Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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LIBER
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TERTIUS.</
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LEMMA XI.
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Si Cometa motu omni privatus de altitudine
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SN
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ſeu
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S
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+1/3I
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demitteretur, ut caderet in Solem, & ea ſemper vi uniformiter
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continuata urgeretur in Solem, qua urgetur ſub initio; idem ſe
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miſſe temporis quo in Orbe ſuo deſcribat arcum
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AC,
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deſcenſu
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ſuo deſcriberet ſpatium longitudini
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I
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æquale.
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<
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>Nam Cometa quo tempore deſcribat arcum Parabolicum
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AC,
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eodem tempore ea cum velocitate quam habet in altitudine
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SP
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(per Lemma noviſſimum) deſcribet chordam
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AC,
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adeoque (per
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Corol. </
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>7. Prop. </
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>XVI. Lib. </
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>I.) eodem tempore in Circulo cujus ſemi
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diameter eſſet
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SP,
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vi gravitatis ſuæ revolvendo, deſcriberet arcum
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cujus longitudo eſſet ad arcus Parabolici chordam
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AC,
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in ſubdu
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plicata ratione unius ad duo. </
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<
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>Et propterea eo cum pondere quod
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habet in Solem in altitudine
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SP,
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cadendo de altitudine illa in
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Solem, deſcriberet ſemiſſe temporis illius (per Corol.9. Prop. </
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Lib. </
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<
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>I.) ſpatium æquale quadrato ſemiſſis chordæ illius applicato
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ad quadruplum altitudinis
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SP,
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id eſt, ſpatium (
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AIq/4SP
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). Unde cum
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pondus Cometæ in Solem in altitudine
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SN,
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ſit ad ipſius pondus
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in Solem in altitudine
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SP,
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ut
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SP
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ad
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S
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: Cometa pondere
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quod habet in altitudine
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SN
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eodem tempore, in Solem caden
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do, deſcribet ſpatium (
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AIq/4S
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), id eſt, ſpatium longitudini
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I
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vel
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M
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æquale.
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Q.E.D.
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PROPOSITIO XLI. PROBLEMA XXI.
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Cometæ in Parabola moti Trajectoriam ex datis tribus
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Obſervationibus determinare.
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<
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>Problema hocce longe difficillimum multimode aggreſſus, com
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poſui Problemata quædam in Libro primo quæ ad ejus ſolutio
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nem ſpectant. </
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<
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>Poſtea ſolutionem ſequentem paulo ſimpliciorem
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excogitavi. </
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<
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>Seligantur tres obſervationes æqualibus temporum intervallis ab
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invicem quamproxime diſtantes. </
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<
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>Sit autem temporis intervallum
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illud ubi Cometa tardius movetur paulo majus altero, ita videlicet </
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