Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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eædem a viribus acceleratricibus ad alia corpora tendentibus, aut
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non urgentur niſi leviſſime, aut urgentur æqualiter & ſecundum li
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neas parallelas quamproxime. </
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LIBER
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PRIMUS.</
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PROPOSITIO LXVI. THEOREMA XXVI.
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Si Corpora tria, quorum Vires decreſcunt in duplicata ratione di
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ſtantiarum, ſe mutuo trahant, & attractiones acceleratrices bi
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norum quorumcunQ.E.I. tertium ſint inter ſe reciproce ut qua
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drata diſtantiarum; minora autem circa maximum revolvan
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tur: Dico quod interius circa intimum & maximum, radiis
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ad ipſum ductis, deſcribet areas temporibus magis proportio
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nales, & Figuram ad formam Ellipſeos umbilicum in concur
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ſu radiorum habentis magis accedentem, ſi corpus maximum
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his attractionibus agitetur, quam ſi maximum illud vel a mi
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noribus non attractum quieſcat, vel multo minus vel multo ma
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gis attractum aut multo minus aut multo magis agitetur.
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<
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>Liquet fere ex demonſtratione Corollarii ſecundi Propoſitionis
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præcedentis; ſed argumento magis diſtincto & latius cogente ſic
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evincitur. </
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Cas.
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1. Revolvantur
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corpora minora
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P
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&
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S
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in eodem plano circa
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maximum
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T,
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quorum
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P
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deſcribat Orbem in
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teriorem
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PAB,
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&
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S
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exteriorem
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SE.
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Sit
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SK
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mediocris diſtan
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tia corporum
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P
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&
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S
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;
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& corporis
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P
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verſus
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S
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attractio acceleratrix in mediocri illa diſtantia exponatur per e
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andem. </
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<
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>In duplicata ratione
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SK
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ad
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SP
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capiatur
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SL
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ad
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SK,
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& e
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rit
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SL
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attractio acceleratrix corporis
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P
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verſus
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S
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in diſtantia quavis
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SP.
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Junge
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PT,
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eique parallelam age
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LM
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occurrentem
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ST
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in
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M,
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& attractio
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SL
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reſolvetur (per Legum Corol 2.) in attractiones
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SM, LM.
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Et ſic urgebitur corpus
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P
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vi acceleratrice triplici: </
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