Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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Corol.7. Ex præmiſſis conſequitur etiam quod Ellipſeos a cor­
pore
Pdeſcriptæ Axis, ſeu Apſidum linea, quoad motum angula­
rem
progreditur & regreditur per vices, ſed magis tamen progre­
ditur
, & in ſingulis corporis revolutionibus per exceſſum progreſ­
ſionis
fertur in conſequentia.
Nam vis qua corpus Purgetur in
corpus
Tin Quadraturis, ubi vis MNevanuit, componitur ex vi
LM& vi centripeta qua corpus Ttrahit corpus P.Vis prior LM,
ſi
augeatur diſtantia PT,augetur in eadem fere ratione cum hac
diſtantia
, & vis poſterior decreſcit in duplicata illa ratione, adeo­
que
ſumma harum virium decreſcit in minore quam duplicata ra­
tione
diſtantiæ PT,& propterea (per Corol. 1. Prop. XLV) efficit
ut
Aux, ſeu Apſis ſumma, regrediatur.
In Conjunctione vero &
Oppoſitione
, vis qua corpus Purgetur in corpus Tdifferentia eſt
inter
vim qua corpus Ttrahit corpus P& vim KL; & differen­
tia
illa, propterea quod vis KLaugetur quamproxime in ratione
diſtantiæ
PT,decreſcit in majore quam duplicata ratione diſtan­
tiæ
PT,adeoque (per Corol. 1. Prop.XLV) efficit ut Aux progre­
diatur
.
In locis inter Syzygias & Quadraturas pendet motus Au­
gis
ex cauſa utraque conjunctim, adeo ut pro hujus vel alterius
exceſſu
progrediatur ipſa vel regrediatur.
Unde cum vis KLin
Syzygiis
ſit quaſi duplo major quam vis LMin Quadraturis, ex­
ceſſus
in tota revolutione erit penes vim KL,transferetque Au­
gem
ſingulis revolutionibus in conſequentia.
Veritas autem hujus
& præcedentis Corollarii facilius intelligetur concipiendo Syſtema
corporum
duorum T, Pcorporibus pluribus S, S, S,&c, in Or­
be
ESEconſiſtentibus, undique cingi. Namque horum actioni-

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