Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <pb xlink:href="039/01/355.jpg" pagenum="327"/>
                <p type="main">
                  <s>In Scholio quod Sectioni ſextæ ſubjunctum eſt, oſtendimus per </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note335"/>
                  experimenta pendulorum quod globorum æqualium & æquivelo­
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                  cium in Aere, Aqua, & Argento vivo motorum reſiſtentiæ ſunt ut
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                  fluidorum denſitates. </s>
                  <s>Idem hic oſtendimus magis accurate per
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                  experimenta corporum cadentium in Aere & Aqua. </s>
                  <s>Nam pendula
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                  ſingulis oſcillationibus motum cient in fluido motui penduli re­
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                  deuntis ſemper contrarium, & reſiſtentia ab hoc motu oriunda, ut
                    <lb/>
                  & reſiſtentia fili quo pendulum ſuſpendebatur, totam Penduli re­
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                  ſiſtentiam majorem reddiderunt quam reſiſtentia quæ per experi­
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                  menta corporum cadentium prodiit. </s>
                  <s>Etenim per experimenta
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                  pendulorum in Scholio illo expoſita, globus ejuſdem denſitatis
                    <lb/>
                  cum Aqua, deſcribendo longitudinem ſemidiametri ſuæ in Aere,
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                  amittere deberet motus ſui partem (1/3342). At per Theoriam in hac
                    <lb/>
                  ſeptima Sectione expoſitam & experimentis cadentium confirma­
                    <lb/>
                  tam, globus idem deſcribendo longitudinem eandem, amittere de­
                    <lb/>
                  beret motus ſui partem tantum (1/4586), poſito quod denſitas Aquæ ſit
                    <lb/>
                  ad denſitatem Aeris ut 860 ad 1. Reſiſtentiæ igitur per experi­
                    <lb/>
                  menta pendulorum majores prodiere (ob cauſas jam deſcriptas)
                    <lb/>
                  quam per experimenta globorum cadentium, idQ.E.I. ratione 4 ad
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                  3 circiter. </s>
                  <s>Attamen cum pendulorum in Aere, Aqua, & Argento
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                  vivo oſcillantium reſiſtentiæ a cauſis ſimilibus ſimiliter augeantur,
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                  proportio reſiſtentiarum in his Mediis, tam per experimenta pen­
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                  dulorum, quam per experimenta corporum cadentium, ſatis recte
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                  exhibebitur. </s>
                  <s>Et inde concludi poteſt quod corporum in fluidis
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                  quibuſcunque fluidiſſimis motorum reſiſtentiæ, cæteris paribus,
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                  ſunt ut denſitates fluidorum. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note335"/>
                  LIBER
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                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>His ita ſtabilitis, dicere jam licet quamnam motus ſui partem
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                  globus quilibet, in fluido quocunque projectus, dato tempore amit­
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                  tet quamproxime. </s>
                  <s>Sit D diameter globi, & V velocitas ejus ſub
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                  initio motus, & T tempus quo globus velocitate V in vacuo de­
                    <lb/>
                  ſcribet ſpatium quod ſit ad ſpatium 2/3D ut denſitas globi ad denſi­
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                  tatem fluidi: & globus in fluido illo projectus, tempore quovis
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                  alio
                    <emph type="italics"/>
                  t,
                    <emph.end type="italics"/>
                  amittet velocitatis ſuæ partem (
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  V/T+
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  ), manente parte (TV/T+
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  ),
                    <lb/>
                  & deſcribet ſpatium quod ſit ad ſpatium uniformi velocitate V eo­
                    <lb/>
                  dem tempore deſcriptum in vacuo, ut logarithmus numeri (T+
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  /T)
                    <lb/>
                  multiplicatus per numerum 2,302585093 eſt ad numerum
                    <emph type="italics"/>
                  t
                    <emph.end type="italics"/>
                  /T, per </s>
                </p>
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          </chap>
        </body>
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    </archimedes>
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