158 DEMONSTRATIO THEOREMATIS 



Solutio. 



Pofitis femiaxibiis CAziza, CB — ^, et breuitatis 

 crgo n~'^j~t diLiidatiir primo tora penpneria eliipfis 

 ita in pundis / et ^, vt partium AB/ , /a^ , g^A 

 differentiae lint geometrice affign^biles. Statuantui: his 

 pdndis / et g- abfciflTae refponaentes AFz:/ et AGz:-^ 

 quatenus haec in plagun oppofitam cadit. Probleroa 

 igitur praecedens ad hunc ca(uni accommodabitur , fi 

 ob pundiim ^ in A incidens ponatur bz:.o et 

 'y/ {bb~hh) — -\-b^ quo fadlo habebimus : 



^ — F_«/* — - — et ^__ -/ 



ficque erit AGr^AFr^/; et teinae partes ellipfis ita 

 difFerent , vt fit : 



/a^-AB/=r_,^^ et AB/-Ap^=:o. 

 Cum autem fit gzn—f erit : 



^bbfV{bb--ff)[bb-nff') — -{b'-nJ')f 

 vnde quadratis iiimtis elicitur : 



nnf-Cnb^f-^^^n-^-i^b^ff-^b^izo. 



Ad hanc aequationem refoluendam fingantur eius 

 fadores : 



(«/H- PJ-4-Q_)(«/*~P/_i-R)-o 



efleque oportet": 



-6nb'-n{Q-\-R)-?F-^ 4(«+i> -P(R-Q.)i -3^'::QR 

 cx quibus fit : 



vndc 



