fiir, qiiod fi in binis ElHpfioiis eodcm axc mafore praediris, 

 vel binis hyperbolis, qiiarnm :i\cs transucrfi acqualcs, dudac 

 fuerinf binac cordac inrcr /c acqualcs cum in ir.odum, Vt li* 

 ncac re(flae a focis EUipfium \cl H^pcrbolarum dudac ad puncfta 

 j'n quibus hae cordac FJlipfcs vcl Hypcrbolas intcrCccant, can- 

 dcm cfficiant fummam pro vtraque Ellipfi vel Hypcrbola, tuni 

 omnino arcus cHipfium vel hypcibolarum qui ab iflis cordis 

 fubtcnduntur, codcm planc tempore percurri. 



§. 12. His quae nd Ccorretricam dcmonflrationcm 

 Thcorematis a Cci. Lrniibcn propofii fpcdant , prnclibatis , 

 nunc quoquc cxan.ip,abimus quomodo eius dcmonllratio pcr 

 Analyfin adornari qucar. Si igitur pro cllipfi quacunque fcn.i- 

 axis maior ponatur — p, cxccntricitas rr.ore Artronomis vfita- 

 to =f, argulus circa focum dcfi:riptns et a vertice axis foco 

 proximiori computatus - (|), radius autcm vcdlor a foco dudus 

 huic angulo correfpondcns mr, tum crit clcmentum fcdoris 

 circa focum dcfcripti .! /' ^ d) — ! — Ell^-_ ob r ~ ^— . 



Nunc fi igiair differentialc '-^^ ■ , in binas has partcs fup- 



ponatnr rc(blutum — ^JiA^ _|, P ^ ^i >■ ^ cor t > . rcducf^ioncm ha- 



rum fraLlionum ad communcm denominatorem (i -t- f cof. (P;% 

 fict a = — L-3- et (3 — — -JL— , fiue 



( I T- <• cji. j;,-" I — Q' ^ I -(- e coj. $ ( I -(- e cj . :p ,» '' * 



Atqui intcgralc ipfius — _i^-^ , pofito ^' < i , ell 

 - — '—- Arc. cof (liLs^). 



> t • — «■■'1 ^ l-l-Ci.-O,.^)-' 



Pofito enim .'-±J?-'l?^ — « , fit 



■ coj. 4> 

 )« — — 



hinc ob 



D « — — ( I — f M _ii/i!L.V ; 



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y(i —!/•) = 



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A^o:/a ^t7fl //(W. /wp. .yi-. 7". /. V fiet 



