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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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RINOIPTA MATIIEMATIOA.
PROPOSITIO LZ. THTEOREMA ZXIII.
Si corpora duo S S P, Viribus quadrato distantiae suae reciproce
proporiionalibus se mutuo trabentia, revolvuntur circa gravi-
tatis centrum commune: dico quod Fllipseos, quam corpus al
terutrum P hoc motu circa alterum S describit. Axis principa
lis erit ad Axem principalem Fllipseos, quam corpus idem P
circa alterum quiescens S eodem tempore periodico describere
posset, ut summa corporum duorum S + P ad primam duarum
medie proportionalium inter hanc summam es corpus illud al
terum S.
NNam s descriptae Ellipses eent sibi invicem equales, tempora
periodica (per Theorema Luperius) Forene in subduplicata ratione
corporis Sad Cummam corporum S. F F. Minuatur in hac ratione
tempus periodicum in Elliph Posteriore, ex tempora periodica era-
dene requalia; Ellipleos autem axis principalis (per Pcop. XV.) minu-
etur in ratione cujus haec est selquiplicata, id est in ratione, cujus
ratio Sad S L F est criplicaca; adeoque erit ad axem principalem
Ellipseos alcerius, ut prima duarum medie provortionalium inter
S FP e S ad S + F. Ec inverse, axis principalis Rllipscos circa
corpus mobile descriper erit ad axem principalem descriptae circa
immobile, uc S F P ad primam duarum medic proporcionalium in-
tex S + P _S. D. F. D.
PROEOSITIO LXI. THEOREMA XXIV.
Si corpora duo viribus quibusvis se mutuo trabentia, neque alias
acitata vel impedita, quomodocunque moveantur; motus eo-
rum perinde se habebunt ac si non traberent se mutuo, sed u
trumque a corpore tertio in communi eravitatis centro constituto
Viribus iisdem traberetur: Ft Virium trahentium eadem erit L ex
respectu distantiae corporum a centro illo communi at que respe-
Etu distantiae totius inter corpora.
Nam vires illae, quibus corpora se mutuo trahune, cendendo
ad corpOra, cendune ad commune graricatis centrum incerme.
dium,
T
PN LMVB.