Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/364.jpg" pagenum="336"/>
                    <arrow.to.target n="note344"/>
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                <p type="margin">
                  <s>
                    <margin.target id="note344"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Aucta autem vel diminuta longitudine aquæ, auge­
                    <lb/>
                  tur vel diminuitur tempus reciprocationis in longitudinis ratione
                    <lb/>
                  ſubduplicata. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XLV. THEOREMA XXXVI.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Undarum velocitas eſt in ſubduplicata ratione latitudinum.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Conſequitur ex conſtructione Propoſitionis ſequentis. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XLVI. PROBLEMA X.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Invenire velocitatem Undarum.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Conſtituatur Pendulum cujus longitudo, inter punctum ſuſpen­
                    <lb/>
                  ſionis & centrum oſcillationis, æquetur latitudini Undarum: & quo
                    <lb/>
                  tempore pendulum illud oſcillationes ſingulas peragit, eodem Un­
                    <lb/>
                  dæ progrediendo latitudinem ſuam propemodum conficient. </s>
                </p>
                <p type="main">
                  <s>Undarum latitudinem voco menſuram tranſverſam, quæ vel val­
                    <lb/>
                  libus imis, vel ſummis culminibus interjacet. </s>
                  <s>Deſignet
                    <emph type="italics"/>
                  ABCDEF
                    <emph.end type="italics"/>
                    <lb/>
                  ſuperficiem aquæ ſtagnantis, undis ſucceſſivis aſcendentem ac deſ­
                    <lb/>
                  cendentem; ſintque
                    <emph type="italics"/>
                  A, C, E,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>undarum culmina, &
                    <emph type="italics"/>
                  B, D, F,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>
                    <lb/>
                  valles intermedii. </s>
                  <s>Et quoniam motus undarum fit per aquæ ſuc­
                    <lb/>
                  ceſſivum aſcenſum & deſcenſum, ſic ut ejus partes
                    <emph type="italics"/>
                  A, C, E,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>
                    <lb/>
                  quæ nunc altiſſimæ ſunt, mox fiant infimæ; & vis motrix, qua
                    <lb/>
                  partes altiſſimæ deſcendunt & infimæ aſcendunt, eſt pondus aquæ
                    <lb/>
                  elevatæ; alternus ille aſcenſus & deſcenſus analogus erit motui re­
                    <lb/>
                  ciproco aquæ in canali, eaſdemque temporis leges obſervabit: &
                    <lb/>
                  propterea (per Prop. </s>
                  <s>XLIV) ſi diſtantiæ inter undarum loca altiſ­
                    <lb/>
                  ſima
                    <emph type="italics"/>
                  A, C, E
                    <emph.end type="italics"/>
                  & infima
                    <emph type="italics"/>
                  B, D, F
                    <emph.end type="italics"/>
                  æquentur duplæ penduli longitu­
                    <lb/>
                  dini; partes altiſſimæ
                    <emph type="italics"/>
                  A, C, E,
                    <emph.end type="italics"/>
                  tempore oſcillationis unius evadent
                    <lb/>
                  infimæ, & tempore oſcillationis alterius denuo aſcendent. </s>
                  <s>Igitur
                    <lb/>
                  inter tranſitum Undarum ſingularum tempus erit oſcillationum
                    <lb/>
                  duarum; hoc eſt, Unda deſcribet latitudinem ſuam, quo tempore
                    <lb/>
                  pendulum illud bis oſcillatur; ſed eodem tempore pendulum, cu­
                    <lb/>
                  jus longitudo quadrupla eſt, adeoque æquat undarum latitudinem,
                    <lb/>
                  oſcillabitur ſemel.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Igitur Undæ, quæ pedes
                    <emph type="italics"/>
                  Pariſienſes
                    <emph.end type="italics"/>
                  (3 1/18) latæ ſunt,
                    <lb/>
                  tempore minuti unius ſecundi progrediendo latitudinem ſuam con­
                    <lb/>
                  ficient; adeoque tempore minuti unius primi percurrent pedes
                    <lb/>
                  183 1/3, & horæ ſpatio pedes 11000 quamproxime. </s>
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