RECTIFICATIONEM ELLIPSIS REQJ^IR. 5^5 



ficilior qu;im praccedcns, in qua tcrminus T deeft ; re- 

 duci cnim poielt liaec acquiuio ad illam , vti iam alibi 

 oltcndi» 



Problema 2- 



§.21. Datis injinitis ellipfibus AOF, ANG,AMH, '''s'"* 3- 



quarwn alter Jeniiaxis AE fit conftans , alter vero 'varia- 

 bilis vt AI , AK , ct AL ; inuenire aequationem pro curua 

 BONMC, quae ab bis omnibus ellipfibus arcus aequa- 

 ks AO, AN, AM abfcindat. 



Soliitio. 



Du(fta ad nxem AC quacunque applicata MP ciir- 

 uae quacfitac; fit AP — /, PM — ?;; et AE — f; Elli- 

 pfis vero AMH fcmiaxis variabilis AI {\x.—a\ et ar- 

 cus ablciflus AM qui eft conftuntis quantitatis fit :=r/. 

 Pofitis nunc x — -^\ et bzzW {a^-c*) erit zzz.f\ et « 

 ~c^{p.X—xx). His igitur fubltitutis generalis aequatio 



intcr ^,.vet^ abit in hanc v^c — {i^^{:Mv^^^\ 

 dx cc-^bb[,ix-xx) ibdx , :lx-xx 



bdb 2.X — XX db cc-]-b{.2x — xx) 



ccdx'(i —x) I dx 



Q. 



db'{^x-xx}iy[cc-\-bb{2x-xx)] db ' db 



cc-\-bb{zx-xx) «» 



y- . Quia vero eft 2.x—xx — -- 



2X — XX ^ c* 



multiplicetur vbique per 'V]_cc-\-bb{'2. x — xx^^zn 



y(c*_f-66uu) -,rrv,q;u;r J^l{c*-^luu) cu(i — x ^ c^dx zbudx 



'c" " prouiDic „,2 ^2 —budb ~~ cdb " 



cSdx*(i — x) (e*-+-66uu) > dx j , ■ r t i 



-^^ rui& — d. j^- Ii^ hac aequatione fi loco^ 



fubfti' 



