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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 418, page id 1041163592:0452
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418
PFITLOSOPHLE NAPORALIS
De Monor est (cum Pp sic ad PG ue sinus Tnelinationis praedictae ad ra-
dium, et
 sic ad 4 AF ut sinus duplicari anguli AFn
ad radium quadruplicatum) ut Inclinationis ejusdem snus ductus
in sinum duplicatae diltancix Nodorum 2 Sole, ad quadruptum
quadratum radii.
Corol. 4. Ouoniam Inelinationis horaria Variacio, ubi Nodi in
Ouadraturis vertaneur, est (per hanc Propositionem) ad angu-
lum 33. 10 33 ut IZZ AZXECZ . 2d AT cub. id cA,
ut
TTXTG, F
X p ad 2 AT; hoc CA, ut sinus duplicatxe di-
Rancixe Lunx a Ouadraturis ductus in x ad radium duplica-
eum: Tumma omnium Variationum horariarum, quo tempore
Luna in hoc situ Nodorum transit a Guadratura ad S72ygiam,
(id cst, spatio horarum 1773,) eric ad summam coridem angulo-
rum 33. 201. 333 Ceu 587d ut summa omnium sinuum dupli-
Caxe distantiae Lunx a Ouadraturis ducta in F C. ad summam co-
E
tidem diametrorum; hoc cA, ut diameter ducta in ∞ ad cir-
cumterentiam; id eAt, s Inclinatio siE 5PL 2, UE 7X = 838 ad 22,
Peu 278 2d 20000. Proindeque Variario tota, ex summa om-
nium horariarum Variacionum cempore praedicto contata, est
263, (Cu 2. 43.
PROPOSITIO ZXXV. PROBLEMA ZVI
Dato tempore invenire Inclinationem Orbis Lunaris ad planum
Eclipticae.
Sic AD sinus Inelinacionis maximaes ee AB sinus Inclinacio.
his minimae. Bilecetur B D in C, _ centro C, intervallo BC,
describatur Circulus BGD. In AC capIAEUT C F in Ca parione
ad F B quam F. B habet ad 2B A: EC S dato tempore consti-
cuacur angulus 2F. C aequalis duplicatae distantiae Nodorum 2
Qu2-
SXSXEM AXB