Tab. V. 



124 ^JIf o 4ii^ 



DISSERTATIO GEOMETRICA , 



PROBLEMATIBVS ALIQVOT CONI- 



CIS PER ANALYSIN CONCINNE SOLVENDIS. 



AVCTORE 

 GEOKG. frOLFFG. KRJFFT. 



Theorema. 

 §. I. 



Si fiierint , in Ellipfi AMB, axisAB, tangens piindt 

 M cuiublibet M T ; centrum C , ordinatim applicata 

 ad axem PM ; erunt CP, CA , CT, proportiouales 

 continue. 



Demonftratio* 



Pofitis A C ~ C B — w/ , femiaxc coniugato C D 



:n M. AbfcilTa e centro computata CP~.r , or- 



dinatim applicata PM— j; erit ex natura Ellipleos PM* 



(/ ) ; CD'(«*)zi:APxPB (?;^ -.v*): ACxCB(»/); adeo- 



que aequatio naturam Ellipfeos exprimens haec , y^—n 



— ^l-. Du(fta ordinatim applicata priori infinite vicina 



pm y ct reda MN ad axem AB parallela, erit, ex na- 



tura trianguli charaderiftici M Nm infinite parui , m N 



{dy):mN{~dx)z:z?M{y):?T{-if). Eft adeoque, 



fubftitucndo pro dy valorem ipfius ex aequatione Elli- 



pfcos defumtum — ^^ , fubtangens PT— ^2^ ; et rur- 



fus fubftituendo valorem ipfius j* , fit eadem (iibtangens 



VT:^^-^—x; ergo CTz:;A'-i-PT:::: ^ ; vnde oritur 



analogia 



