to DE SOLIDIS QVOR. SVPERFIC. 



En ergo idoneos valores pro littcris /, X , w, )x ct 

 n,v, qiii ita funt comparati , vt tres illas forniulas 

 /d^T4-Xfl?U, mdT^ ix.dV et tidT-{-vdU 

 fiant integrablles , atque adeo ipfa integralia facile 

 exhiberi queant , quippe quae funt 

 X =z f — s CmJ fio. ^ ij — u ~ s CinJ coC ^ ; z—v- xcoC^. 

 31. Quoniam ambae noftrae folutiones penitus 

 inter fe conuenire debent, nullum eft dub um , quia 

 ctiam reliquae conditiones fupra memoratae impleaii- 

 tur , fcilicet certo erit : 



ll+mm-\-nn-i\ XX+ixjx + vj^ri ; /X + wjx+wvro. 

 Ad quod oftendendum ponamus breuitatis gratia 

 fin.<^.finj— /),• co^.^.Cn\.Q—q et cof.6-r, ita vt fit 



pp-{-qq-\-rr-=: 1 , ideoque pdp-\-qdq-\-rdr — o^ 

 iam vero quum habeamus 



/ — pfin.o)-!-^. cof.o)} ;;;zryfin.(o-4-^. cofw,- n 

 — r fin. oj-^-^ cof 0) 



Xrrpcof 0) — ^-£-. fia.u ; }x— ^cof w- j^. fin.w; K 

 — rcof 0) — ii-. fin. u 



d L» 



hlnc inflituto calculo rcpcriemus , 

 i°Il-\-mm+nn-(pp+qq+rr)au.io'-+'^^^-^(pdp-\'qdq 

 + rdr) + '-^(dp' + dq' + dr') fiuc 

 n-}-?aM+nn:={in.(ji'~]-'j~i^idp^-hdq'-{-dr') , 



Ccque tota quaeftio in valore d p" -\- d q"- -\- d r* iri' 

 Yeftigando verfatur. Quum autem fit 



dp~d^co[.^^n.^-\-dH\v\.^coi ^ 

 rf^— --</<fm.2;finJ-i-«/dcof.^cof.det</rrr-//^nn.^, 



coiii* 



