Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="039/01/031.jpg" pagenum="3"/>
              actus, a circumagente manu abire conatur; & conatu ſuo fundam
                <lb/>
              diſtendit,
                <expan abbr="eoq;">eoque</expan>
              fortius quo celerius revolvitur; &, quamprimum di­
                <lb/>
              mittitur, avolat. </s>
              <s>Vim conatui illi contrariam, qua funda lapidem
                <lb/>
              in manum perpetuò retrahit & in orbe retinet, quoniam in manum
                <lb/>
              ceu orbis centrum dirigitur, Centripetam appello. </s>
              <s>Et par eſt ratio
                <lb/>
              corporum omnium, quæ in gyrum aguntur. </s>
              <s>Conantur ea omnia a
                <lb/>
              centris orbium recedere; & niſi adſit vis aliqua conatui iſti contra­
                <lb/>
              ria, qua cohibeantur & in orbibus retineantur, quamQ.E.I.eò Centri­
                <lb/>
              petam appello, abibunt in rectis lineis uniformi cum motu. </s>
              <s>Pro­
                <lb/>
              jectile, ſi vi Gravitatis deſtitueretur, non deflecteretur in terram, ſed
                <lb/>
              in linea recta abiret in cælos; idque uniformi cum motu, ſi modo
                <lb/>
              aeris reſiſtentia tolleretur. </s>
              <s>Per gravitatem ſuam retrahitur a curſu
                <lb/>
              rectilineo & in terram perpetuo flectitur, idque magis vel minus
                <lb/>
              pro gravitate ſua & velocitate motus. </s>
              <s>Quo minor erit ejus gravitas pro quantitate materiæ vel major &c. </s>
              <s>
                <lb/>
              vel major velocitas quacum projicitur, eo minus deviabit a curſu
                <lb/>
              rectilineo & longius perget. </s>
              <s>Si Globus plumbeus, data cum velo­
                <lb/>
              citate ſecundum lineam horizontalem a montis alicujus vertice vi
                <lb/>
              pulveris tormentarii projectus, pergeret in linea curva ad diſtantiam
                <lb/>
              duorum milliarium, priuſquam in terram decideret: hic dupla cum
                <lb/>
              velocitate quaſi duplo longius pergeret, & decupla cum velocitate
                <lb/>
              quaſi decuplo longius: ſi modo aeris reſiſtentia tolleretur. </s>
              <s>Et augendo
                <lb/>
              velocitatem augeri poſſet pro lubitu diſtantia in quam projiceretur,
                <lb/>
              & minui curvatura lineæ quam deſcriberet, ita ut tandem caderet
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              ad diſtantiam graduum decem vel triginta vel nonaginta; vel etiam
                <lb/>
              ut terram totam circuiret priuſquam caderet; vel denique ut in
                <lb/>
              terram nunquam caderet, ſed in cælos abiret & motu abeundi per­
                <lb/>
              geret in infinitum. </s>
              <s>Et eadem ratione, qua Projectile vi gravitatis
                <lb/>
              in orbem flecti poſſet & terram totam circuire, poteſt & Luna vel
                <lb/>
              vi gravitatis, ſi modo gravis ſit, vel alia quacunque vi, qua in ter­
                <lb/>
              ram urgeatur, retrahi ſemper a curſu rectilineo terram verſus, &
                <lb/>
              in orbem ſuum flecti: & abſque tali vi Luna in orbe ſuo retineri
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              non poteſt. </s>
              <s>Hæc vis, ſi juſto minor eſſet, non ſatis flecteret Lunam
                <lb/>
              de curſu rectilineo: ſi juſto major, plus ſatis flecteret, ac de orbe
                <lb/>
              terram verſus deduceret. </s>
              <s>Requiritur quippe, ut ſit juſtæ magnitudinis:
                <lb/>
              & Mathematieorum eſt invenire Vim, qua corpus in dato quovis
                <lb/>
              orbe data cum velocitate accurate retineri poſſit; & viciſſim inve­
                <lb/>
              nire Viam curvilineam, in quam corpus e dato quovis loco data
                <lb/>
              cum velocitate egreſſum a data vi flectatur. </s>
              <s>Eſt autem vis hujus cen­
                <lb/>
              tripetæ Quantitas trium generum, Abſoluta, Acceleratrix, & Motrix. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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