242 DE TRANSLATIONE 



Dcmonftratio. 



Quia (itus pundi z refp^du pundorum ^, b, 

 c idem ert, ac fitus pundi 2 rclpedu pundorum A, 

 B, C, erit z a ziz Z k; z b — Z l^; z c ~ Z Q, Per 

 Lemma autem modo demonflratum conllat efle 



cof.s A=rcnr.Q;«cof A^r-Hcof.xi^cof.A^-f-cof crcof A<; 



cof. i: B rr col. z a col. Ba-\-<o[.zb col.BZ^-hcof Cf cof B^ 



cof. c; C n; cof. s tf cof Crf -+-corx:i^ colX^-l-cof st' cof.C^: 



vnde fi pro za^ zb, zc fublbtuantur Z A, Z B, 



ZC, prodibunt aec]ualitates in Theoremate ncftro 



cxpreffie. 



4. Confimili quoque ratione oftendi potcfl cfle ; 



cof. Za~ cof z a cof a A + cof zb cof.aB+cof.cf cof ^C 

 cof. Z ^ — cof. ^a cof. b A 4-cof. cZ^cof./^B+cof.tfcof ^C 

 COf Z £•— COf CflCOf. fA+cof :2^cof. ^B-l-cofc^coffC 



per quas formuhis pundi Z in flatu initiali fitus , 



ad puncfla <7, b, c determinatur. 



5. Si pundum z in iplum Z incidat , ideo- 

 que Z fit pundum quod port conuerfionem fphac 

 rae eundem tenet Ctum , ac in flatu initiali , aequa- 

 tiones fupra in Theoremate allat.ie , in has transfor- 

 mabuntur: 



cof ZA(cof.Aa— O-fcofZBcofAZi-fcorZCcorAt-zro 

 cof ZAcof.B^4-cof ZBCcof.BZ^-O+cofZCcofBt-o 

 cof. Z A cof Cd!-f cof Z Bcof. C^+cof ZC(cof.Cr-i)rzo. 

 Nunc fi breuitatis gratia , loco harum aequationum 

 fequentes adhibeantur: 



L ax-^-^y-^-yz-zio; U. aJ x-\-g,' j -+ y' zzzo ; 

 IIL ft"A' + (3V + Y'- — o vbi 



