1
DE MUNDI
SYSTEMATE
SYSTEMATE
LEMMA VII.
Per datum punctumP ducere rectam lineamBC, cujus partes
PB, PC, rectis duabus poſitione datisAB, AC abſciſſæ, da
tam habeant rationem ad invicem.
PB, PC, rectis duabus poſitione datisAB, AC abſciſſæ, da
tam habeant rationem ad invicem.
228[Figure 228]A puncto illo Pad rectarum al
terutram ABducatur recta quævis
PD,& producatur eadem verſus
rectam alteram ACuſque ad E,ut
ſit PEad PDin data illa ratione.
Ipſi ADparallela ſit EC; & ſi
agatur CPB,erit PCad PBut
PEad PD. q.E.F.
terutram ABducatur recta quævis
PD,& producatur eadem verſus
rectam alteram ACuſque ad E,ut
ſit PEad PDin data illa ratione.
Ipſi ADparallela ſit EC; & ſi
agatur CPB,erit PCad PBut
PEad PD. q.E.F.
LEMMA VIII.
SitABC Parabola umbilicum habensS. ChordaAC biſecta
inI abſcindatur ſegmentumABCI, cujus diameter ſitI μ &
vertexμ. InI μ producta capiaturμ O æqualis dimidio ipſius
229[Figure 229]
I μ. JungaturOS, & producatur ea ad ξ, ut ſitS ξ æqualis
2SO. Et ſi CometaB moveatur in arcuCBA, & agatur
ξ B ſecansAC inE: dico quod punctumE abſcindet de chordo
AC ſegmentumAE tempori proportionale quamproxime.
inI abſcindatur ſegmentumABCI, cujus diameter ſitI μ &
vertexμ. InI μ producta capiaturμ O æqualis dimidio ipſius
229[Figure 229]I μ. JungaturOS, & producatur ea ad ξ, ut ſitS ξ æqualis
2SO. Et ſi CometaB moveatur in arcuCBA, & agatur
ξ B ſecansAC inE: dico quod punctumE abſcindet de chordo
AC ſegmentumAE tempori proportionale quamproxime.
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