(itfo) 

 et fumtls quadra^is 



(i -+-^coi".(|)j ( iH- f cof.cp^; ( iH-^cor.Cp; ( I -f-f coi.cp ; 



C I — f^^y r I ^- cof. (viy — v^o ) . 



( i -f- ^^ col". \4/ j ( I H- ^^ cof. \\/^ ) 

 vnde multipJicando \ trinque per a% colligetur : 



rr' (i -+-cof. (Cp — (pO ) = ??'( I -^cof. (v|y — vf>'))j 

 hincque ob (r -f- >''/ = (f -t- ^'')% fiet quoque 

 j r=-Hr"^— 2rKcof.((|)— CpO^e'-^-?''— ^?f'cor.(\|/ — \jy'), 



§. 15. Quoniam demonftrationes m.odo allatae ita in« 

 ftrudae funt, vt ex fuppofita iJla ratione feforum EJiipticoruni 

 circa focos dtfcriptorum, in binis EJJipf bus eodem axe maiori 

 pracditis , quae fubdupla ell: paran etrorum principalium, de- 

 monftretur fummam radiorum vedorum pro his fedoribus in 

 vtraque EUipfi efie eandem , tumque cordas quae arcus Eliip- 

 ticos fubtendunt quoque in^^er fe eile aequalesi in hoc autem 

 negotio id po.ius agitur vt inuerfi illius piopofitionis demon- 

 ftreturj nimirum fi in binis Ellipfibus eodem axe maiori prae- 

 ditis, binae cordae inter fe aequales ita ducantur, vt redae ab 

 extremis punctis cordarum ad focos dutflae confticuant fum- 

 mam inter fe aeqiialem in vtraque Ellipfi, tum fedores Ellip- 

 ticos circa focos defcrip:os fore in ratione fubdupla parame- 

 trorum principalium. j nunc fane haud praeter rem erit vt oden- 

 damus quomodo dem.onftratio direda procedat. Quia igitur 

 ponitur efle r -f- r ~ ^'^ -1- ^^ et j — cr, ob 



s' —r'^/^- — ti r / cof. (C|) — Cp') — 

 (r -}- r')^ — 2 r r" ( I 4- cof. (Cp — (J)') ) = 

 ( r -I- K)' — 4 r r' cof. ■ ( (p — CpO' et 



0- — (^ -\- ^"y ~ 4- ? ?^ cof. U^ •— ^0% fiet 



cof. 



