€ DE SOLTDTS Cn^OR. SVPERFTC. 



fllio \ero pundo proximo x\ \'\ ct z\ tum corum 

 pundorum dinantiam fore — V((a,-' — a) -^('y^— J)' 

 -4-(s^— xr)'"); hinc pro triangulo Z z z' habebimus 

 fingula eius latera i°. Z z — d u^V (W -^- \x.~ -{- v^); 

 2.\ 7.z'-dty{l'-\-m-\-n) ct :i^" zz'—-V{{-kdu-ldtf 



-^-f )x d u — }H d tV+lv d u-nd tY) C)uezz'—y(dr.\//j^mtft 

 4-« ;/) -f^w' (X A + |x jx + vv )- 2 rt'; tf^w (/X + ;// jj. +;; K^). 



7. lam quum (uperficies folidi prorfiis debent 



conuenire cum figuru plana (Fig. 2 ) necclTe eft , \t 



triangula 7. z z^ et V -y 'y'' fint non fohim acquaha, 



fed etiam fimiUa ideoque latcra homologa acqualia , 



fcilicet: 



r. ZzznY-v, IV. Zz'—M -r" et z z'' ~ c n^' 



Tnde tres fequentes nancifcimur aequationes 



1°. y^-^-xiS -^-v-x; \\\ f-\-m~^"n—i; 



III". dt\f+m'-{-n]-\-du^>.''^\k-\v")-:idtdu[l'K-\-m\x. 



-\-nv)z:zdt^ -\-du 



tertia autem ob binas priorcs rcducitur ad hanc 



l\-{-m [X -\- nv — o , 



quibus tribus acquationibus folutio problemntis noflri 



continctur, ex quo intelligitur eam reduci ad fequens 



problema analyticum : 



Propo/itis duabuf variahilibus t et u earum fex 



inuenire funCtiones I, m, n ^; X, jjl, y ita comparatas^ 



vt fex fequentibus conditionibus fati^Jiat 



r. (S=(jT); nM'-T)=(2r); iii"Ma-:)=d-P 



IV. ll-\-mm-\-nn—i :, V°. XX-h^Ljji. + vv— i ; 

 Vr. l\-\-m\K-\rny—o 



quod 



