Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="039/01/015.jpg"/>
            <p type="main">
              <s>Ex iis quæ hactenus dicta ſunt, conſtat Planetas in Orbitis ſuis
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              retineri per Vim aliquam in ipſos perpetuo agentem: conſtat
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              Vim illam dirigi ſemper verſus Orbitarum centra: conſtat hujus
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              efficaciam augeri in acceſſu ad centrum, diminui in receſſu ab eo­
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              dem: & augeri quidem in eadem proportione qua diminuitur qua­
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              dratum diſtantiæ, diminui in eadem proportione qua diſtantiæ
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              quadratum augetur. </s>
              <s>Videamus jam, comparatione inſtituta inter
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              Planetarum Vires centripetas & Vim Gravitatis, annon ejuſdem
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              forte ſint generis. </s>
              <s>Ejuſdem vero generis erunt, ſi deprehendan­
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              tur hinc & inde leges eædem eædemque affectiones. </s>
              <s>Primo ita­
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              que Lunæ, quæ nobis proxima eſt, Vim centripetam expendamus. </s>
            </p>
            <p type="main">
              <s>Spatia rectilinea, quæ a corporibus e quiete demiſſis dato tem­
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              pore ſub ipſo motus initio deſeribuntur, ubi a viribus quibuſcun­
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              que urgentur, proportionalia ſunt ipſis viribus: Hoc utique con­
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              ſequitur ex ratiociniis Mathematicis. </s>
              <s>Erit igitur Vis centripeta
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              Lunæ in Orbita ſua revolventis, ad Vim Gravitatis in ſuperficie
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              Terræ, ut ſpatium quod tempore quam minimo deſcriberet Luna
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              deſcendendo per Vim centripetam verſus Terram, ſi circulari om­
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              ni motu privari fingeretur, ad ſpatium quod eodem tempore quam
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              minimo deſcribit grave corpus in vicinia Terræ, per Vim gravita­
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              tis ſuæ cadendo. </s>
              <s>Horum ſpatiorum prius æquale eſt arcus a Luna
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              per idem tempus deſcripti ſinui verſo, quippe qui Lunæ tranſla­
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              tionem de Tangente, factam a Vi centripeta, metitur; atque adeo
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              computari poteſt ex datis tum Lunæ tempore periodico tum di­
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              ſtantia ejus a centro Terræ. </s>
              <s>Spatium poſterius invenitur per Ex­
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              perimenta Pendulorum, quemadmodum docuit
                <emph type="italics"/>
              Hugenius.
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              Inito
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              itaque calculo, ſpatium prius ad ſpatium pofterius, ſeu vis cen­
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              tripeta Lunæ in Orbita ſua revolventis ad vim Gravitatis in ſu­
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              perficie Terræ, erit ut quadratum ſemidiametri Terræ ad Orbitæ
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              ſemidiametri quadratum. </s>
              <s>Eandem habet rationem, per ea quæ
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              ſuperius oſtenduntur, vis centripeta Lunæ in Orbita ſua revol­
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              ventis ad vim Lunæ centripetam prope Terræ ſuperficiem. </s>
              <s>Vis
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              itaque centripeta prope Terræ ſuperficiem æqualis eſt vi Gravita­
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              tis. </s>
              <s>Non ergo diverſæ ſunt vires, ſed una atque eadem: ſi enim
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              diverſæ eſſent, corpora viribus conjunctis duplo celerius in Ter­
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              ram caderent quam ex vi ſola Gravitatis. </s>
              <s>Conſtat igitur Vim
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              illam centripetam, qua Luna perpetuo de Tangente vel trahitur
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              vel impellitur & in Orbita retinetur, ipſam eſſe vim Gravitatis
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              terreſtris ad Lunam uſque pertingentem. </s>
              <s>Et rationi quidem con­
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              ſentaneum eſt ut ad ingentes diſtantias illa ſeſe Virtus extendat, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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