(14-5) 



§. <f. His iraquc pnicn.liris T cmmatlbiis, niinc dcmon- Tab. IV, 

 ftrationcm Thcorctr.atis a Cel. Lon:bvrt propofiti adgredi lice- Fig. 3. 

 bir. Si igiriir in Kiiipri .AQB, fcniiiixibus principalibus CA^ 

 CH conllruda , fumatur punclum quoduis Q, atijuc ihicatur 

 fcniidiametcr C Q^ tangcns QT axi maiori in T occurrcns, 

 hincque tangenti parillcla corJa N M, tumque focus F iun- 

 gatur cum pundo Q linci recfia F Q, quac cordac N M in 

 E occurrit, iltaquc rcda FQ produdia intclligatur vsque dum 

 diamctro coniugatae C O ipfis N M, T Q parallclae in D 

 occurratj iam fi foco F, ccntro D et femiaxc mai<#i QD 

 dclcribatiir cllipfib, ciu^qne ordinata ad axin m.aiorem per C 

 ducatur w;/, ct iungautur F w, Y n; dico forc i'. E /« — 

 F « = C M ; 2^ lm — Vn~\ (F M -{- F N) ; 3^ fcgmcnra 

 elliptica N Q .M N et /7 Q m n fore in rationc fubdupla para- 

 mctrorum principalium pro Ellipftbus AHB et Qnq; cr de- 

 nique 4°. candcm quoque eCe rarioncm triangulorum N F M , 

 n¥ w. Pcr ccntrum D Kllipfcos Q y ^/ dudus intclligatur fe- 

 m.iaxis minor D y. Quum igiiur fit per 1 emma 1. Q D — 

 C A et F D^ = C A^ — O C, at pro Eilipfi Q y ./ habcatur 

 FD'i=QD' — Dy% fiet omnino D y — C O. Porro ob 

 N M parallclam ipfi C O, fit Q C : G C z= Q D : E D , hinc- 

 quc QC^— GC':QC'=QD' — ED^- QD^ at in Kllipfi 

 A H B cft G M' : C O^ =r Q C^ — G C' : Q C% et in Ellipfi 

 Q V 9 habctur E ;;;' : D y' rz Q D» — E D= : Q D^ ; quamob-- 

 rcm crit G M^ : C O^ 1=: E w= : D y% vnde ob C O ~ D y»" 

 fir quoque E;;;=iiGw. Nunc fi cx Q in axin AB dcmirrarur 

 pcrpcndicularis QK er pcr puncflum G pcrpcndicularis G P, quac 

 Kllipfi in punclo K occurrat ct iungatur F K, erit pcr 1 cmma 

 IV. F K ^ ; (F M -h F N). At pcr J cmm.iris HI. Corol. ha- 

 bcmus FK.CAr=:CA^ — CP.CF, fimiiiiiuc rarionc F;;;. 

 (^ D = Q D* — D E . D F. lain quia cft /Q' - F i\' ~fR' 

 — FKS fit (/Q-4-FQ) (/Q_FQ) := +QD.DF-r= 

 Noua Acla Acad. Iwp. Sc. T I. £ (j K 



