Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="039/01/014.jpg"/>
            <p type="main">
              <s>Jam illud concedi æquum eſt, quod Mathematicis rationibus
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              colligitur & certiſſime demonſtratur; Corpora nempe omnia, quæ
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              moventur in linea aliqua curva in plano deſcripta, quæque radio
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              ducto ad punctum vel quieſcens vel utcunque motum deſcribunt
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              areas circa punctum illud temporibus proportionales, urgeri a
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              Viribus quæ ad idem punctum tendunt. </s>
              <s>Cum igitur in confeſſo
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              ſit apud Aſtronomos, Planetas primarios circum Solem, ſecunda­
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              rios vero circum ſuos primarios, areas deſcribere temporibus pro­
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              portionales; conſequens eſt ut Vis illa, qua perpetuo detorquen­
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              tur a Tangentibus rectilineis, & in Orbitis curvilineis revolvi co­
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              guntur, verſus corpora dirigatur quæ ſita ſunt in Orbitarum cen­
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              tris. </s>
              <s>Hæc itaque Vis non inepte vocari poteſt, reſpectu quidem
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              corporis revolventis, Centripeta; reſpectu autem corporis cen­
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              tralis, Attractiva; a quacunQ.E.D.mum cauſa oriri fingatur. </s>
            </p>
            <p type="main">
              <s>Quin & hæc quoque concedenda ſunt, & Mathematice demon­
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              ſtrantur: Si corpora plura motu æquabili revolvantur in Circulis
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              concentricis, & quadrata temporum periodieorum ſint ut cubi di­
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              ſtantiarum a centro communi; Vires centripetas revolventium
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              fore reciproce ut quadrata diſtantiarum. </s>
              <s>Vel, ſi corpora revol­
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              vantur in Orbitis quæ ſunt Circulis finitimæ, & quieſcant Orbita­
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              rum Apſides; Vires centripetas revolventium fore reciproce ut
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              quadrata diſtantiarum. </s>
              <s>Obtinere caſum alterutrum in Planetis
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              univerſis conſentiunt Aſtronomi. </s>
              <s>Itaque Vires centripetæ Plane­
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              tarum omnium ſunt reciproce ut quadrata diſtantiarum ab Or­
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              bium centris. </s>
              <s>Si quis objiciat Planetarum, & Lunæ præſertim,
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              Apſides non penitus quieſcere; ſed motu quodam lento ferri in
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              conſequentia: reſponderi poteſt, etiamſi concedamus hunc mo­
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              tum tardiſſimum exinde profectum eſſe quod Vis centripetæ pro­
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              portio aberret aliquantum a duplicata, aberrationem illam per
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              computum Mathematicum inveniri poſſe & plane inſenſibilem
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              eſſe. </s>
              <s>Ipſa enim ratio Vis centripetæ Lunaris, quæ omnium ma­
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              xime turbari debet, paululum quidem duplicatam ſuperabit; ad
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              hanc vero ſexaginta fere vicibus propius accedet quam ad tripli­
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              catam. </s>
              <s>Sed verior erit reſponſio, ſi dicamus hanc Apſidum progreſ­
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              ſionem, non ex aberratione a duplicata proportione, ſed ex alia
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              prorſus diverſa cauſa oriri, quemadmodum egregie commonſtratur
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              in hac Philoſophia. </s>
              <s>Reſtat ergo ut Vires centripetæ, quibus Pla­
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              netæ primarii tendunt verſus Solem & ſecundarii verſus primarios
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              ſuos, ſint accurate ut quadrata diſtantiarum reciproce. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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