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| Newton, Isaac Philosophia naturalis principia mathematica 1713 | ||||||
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408
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,
& 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