Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                    <pb xlink:href="039/01/370.jpg" pagenum="342"/>
                    <arrow.to.target n="note350"/>
                    <emph type="italics"/>
                  PO
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                  ad V. </s>
                  <s>Quare cum tempora, quibus æqualia corpora per
                    <lb/>
                  æqualia ſpatia impelluntur, ſint reciproce in ſubduplicata ratione
                    <lb/>
                  virium, erit tempus vibrationis unius urgente vi illa Elaſtica, ad
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                  tempus vibrationis urgente vi ponderis, in ſubduplicata ratione
                    <lb/>
                  VV ad
                    <emph type="italics"/>
                  PO
                    <emph.end type="italics"/>
                  XA, atque adeo ad tempus oſcillationis Penduli cu­
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                  jus longitudo eſt A, in ſubduplicata ratione VV ad
                    <emph type="italics"/>
                  PO
                    <emph.end type="italics"/>
                  XA, &
                    <lb/>
                  ſubduplicata ratione
                    <emph type="italics"/>
                  PO
                    <emph.end type="italics"/>
                  ad A conjunctim; id eſt, in ratione in­
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                  tegra V ad A. </s>
                  <s>Sed tempore vibrationis unius ex itu & reditu com­
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                  poſitæ, pulſus progrediendo conficit latitudinem ſuam
                    <emph type="italics"/>
                  BC.
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                  Ergo
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                  tempus quo pulſus percurrit ſpatium
                    <emph type="italics"/>
                  BC,
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                  eſt ad tempus oſcillati­
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                  onis unius ex itu & reditu compoſitæ, ut V ad A, id eſt, ut
                    <emph type="italics"/>
                  BC
                    <emph.end type="italics"/>
                    <lb/>
                  ad circumferentiam circuli cujus radius eſt A. </s>
                  <s>Tempus autem,
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                  quo pulſus percurret ſpatium
                    <emph type="italics"/>
                  BC,
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                  eſt ad tempus quo percurret
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                  longitudinem huic circumferentiæ æqualem, in eadem ratione;
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                  ideoque tempore talis oſcillationis pulſus percurret longitudinem
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                  huic circumferentiæ æqualem.
                    <emph type="italics"/>
                  Q.E.D.
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                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note350"/>
                  DE MOTU
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                  CORPORUM</s>
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                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
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                  1. Velocitas pulſuum ea eſt quam acquirunt Gravia, æqua­
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                  liter accelerato motu cadendo, & caſu ſuo deſcribendo dimidium
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                  altitudinis A. </s>
                  <s>Nam tempore caſus hujus, cum velocitate cadendo
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                  acquiſita, pulſus percurret ſpatium quod erit æquale toti altitu­
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                  dini A, adeoque tempore oſcillationis unius ex itu & reditu com­
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                  poſitæ, percurret ſpatium æquale circumferentiæ circuli radio A
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                  deſcripti: eſt enim tempus caſus ad tempus oſcillationis ut radius
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                  circuli ad ejuſdem circumferentiam. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Unde cum altitudo illa A ſit ut Fluidi vis Elaſtica di­
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                  recte & denſitas ejuſdem inverſe; velocitas pulſuum erit in ratione
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                  compoſita ex ſubduplicata ratione denſitatis inverſe & ſubdupli­
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                  cata ratione vis Elaſticæ directe. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO L. PROBLEMA XII.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Invenire pulſuum diſtantias.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Corporis, cujus tremore pulſus excitantur, inveniatur numerus
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                  Vibrationum dato tempore. </s>
                  <s>Per numerum illum dividatur ſpa­
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                  tium quod pulſus eodem tempore percurrere poſſit, & pars in­
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                  venta erit pulſus unius latitudo.
                    <emph type="italics"/>
                  Q.E.I.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>Spectant Propoſitiones noviſſimæ ad motum Lucis & Sonorum. </s>
                  <s>
                    <lb/>
                  Lux enim cum propagetur ſecundum lineas rectas, in actione ſola </s>
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