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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 124, page id 1041163592:0158
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LIIIIIIIIIIIIIIII
124
PFITLOSODETLLE NATDRALIS
Mk X M5
t
ac
rk4
2kC
vel ut mkZmS ad rk quadratum; hOc eA, (
capiantur dacae quancitares F, C in ea ratione ad invicem quam
habeE angulus VCZ ad angulum V Cp, UE G GE - F F adFF. FE
pFOPTErCa, A centro C intervallo quoris C F vel Cp describatur
Sector circularis aequalis area Fori V P C, quam corDuS F cempore
quoris in Orbe immobili revolvens radio ad cenerum ducto de-
fcripsIc: differentia virium, quibus corpus F in Orbe immobili et
corpus p in Orbe mobili revolvuntur, erit ad rim centrixetam qua
corpus aliquod radio ad centrum ducto Sectorem illum, eodem tem-
pore quo descripta sic arca V F C uniformiter describere poruissee,
ut GC = F F ad F F. Namque Sector ille de area pC k lunt adt in-
vicem uE tempora quibus describunEUr.
Corot. 2. Si Orbis VP X Fllipsis sic umbilicum habens C e AD.
sidem Cummam V; eique similis ec aequalis ponatur EIlipES ut p k,
ica uE sic semper pC aequalis F C, ec angulus V Cp Sc ad anoulum
CF in data ratione C ad F; pro alcicudine autem FC vel pC
Scribatur A, ex pro FIlipleos latere recto ponatur 2R: erit ris qua
corpus in Ellips mobili revolvi pocest, uc
E, R C C+ - R F F
A cub.
_E COntra. Exponatur enim ris qua corpus revolvatur in immota
si
P
EIliBA per quantitatem , et vis in V eric.
CV quad. Visau-
tem qua corpus in Circulo ad distantiam C V ea cum velocieate
revolri posset quam corpus in Ellipa revolvens habet in V,
est ad rim qua corpus in Ellipsi revolvens urgetur in Apside V
uc dimidium laceris recti Ellipseos ad Circuli semidiametrum CV.
E FV: e vis qU_e SIc ad haHC Ut C C - F F ad
adeoque ralet
E F, valet
CVCub
R C C+ =RF F
CV Cub.
: eAtque haec ris (per hujus C Orol. T.)
difterentia ririum in V quibus corpuS D in ENIpSI imMOT V P R
e corpus p in FIlips mobili ups revolruntur. Unde cum (per
hanc PxoD.) differencia illa in alia quaris alcitudine A St ad sC-
A CUB.
in omni alcitudine A ralebit RGC -R F F
A cub.
eadem difterentia
Igicur ad vim
qua corpus revolri porest in FIlips immobili V P K, addatur ex-
ceNTus RGC RFF ex componetur vis tota
A cub.
S F
RC C =R F I
A cub.
qu
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DE MOXV
CORPONVIIUE