Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/315.jpg" pagenum="287"/>
                    <arrow.to.target n="note263"/>
                    <arrow.to.target n="table1"/>
                    <arrow.to.target n="table2"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note263"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <table>
                  <table.target id="table1"/>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Deſcenſus primus
                      <emph.end type="italics"/>
                    </cell>
                    <cell>2</cell>
                    <cell>4</cell>
                    <cell>8</cell>
                    <cell>16</cell>
                    <cell>32</cell>
                    <cell>64</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Aſcenſus ultimus
                      <emph.end type="italics"/>
                    </cell>
                    <cell>1 1/2</cell>
                    <cell>3</cell>
                    <cell>6</cell>
                    <cell>12</cell>
                    <cell>34</cell>
                    <cell>48</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Numerus Oſcillat.
                      <emph.end type="italics"/>
                    </cell>
                    <cell>374</cell>
                    <cell>272</cell>
                    <cell>162 1/2</cell>
                    <cell>83 1/3</cell>
                    <cell>41 2/3</cell>
                    <cell>22 2/3</cell>
                  </row>
                </table>
                <p type="main">
                  <s>Poſtea Globum plumbeum, diametro digitorum 2, & pondere
                    <lb/>
                  unciarum
                    <emph type="italics"/>
                  Romanarum
                    <emph.end type="italics"/>
                  26 1/4, ſuſpendi filo eodem, ſic ut inter cen­
                    <lb/>
                  trum Globi & punctum ſuſpenſionis intervallum eſſet pedum 10 1/2,
                    <lb/>
                  & numerabam oſcillationes quibus data motus pars amitteretur.
                    <lb/>
                  Tabularum ſubſequentium prior exhibet numerum oſcillationum
                    <lb/>
                  quibus pars octava motus totius ceſſavit; ſecunda numerum oſcil­
                    <lb/>
                  lationum quibus ejuſdem pars quarta amiſſa fuit.
                    <lb/>
                  </s>
                </p>
                <table>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Deſcenſus primus
                      <emph.end type="italics"/>
                    </cell>
                    <cell>1</cell>
                    <cell>2</cell>
                    <cell>4</cell>
                    <cell>8</cell>
                    <cell>16</cell>
                    <cell>32</cell>
                    <cell>64</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Aſcenſus ultimus
                      <emph.end type="italics"/>
                    </cell>
                    <cell>7/8</cell>
                    <cell>7/4</cell>
                    <cell>3 1/2</cell>
                    <cell>7</cell>
                    <cell>14</cell>
                    <cell>28</cell>
                    <cell>56</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Numerus Oſcillat.
                      <emph.end type="italics"/>
                    </cell>
                    <cell>226</cell>
                    <cell>228</cell>
                    <cell>193</cell>
                    <cell>140</cell>
                    <cell>90 1/2</cell>
                    <cell>53</cell>
                    <cell>30</cell>
                  </row>
                  <row>
                    <cell/>
                    <cell/>
                    <cell/>
                    <cell/>
                    <cell/>
                    <cell/>
                    <cell/>
                    <cell/>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Deſcenſus primus
                      <emph.end type="italics"/>
                    </cell>
                    <cell>1</cell>
                    <cell>2</cell>
                    <cell>4</cell>
                    <cell>8</cell>
                    <cell>16</cell>
                    <cell>32</cell>
                    <cell>64</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Aſcenſus ultimus
                      <emph.end type="italics"/>
                    </cell>
                    <cell>3/4</cell>
                    <cell>1 1/2</cell>
                    <cell>3</cell>
                    <cell>6</cell>
                    <cell>12</cell>
                    <cell>24</cell>
                    <cell>48</cell>
                  </row>
                  <row>
                    <cell>
                      <emph type="italics"/>
                    Numerus Oſcillat.
                      <emph.end type="italics"/>
                    </cell>
                    <cell>510</cell>
                    <cell>518</cell>
                    <cell>420</cell>
                    <cell>318</cell>
                    <cell>204</cell>
                    <cell>121</cell>
                    <cell>70</cell>
                  </row>
                </table>
                <p type="main">
                  <s>In Tabula priore ſeligendo ex obſervationibus tertiam, quintam
                    <lb/>
                  & ſeptimam, & exponendo velocitates maximas in his obſerva­
                    <lb/>
                  tionibus particulatim per numeros 1, 4, 16 reſpective, & genera­
                    <lb/>
                  liter per quantitatem V ut ſupra: emerget in obſervatione tertia
                    <lb/>
                  (1/2/193)=A+B+C, in quinta (2/90 1/2)=4A+8B+16C, in ſeptima
                    <lb/>
                  (8/30)=16A+64B+256C. Hæ vero æquationes reductæ dant
                    <lb/>
                  A=0,001414, B=0,000297, C=0,000879. Et inde prodit reſi­
                    <lb/>
                  ſtentia Globi cum velocitate V moti, in ea ratione ad pondus ſuum
                    <lb/>
                  unciarum 26 1/4, quam habet 0,0009V+0,000207V1/2+0,000659V
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                    <lb/>
                  ad penduli longitudinem 121 digitorum. </s>
                  <s>Et ſi ſpectemus eam ſo­
                    <lb/>
                  lummodo reſiſtentiæ partem quæ eſt in duplicata ratione velocitatis,
                    <lb/>
                  hæc erit ad pondus Globi ut 0,000659V
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  ad 121 digitos. </s>
                  <s>Erat au­
                    <lb/>
                  tem hæc pars reſiſtentiæ in experimento primo ad pondus Globi
                    <lb/>
                  lignei unciarum (57 7/22), ut 0,002217V
                    <emph type="sup"/>
                  2
                    <emph.end type="sup"/>
                  ad 121: & inde fit reſiſtentia
                    <lb/>
                  Globi lignei ad reſiſtentiam Globi plumbei (paribus eorum velocita­
                    <lb/>
                  tibus) ut (57 7/22) in 0,002217 ad 26 1/4 in 0,000659, id eſt, ut 7 1/3 ad 1.
                    <lb/>
                  Diametri Globorum duorum erant 6 7/8 & 2 digitorum, & harum
                    <lb/>
                  quadrata ſunt ad invicem ut 47 1/4 & 4, ſeu (11 11/16) & 1 quamproxime.
                    <lb/>
                  Ergo reſiſtentiæ Globorum æquivelocium erant in minore ratione
                    <lb/>
                  quam duplicata diametrorum. </s>
                  <s>At nondum conſideravimus reſi-</s>
                </p>
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          </chap>
        </body>
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    </archimedes>
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