutatio 

 in utroque hujus aequationis membro ,. posterius ejus- 

 dem membrum evidenter ad nihilum redigilur ; quicun- 

 que aliunde valores tribuanfur literis p -, q -, etc: igitur 

 prò aequationibus (8) usurpare possumus aequafioncs 

 {<jj quibus in aequationem (2) introdurtis reperimus 

 p X-*-/Xz — it\y -+- y Y -^ uYx — sXz -*- Z.Z-»- s7iy — /Z.c ì 

 -*-py>^-i-t'^z-u^y+qY'+uYx'-sY'z-*-z7J-^s7j'y'-i7Jx' ì =0 

 -i-etc. eie. etc. etc. etc. etc. etc. etc. etc. ' 

 seu 



f (X+X'H-Ptc.)yf7+(Y+Y'-K>fc.)7-.-(Z+Z'-Hetc.)r 

 \ -^ (Z/-Yi)+(Zy-Y'zVetc.'5+f(Xc-Zx) r- 



(+(X'i'-Z'x>otc.</+i(Y^-X»+(YV-X»etc. \ ] 



L 



