Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/317.jpg" pagenum="289"/>
                    <lb/>
                  untur ex reſiſtentiis, ſuntque ut reſiſtentiæ directe & pondera in­
                    <lb/>
                    <arrow.to.target n="note265"/>
                  verſe. </s>
                  <s>Sunt igitur reſiſtentiæ ut numeri 318,136 & 49,396. Pars
                    <lb/>
                  autem reſiſtentiæ Globi minoris, quæ eſt in duplicata ratione velo­
                    <lb/>
                  citatis, erat ad reſiſtentiam totam, ut 0,56752 ad 0,61675, id eſt, ut
                    <lb/>
                  45,453 ad 49,396; & pars reſiſtentiæ Globi majoris propemodum
                    <lb/>
                  æquatur ipſius reſiſtentiæ toti; adeoque partes illæ ſunt ut 318,136
                    <lb/>
                  & 45,453 quamproxime, id eſt, ut 7 & 1. Sunt autem Globorum
                    <lb/>
                  diametri 18 1/4 & 6 7/8; & harum quadrata (351 9/16) & (47 17/64) ſunt ut 7,438
                    <lb/>
                  & 1, id eſt, ut Globorum reſiſtentiæ 7 & 1 quamproxime. </s>
                  <s>Diffe­
                    <lb/>
                  rentia rationum haud major eſt quam quæ ex fili reſiſtentia oriri po­
                    <lb/>
                  tuit. </s>
                  <s>Igitur reſiſtentiarum partes illæ quæ ſunt, paribus Globis, ut
                    <lb/>
                  quadrata velocitatum; ſunt etiam, paribus velocitatibus, ut qua­
                    <lb/>
                  drata diametrorum Globorum.
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note265"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>Cæterum Globorum, quibus uſus ſum in his experimentis, max­
                    <lb/>
                  imus non erat perfecte Sphæricus, & propterea in calculo hic allato
                    <lb/>
                  minutias quaſdam brevitatis gratia neglexi; de calculo accurato in
                    <lb/>
                  experimento non ſatis accurato minime ſollicitus. </s>
                  <s>Optarim itaque
                    <lb/>
                  (cum demonſtratio Vacui ex his dependeat) ut experimenta cum
                    <lb/>
                  Globis & pluribus & majoribus & magis accuratis tentarentur. </s>
                  <s>Si
                    <lb/>
                  Globi ſumantur in proportione Geometrica, puta quorum diametri
                    <lb/>
                  ſint digitorum 4, 8, 16, 32; ex progreſſione experimentorum col­
                    <lb/>
                  ligetur quid in Globis adhuc majoribus evenire debeat.
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>Jam vero conferendo reſiſtentias diverſorum Fluidorum inter ſe
                    <lb/>
                  tentavi ſequentia. </s>
                  <s>Arcam ligneam paravi longitudine pedum qua­
                    <lb/>
                  tuor, latitudine & altitudine pedis unius. </s>
                  <s>Hanc operculo nuda­
                    <lb/>
                  tam implevi aqua fontana, fecique ut immerſa pendula in medio
                    <lb/>
                  aquæ oſcillando moverentur. </s>
                  <s>Globus autem plumbeus pondere
                    <lb/>
                  166 1/6 unciarum, diametro 3 5/8 digitorum, movebatur ut in Tabula
                    <lb/>
                  ſequente deſcripſimus, exiſtente videlicet longitudine penduli a
                    <lb/>
                  puncto ſuſpenſionis ad punctum quoddam in filo notatum 126 di­
                    <lb/>
                  gitorum, ad oſcillationis autem centrum 134 1/8 digitorum.</s>
                </p>
                <table>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Arcus deſcenſu primo a puncto in
                      <lb/>
                    filo notato deſcriptus, digitorum
                      <emph.end type="italics"/>
                    </cell>
                    <cell>64</cell>
                    <cell>32</cell>
                    <cell>16</cell>
                    <cell>8</cell>
                    <cell>4</cell>
                    <cell>2</cell>
                    <cell>1</cell>
                    <cell>1/2</cell>
                    <cell>1/4</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Arcus aſcenſu ultimo deſcriptus,
                      <lb/>
                    digitorum
                      <emph.end type="italics"/>
                    </cell>
                    <cell>48</cell>
                    <cell>24</cell>
                    <cell>12</cell>
                    <cell>6</cell>
                    <cell>3</cell>
                    <cell>1 1/4</cell>
                    <cell>1/4</cell>
                    <cell>1/8</cell>
                    <cell>(1/16)</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Arcuum differentia motui amiſſo
                      <lb/>
                    proportionalis, digitorum
                      <emph.end type="italics"/>
                    </cell>
                    <cell>16</cell>
                    <cell>8</cell>
                    <cell>4</cell>
                    <cell>2</cell>
                    <cell>1</cell>
                    <cell>1/2</cell>
                    <cell>1/4</cell>
                    <cell>1/8</cell>
                    <cell>(1/16)</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Numerus Oſcillationum in aqua
                      <emph.end type="italics"/>
                    </cell>
                    <cell/>
                    <cell/>
                    <cell>(29/60)</cell>
                    <cell>1 1/5</cell>
                    <cell>3</cell>
                    <cell>7</cell>
                    <cell>11 1/4</cell>
                    <cell>12 2/3</cell>
                    <cell>13 1/3</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Numerus Oſcillationum in aere
                      <emph.end type="italics"/>
                    </cell>
                    <cell>85 1/2</cell>
                    <cell/>
                    <cell>287</cell>
                    <cell>535</cell>
                    <cell/>
                    <cell/>
                    <cell/>
                    <cell/>
                    <cell/>
                  </row>
                </table>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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