(mO 



nc .F.llipfes aclpliciiri pofTc. Nnm pro T.cmm:Ue quidcm T. fi 

 confln!(flio fimiiis illi qiiain §. 2. acll.ibiiinuis, in \l\\m vocc- 

 tur, habtbiniub Q J) acc]ualcm fcmiaxi transuerfo hjpcrbolac , 

 F 1) vcro erit acqualis rcmifummae rccflarum cx focis Hypcr- 

 bolae ad pundum Q duclarum ct dcuiquc fict F D' — C A* 

 m C O'. ]-cnnnata vero rcliqua II., III. ct IV. pro hypcr- 

 bolis acquc ac Ellipfibus v.alcnt. Ktis igitnr Lemmatibus prac- 

 ftru(fLis iam omnino patct, quod fi binae proponantur hypcr- 

 bolac, quarum axcs transucrfi inter fc funt acqualcs, ct in 

 iilis hyperbolis biuae ducantur cordac intcr fe acqualcs, ifta 

 ratione, vt fumma rctflarum a foco altcrutro vnius hypcrbolae 

 ad puujfla cxtrcma irtius cordac du(fl;arum aequalis fit fummac 

 rc(ftarum confimili rationc ad focum cognominem altcrius hy- 

 pcrbolac duclarum; crunt fctflorcs hyperbolici circa focos de- 

 fcripti et cordis mcmoratis rclpondcntes in rationc axium 

 coniugatorum pro hvpcrbolis. Vt aurcm fpccimcn huius dc- ^- , y 

 monltrationis ob oculos ponatur, fit NAM hyperbola cuiusfig. 7. 

 axis transucrfus CA, coiiiugatus CH, foci autem F, /, tum- 

 iquc ducld corda MN fi bifecetur in G, per G ducatur dia- 

 mctcr C Q, huiusque fcmidiameter coniugata CO, quae ipfi 

 N M erit parallcla. Pcr Q autcm ducatur Q S tangcns hy- 

 perbolam, quac adcoque etiaiTi ipfi NM crit parallcla, ct 

 iungantur FQ, fQ, quarum illa producfla occurrat ipfis N M, 

 C O in E et 1) , atque ducatur C S parallcla ipfi F D. Dc- 

 niquc per pun(fta Q, G ducantur ad axin transuerliim nor- 

 malcs QR, G P, quarum hacc hypcrbolac occurrat in K, et 

 iungantur FM, FN, F K. Primum igitur demonllratur pcr- 

 indc ac pro Eliipfi eflc CSznCA, idcoqnc in parallelf)- 

 grammo D C S Q crit DQ — CSzizCA; tum vcro crit 

 DF — QF^D Qi:Qf-DQ, hincnue iDF=rQ/-QF, 

 ct dcnjque F D^ — D Q' =: F Q ./Q zz: C O--. Confcr lo- 

 cum cititum in Elemcntis Sinifoni. Nuiic fi c.\ Q in C O nor- 



nialis 



