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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 163, page id 1041163592:0197
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DRINOTDLA MATHEMATICA.
de maxima Ae ubi ApSides sunE in Syzygiis. Si Apsides constituan-
LTBER
cur in Ouadraturis, ratio prope Aplides minor eA eE PFODC SyZY - PRIMVS
Sias major quam duplicata distanciarum, et ex ratione illa majori
Oritur Rugis motus velocissimus, uti jam dictum cst. AC A COn-
lideretur ratio incrementi vel decrementi torius in progressu inter
ApSdes, haec minor est quam duplicara distanciarum. Vis in AP.
side ima est ad vim in Apscc summa in minore quam duplicata
ratione dictantix Apsidis summae ab umbilico Fllipseos ad di-
stantiam Apsidis imae ab eodem umbilico: ec c contra, ubi
Apsides constituuntur in Syzrgiis, vis in ApEdc ima est ad vim
in Apside summa in majore quam duplicata ratione dictantiarum.
Nam vires L. M in Ouadraturis additae viribus corporis Y compo-
nunc vires in ratione minore, de vires R L. in Syzysiis lubductx
viribus corporis Y relinquune vires in ratione majore. Ult 1981-
cur ratio decrementi ex incrementi totius, in transitu incer ApEIdes,
minima in Ouadracuris, maxima in Syzsgiis: ec Propterea in tran-
sicu APCidum a Ouadraturis ad SyZygias Perpetuo ausetur, ausct-
que Lxcentricicatem Fllipseos; inque transitu a Syryoiis ad
Duadraturas perpecuo diminuitur, ex Lxcencricitatem diminuit.
Corol. 20. VE rarionem ineamus errorum in Lacicudinem, Ainga-
mus planum Orbis L.ST immobile MaHeTC; eC ex CrTOrUM eXPO.
Sita CauTa manifestum est quod, ex viribus NA, MIL, aux TunE
causa illa eora, vis ML agendo semper secundum planum Orbis
F AB, nunguam perturbat motus in Laticudinem; quodque ris NVNI.
ubi Nodi sunc in Syzygiis, agendo etiam secundum idem Orbis
Planum, non percurbat hos mocus; ubi vero sune in Guadraturis
cosmaxime perrurbat, corpusque P de plano Orbis lui perpetuo
trahendo, minuit inclinationem plani in transieu corporis a Oua-
draturis ad Syzy gias, augetque ricissim eandem in cranSEu 2 SyZY.
siis ad Ouadraturas. Onde At ut corpore in Syrygiis existente in
clinatio cradat omnium minima, redeacque ad priorem magnicudi-
nem circiter, ubi corpus ad Nodum proximum accedit. AEsI Nodi
constituantur in Octantibus post Guadraturas, id cA, inter C ec A.
D ec B, intellioetur ex modo expolitis quod, in transitu corporis
Pa Nodo alterutro ad gradum inde nonagesimum, inclinatio pla-
ni perpetuo minuitur; deinde in cransitu per proximos 45 gradus.
ulque ad Duadraturam proximam, inclinatio augetur, et postea de-
nuo in transitu per alios 45 gradus, ulque ad Nodum proximum,
diminuitur. Magis itaque diminuicur inclinario quam auSCtuE, de
proxcerea minor est semper in Nodo subsequente quam in praece
AeNEC.
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