CARTESII CONCINNE CONSTRUENDIS. ^3 



Dii<ft.i enim ubilibet FK , dicantur AEzz a-, 

 EFz^y, erit EK-'^;^- et FK:=:j-i-?^-, cx niitura 

 vero Ellipfis fit FK^Vir^p). Pcr conftr. hiibc- 

 mus oiz=i'cSm^J et propter paniUelas AB_, EK, 

 reanm GKcnfe"?:^, quarc fit iLSlLUi—^y^ii^ji^j^i- 



fcd ;/E.NEz=M/i-ME=|uL-f-XX,-XX-f-2X.r-.v.r— - 

 A-A--f-2X.v-H|Ji., ergo ¥K—^^^^KV(-xx~\-2Xx-i-^) 



J^^-|-i:>'(^4-f.v.v-t-^.^.v+'-^f j. Q^„ ,„, 



locus conlUucndiis. 



VII. Omnes rcliquos cafiis pcrcenfcre , qui 

 a fignorum viirietiite pendent, nimis longiim forer, 

 fed eorum loco libet condriiere cequationem gene- 

 ralcm quam IllullrifT. Marcbio Hofpitalius in fiiis fe- 

 (ftionibub conicis pag. iz6 pro cllipfibus inftar ca- 

 nonis dcdir, ci:m qiia omnes calus particulares lo- 

 corum ad EUipfis comparavir. Ejus cequatio hacc cft 



n-^-^^^>--x-2ry^"=^x-^rr-^-^'i{:^o. 



i_eej>__ _ 2ppy 



Sunt ergo a=ri, (3=:^% Y=S,,-f-S/^ ^=-^, 

 c-^-2-, (p;=:r;-t7-|-fF- Ergo ay-pp-'^, 

 po-ae^JJi,-, , (3^-as=zf^, , S$-a<p=^'-^ , ct 

 >^(=a7r(3]j)=^ r ) M.(=r„^pj3)— jT^ , ergo ^(XX-f-^) 



— "^^, hinc Q.(—2±f^r'>^'-^ ( Ycl propter «-y]rz:fr) 



— 2t. Denique 7r.'==iS^'^^ite^)— ffii— p. Ex hifce 

 jam manat conftrudio facilis. , 



Ca- 



