cm eft fummd imrum pirtium^ qmrum in priori amlogia fuit different 
iix : Hujus Theorematis demopijlrationem mmi»em Amlytices modici 
feritum Utere poffe arbitror^ idcirco ei fu^erfedeo:^ Jamin Tri^ 
angulo KSL dantur later a KS, LS^ (3" 4?7gf^iuiKSLy^U£rm fur Latr^ 
KL^& iinguli SKL, SLK: Deinde in Xrimgulo )L\J^^ dantur KL, 
KL\\ diferenSia objerv^arum Longitudinumpr^af^eU J PKL diffe- 
rentia angulorum 'SKL ultimo inventiy ^ SKP Elong^tiom Flaneta a 
Sole in prima obfervAtione ^ qu£ritur LP : Turn in trian^lo LS!\ 
UtertL LS,LP, & angulus PLS ekngAtivrPUnet^ a Sole in jecunda oh- 
fervAtione Jantur\latU5 SPc^ angulai LSP requiruntur^quibus inven- 
tis, utS?ad LPiita TangensLatitudim obfervat£ exL^ad tangent em 
Inclinationis pve Latitudinis ad Sofem) & ut Co-finm Inclmaiionis ad 
Vadium . it a Sf cur tat a dijlantia'^ad veram difiantiam planets a Sole : 
Sic tandem invenimm pofitionem ^ longitudinem defideratam. Jam 
rejlat ut oftendam^ qmmodo ex datis trihm d[ftantiis a Sole cum angulk 
intiYceptis^mvenienda fit media dijlantia cum Eccentricitate Ellipjeos^ 
Sit S Sol^d^ SA,SB5SC tres dijlantia in debit a ffitione^ du^ijque ^^y^-^ 
AB, BC,^^ AB dijlantia foscrum HyferboU^ e^SA-bB=:EH tranj- Fig,4,' 
ruerfa dimeter ^ qmbti^fofttis^ defiribatur linea ijia Hyper bo'isa, cujm 
foetid interior eji pun urn A^extremitas line£ longtoru S A : Vari modo 
JintE, foci alterius HyperboU , cujm dhmeter SB-SC-KLj ex 
qmbu4 defer ihdtur line a Hyper bo lie a fomm habens interior em ir4 pun- 
do B : Dico h^ duits Hyperbola fic defer ipt/u fefe interfecare in pun- 
[to V^quieji alter EHiffeos quji(it£ focus j du5taque lineor FA,FB, a'd'/ 
FC, SAtFA, SBtFB vel^C'^^Caquabitur tranjverf(B diametroy^ 
SF efl dijlantia focorum : qmbtis pojitis defcriptio Ellipfm facillima ejh 
Cumvero hujmconfiruStionis ratio non omnibm it& facile per ci fiat ur^ 
non abs re erit^ illuflrationem ejtu aliquam ajferre 5 Ideo dico , quod ex 
notiffima Ellipfeos proprietate SB+FFsSA+FAj ^ tran(pofitis aquati- 
mis partibm FB-FA-SA-^SB , itaut etiamfi V^&fhnos htean^, 
earum tamen differentia squalls fit SA-SB , hoc efl^ EH, cumque fit 
exnatura Hyperbola ^ ul habeat quafvis dua4 limas a [m focis ad 
quodvis punStumin fuacurva conftanter dijjerentes quantitate tranf 
^erfa diametri\ conflatj punUumY effe alicubiin curva HyperboU^ 
cujus diameter tranfverfa <equatur SA-SB» ^ Foci A, B r Fari modo 
demonflrari pot efl puni^um F ej[e in Hyperbola cujus diameter ejl 
SB-SC , drfoei^^C Ergo neceffe efl ^ utjit in interfeffione dua* 
rum iflarum Hyperbolarum, qu£, cum Jefe interfecent in unico flum 
punUoy dare ofiendunt ubi Jit Focud alter Ellipfeos qu<ejif£. 
Jam ut id ipfum Analytic} expediatur, putafalfum^ fitque FE=:3, - 
SA-SB=FB-FA=b , AB=c, SB-SC=FG-FB=dl, BC=^f Jitqt^e 
Sims anguU ABC==Sy Co-finus ejufdem^* Turn 
