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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 413, page id 1041163592:0447
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PRINCTPTA MATETEMAETEA.
4 13
cus medius Nodorum circulo tori respondens. Et motus Nodo- L. IBEK
rum, quo cempore Sol vergit ab N ad , CA act 1961. 49. 3. 55. TERTIVS.
ut arca NA Z ad circulum cOrUM.
IIaec ita se habene, ex Hypochesi quod Nodus horis singulis in
locum priorem retrahitur, lic ue Sol anno toro completo ad No-
dum cundem redeat a quo Cub inicio digrestus fuerac. Verum per
motum Nodi AC uE Sol cicius 2d NTOdum ROVENEAEUE, et compu-
eanda jam es abbreviatio temporis. Cum Sol anno toro conticiae
360 gradus, ec Nodus motu maximo codem. tempore conticeret
395r. 38. 71. 50, Tcu 39,6355 gradus; et motus: mediocris Nodi
in loco quovis N ic ad ipsius motum mediocrem in Ouadraturis
SuIS, UE A Z 9 ad ATg: erit motus Solis ad morum Nodi in NV, ut
360 AT9 ad 39,63554Z9; id elt,. ut 9,0827646 A. T9 2d A2, 9.
Onde si circuli corius circumferencia N An diridatur in particu-
a5 aequales Aa tempus quo Sol percurrac parriculam A a, s cir-
culus quielceret, erit ad tempus quo percurrit eandem parri
culam. Si circulus una cum Nodis circa cenerum Y revolvatur,
reciprOCC UE 9,0827646 ATg ad 9, 0827646 ATg + AZ 9. Nam
cempus est reciproce ut relocitas qua particula percurritur, de
haec relocitas est summa relocicatum Solis et Nodi. Igieur A cem-
Dus, quo Sol absque motu Nodi perCurrCret arcum NV A, exPO-
natur per Sectorem NI A, _ Particula tempOrIS qUO PCTCUEFCRCE
arcum quam minimum Aa exponatur per Sectoris particulam
ATa; ex (perpendiculo aY in NVn demisto) si in AZ capiatur
aZ, ejus longitudinis ut sic rectangulum dZ in Z V ad Sectoris
parciculam AT a ue AZ9 2d 9,0827546 ATg + AZ 9, id CAt, uE
AC aZ 2d 2 AZ uE AT g 2d 9,0827646 AF9 + AZ g; rectangu-
lum aZ in Q Y delignabit decrementum temporis ex moru Nodi
Oriundum, TeMPOTC EOTO quo arCUS Aa PCFCUrrIEUF. EC Si pun-
ctum a tansit Curvam NdCn arca curvilinca Nd Z crit decre-
MENEUM FOTuM, quo temPOrC arCUS EOtuS N A percurritur; et
propterea excessus Sectoris N AY supra aream N d Z erit tempus
illud Eorum. F.F quoniam motus Nodi cempore minore minor cst
in ratione cemporis, debebit etiam arca Aa Y Z diminui in cadem
ratione. Id quod AcE si capiatur in AZ longitudo eZ, guxe BF
ad lonsitudinem AZ ut A29 ad 9,0827646 ATg + AZ g. Sic
enim rectangulum e. Z in Z Y erit ad aream AZ Ta ut decremen-
tum temporis quo areus A PCrCUrRItUT, ad tempuS EOtuM quo
Percurreretur A Nodus quielceret: EF propterea rectangulum illud
respondebit decremento motus NVodi. EF S punctum e tansaE
Curram