«4 DE SOUmS Q.VQR. SVPERFIC 



35. QiioJ fi haec probe perpendamus, veftigia 



quaedam deprehcndinius qmbiis inullentes lolutioncin 



dirc(flam problc mtis huius ditTicilliirii indagare po- 



terimus, Scilicct conllitutis his aequationibus : 



dx-UT-^-XdVi dy-mdT-\-[i.d\};dz-ndY + vd\} 



primum obfcruari coiiueuit quantitates l, m, n et 

 X, fx, V funcfliones efTe dcbere vnicae nouae variabi- 

 lis , quac tamcn ad binas principes ■variabiles T ct U 

 certam quandam teneat relationem. Sit igiiur w i(ta 

 iioua variabilis , cuius fex nolhae quantu;)tcs fint 

 certae quaedam funAiones. Atque iam vidimus fi 

 Ijtttrae p^ q zt r tales fun(5lioncs ipfius w dcnotcnt , 

 Yt^ fit 



pp-^qq-\-rrzzi ct dp' -{-dq' -\-dr'' zi:d(:i\ 

 tum flatuendo : 

 J—p fin. w^- ^. coC ftj; w :=: g fin. uj-\- ^-£ cof «; 

 n zz r fin, w-i- ^J-'". cof. cj) 



Xzzp cof.o) — ^J. fin. u: ^ |jl — <7 cof oj — ^ ^. fin. (d; 

 dvzz.r cof oj— ^-^. fin. &) 

 .bastres conditipncs jam adimpleri fcilicct : 



tl+mm->rnn-i i XX + jjljx+vv - 1 5 ct /X+w/|j.+;;v-o 



practcrea vcro h;nc modt^ dcduximus iflam infigncm 



proprict.uem , vt fit 



<^X--<//tang. w ; </|jLr:-^/;;tang. oj; ct rt^v-^ -</;;tang.u 



quac nobis infigncm praeflabit vfum aj reliquas con- 

 ^tioucji udimplend^s vtj piox patcbit. 



