1
DE MUNDI
SYSTEMATE
SYSTEMATE
PROPOSITIO XXXI. PROBLEMA XII.
Invenire motum horarium Nodorum Lunæ in Orbe Elliptico.
Deſignet QpmaqEllipſin, axe majore Qq,minore abde
ſcriptam, QAqCirculum circumſcriptum, TTerram in utriuſque
centro communi, SSolem, pLunam in Ellipſi motam, & pmar
cum quem data temporis particula quam minima deſcribit, N& n
Nodos linea Nnjunctos, pK& mkperpendicula in axem Qq
demiſſa & hinc inde producta, donec occurrant Circulo in P& M,
214[Figure 214]
& lineæ Nodorum in D& d.Et ſi Luna, radio ad Terram du
cto, aream deſcribat tempori proportionalem, erit motus Nodi in
Ellipſi ut area pDdm.
ſcriptam, QAqCirculum circumſcriptum, TTerram in utriuſque
centro communi, SSolem, pLunam in Ellipſi motam, & pmar
cum quem data temporis particula quam minima deſcribit, N& n
Nodos linea Nnjunctos, pK& mkperpendicula in axem Qq
demiſſa & hinc inde producta, donec occurrant Circulo in P& M,
214[Figure 214]& lineæ Nodorum in D& d.Et ſi Luna, radio ad Terram du
cto, aream deſcribat tempori proportionalem, erit motus Nodi in
Ellipſi ut area pDdm.
Nam ſi PFtangat Circulum in P,& producta occurrat TN
in F,& pftangat Ellipſin in p& producta occurrat eidem TN
in F,& pftangat Ellipſin in p& producta occurrat eidem TN