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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 405, page id 1041163592:0439
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PRINOIPLA MATHEMATICA.
40
Designet jam. P M arcum; quem Luna dato tempore quam LIvEn
minimo describie, ec ML. lincolam quam Luna, impellence vi TEnrIVS.
praetata 3TT, eodem tempore describere posset. Junsantue
F L MIF, e producantur cx ad m ec l. ubi secent planum l
elipeicae; inque Tm demittatur perpendiculum P HI. lC quo-
niam recta MC. Parallela est plano Lclipricae, ideoque cum recta
mt quae in plano illo jacet concurrere non porest, ex tamen ja-
cent hae rectae in plano communi L. MD ml; Parallelae crunt hxe
rectae, de propterea similia crune triangula L. MF, Lmp. Jam.
cum MP m sic in plano Orbis, in quo Luna in loco F moreba-
tur; incidec punctum m in lineam dn per Orbis illius Nodos.
N,n ductam. Ec quoniam vis qua lincola L. M genCrATUE, (I
tora simul ex semel in loco P imprecta cHet, CfCCreE uE L una
moreretur in areu, cujus chorda cAet L. P, aeque adeo EraNS.
Ferree Lunam de plano MF mT in planum L P VT; mOrUS an
sularis Nodorum a vi illa genicus, aequalis erit angulo mTI. Fst
autem nb ad m F UE ML ad MF, adeoque cum MF ob da-
cum cempus daca siC, CR mI uE rectangulum M L X M F, id cA,
ut rectangulum ITXm P. Ec angulus m FI, si modo angulus
E
TmD rectus SIC, CAt UE X dC PFOPECrCA UE
TX Fn
(ob proportionales Tm et m F, TF et PII
Im id CAt,
adeoque ob datam TP, uE TYX P FI. Ouod A angulus T mh
Peu ST N obliguus sic, eric angulus mTV adhuc minor, in rati-
one linus anguli ST N ad Radium. FA igitur velocitas NO-
dOrUM UE TTZ P FIZ AZ, sive ut contentum sub sinubus crium
angulorum TPL, FTN e STN.
Si anguli illis Nodis in Ouadracuris ee Luna in Syzygia existen.
tibus, recti sine, lineola mi abibie in infinitum, ee angulus mZl
eradet angulo m PV aequalis. Hoc aucem in casu, angulus m F
est ad angulum F F M, quem Luna eodem tempore motu uo
apparente circa Terram deseribit uc 2 ad 59,575. Nam angulus
im Fb aequalis est angulo L. F M, id est, ansulo deRexionis Lunx
a recto eramite, quem sola vis praetara Solaris 3TF A cum cesta-
ret Lunae gravitas dato illo rempore generare pollet; ec angulus
P TM aequalis est angulo defexionis Lunae a recto cramite, quem
vis illa, qua Luna in Orbe suo recinetur, si cum cellaret vis Sola-
rio 3YZ EOAEM LEPOTE SCMETArET LC ha VireS, ut supra dixi
MUSs