confiderarl debuiffct motiis cometae, ciiius orbita parabo- 

 lica in ipfum planum eclipticae incidit. Huic triplici de- 

 fedo fequentibus pioblematibus hejc occurrere mecum con- 

 ftitui. 



Problema i. 



Tab. V. §,2. "Datis diiabus cometae a foJe dijiamiis FSzif 



^ig- '• et G S - g, ina ciim angulo imercepto F S G - ^ , inuenire 

 aream fe&oris paraboUci F S G - A. 



Solutio. 



Sit n vertex parabolne, fiue perihelium comctae, 

 pofitaque eiiis diflantia a Sole 11 S - p, erit parameter hii- 

 his parabolae — 4p; vnde fi ex puni^o F ad axem IIB 

 demittatur perpendiciilum FP, pofita abfciflli 11 P — jr et 

 applicata P F — j erit ex natura parabolae yy — z^px et 

 y — PFzr cypjr. Hinc autem fiet area 



UV^P -fy dx-^y pfdxV x-^^xVpx. 

 Cum autem fit 



F S - y (P S' 4- P F^) = y {[x-pY + 4p A-), 

 erit Y S- f - X -^- p^ ideoque xzzf — p^ vnde fit area 



nPF-;(/-p)y(/p-pp). 



Hinc fubtrahi dcbet area trianguli S P F r I P F. P S, quae efl: 



SV¥-{x-p)Vpx-{x-p)V ,pf-pp)j 

 qua fublata remanebit area 11 SF, fcilicet 



nsFri(/+2p)y(p/^/>p). 



Quodfi iam puncf^um alterum G fimilf modo traAc- 

 Cur, demifla applicata G Q et faflis rcliquis opcrationibus 



-vt 



