Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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DE MOTU
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CORPORUM</
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PROPOSITIO LXVIII. THEOREMA XXVIII.
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Poſitis iiſdem attractionum legibus, dico quod corpus exterius
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S,
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circa interiorum
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P & T
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commune gravitatis centrum
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C,
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ra
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diis ad centrum illud ductis, deſcribit areas temporibus magis
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proportionales, & Orbem ad formam Ellipſeos umbilicum in
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centro eodem habentis magis accedentem, ſi corpus intimum &
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maximum his attractionibus perinde atque cætera agitetur, quam
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ſi id vel non attractum quieſcat, vel multo magis aut multo
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minus attractum aut multo magis aut multo minus agitetur.
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<
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>Demonſtratur eo
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dem fere modo cum
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Prop. </
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>LXVI, ſed ar
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gumento prolixiore,
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quod ideo prætereo. </
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Suffecerit rem ſic æſti
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mare. </
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>Ex demonſtra
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tione Propoſitionis
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noviſſimæ liquet cen
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trum in quod corpus
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S
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conjunctis viribus urgetur, proximum eſſe communi centro gra
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vitatis duorum illorum. </
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illo communi, & quieſceret commune centrum gravitatis corporum
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trium; deſcriberent corpus
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S
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ex una parte, & commune centrum
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aliorum duorum ex altera parte, circa commune omnium centrum
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quieſcens, Ellipſes accuratas. </
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<
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>Liquet hoc per Corollarium ſecun
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dum Propoſitionis LVIII collatum cum demonſtratis in Propoſ. </
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LXIV & LXV. </
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>Perturbatur iſte motus Ellipticus aliquantulum per
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diſtantiam centri duorum a centro in quod tertium
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S
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attrahitur. </
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Detur præterea motus communi trium centro, & augebitur per
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turbatio. </
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>Proinde minima eſt perturbatio ubi commune trium
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centrum quieſcit, hoc eſt, ubi corpus intimum & maximum
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T
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lege
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cæterorum attrahitur: fitque major ſemper ubi trium commune il
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lud centrum, minuendo motum corporis
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T,
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moveri incipit & ma
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gis deinceps magiſque agitatur. </
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