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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 414, page id 1041163592:0448
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AT 4
PHTLOSOPETTLE NATURALIS
DEMONDI Curram NC Fn area tota NCZ, quae summa est omnium decre-
meneorum, respondebit decremento toris quo tempore arcuS A W
percurritur; Sc area reliqua  Le respondebit motui reliquo, qui
verus CA Nodi mOFUS quO TOMPOTC ArCUS FOtS N A, per Solis e
Nodi conjunctos motus, percurritur. Jam vero area semicircule
est ad aream Figurx NVe Fn T, per methodum Scrierum inhinita-
rum quxe(IEam, ut 793 2d 60 quamproxime. Motus autem qui
respondet Circulo tori crat 198. 49. 3. 553 _E prODECrCa MOTS,
qui Fisura NCFn T duplicatae respondet, CA 161. 29. 58. 2
Oui de motu priore subductus relinquit 1881. 19. 5. 53 mocum
eocum Nodi incer sui ipsus Conjunctiones cum Sole; ex hic mo-
tus de Solis motu annuo gradtuum 360 Tubductus, relinquie 34. L8
40. 54. 7 motum Solis inter ealdem Conjunctiones. IAC au-
tem motus est ad mocum annuum 3608. ue Nodi motus jam in-
VenEuS 1881. 19. 5. 53 ad ipsius mocum annuum, qui propterca
CrIE T9e. 18. 1. 23. HIic eA motus medius Nodorum in anno
Sidereo. Idem per Tabulas AAronomicas CA 198. 21. 21. 50.
DISTCTENLIA MINOE CR DATEO ERCCENECSIMA MOEUS FOFIUS, ex 2b Or-
bis Lunaris Recentricitace ex Inclinatione ad planum Rclipricae
oriri videtur. Per Eccentricitatem Orbis motus Nodorum nimis
acceleratur, ex per ejus Inclinationem vicissim recardatur aliquan-
tulum, ec 2d justam velocitatem reducitur.
PROPOSTTIOXXXIH PROBLEMA XIV.
Invenire motum verum Nodorum Lunae.
In tempore quod est ut area NT A = N d Z, (in Fic. Praeced.)
mocus iste eA uc arca N Ae NV, et inde datur. Verum ob nimiam
calculi difticultatem, praestat sequentem Problematis constructio-
nem adhibere. Centro C, interrallo quoris CD, describatur
circulus BF FD. PrOducatur DC ad A, ue sIC AB ad AC
uc mocus medius ad semissem mocus reri medioeris, ubi Nodi
lunc in Ouadracuris, (id est, uE 798. 18. 2. 23. 2d 198. 49.
acque adeo BC ad AC ue moruum diAerentia 08c. 31.
2. 32, 2d mocum Posteriorem 19er 49. 3. 551) hoc eAt, uE
12d 382 dein per punctum D ducatur inFInITa (78, QuX tanSAC
circulum in D; ec s capiatur angulus BC F. vel BC F aquaIS
duplae dittantiae Solis a loc0 Nodi, Der mocum medium invento;
STSTEMAT