Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/374.jpg" pagenum="346"/>
                    <arrow.to.target n="note354"/>
                  minor ex parte concava quam ex parte convexa; prævalebit im­
                    <lb/>
                  preſſio fortior, & motum Orbis vel accelerabit vel retardabit,
                    <lb/>
                  prout in eandem regionem cum ipſius motu vel in contrariam di­
                    <lb/>
                  rigitur. </s>
                  <s>Proinde ut Orbis unuſquiſQ.E.I. motu ſuo uniformiter
                    <lb/>
                  perſeveret, debent impreſſiones ex parte utraque ſibi invicem æqua­
                    <lb/>
                  ri, & fieri in regiones contrarias. </s>
                  <s>Unde cum impreſſiones ſunt ut
                    <lb/>
                  contiguæ ſuperficies & harum tranſlationes ab invicem, erunt tran­
                    <lb/>
                  ſlationes inverſe ut ſuperficies, hoc eſt, inverſe ut ſuperficierum di­
                    <lb/>
                  ſtantiæ ab axe. </s>
                  <s>Sunt autem differentiæ motuum angularium circa
                    <lb/>
                  axem ut hæ tranſlationes applicatæ ad diſtantias, ſive ut tranſlati­
                    <lb/>
                  ones directe & diſtantiæ inverſe; hoc eſt (conjunctis rationibus)
                    <lb/>
                  ut quadrata diſtantiarum inverſe. </s>
                  <s>Quare ſi ad infinitæ rectæ
                    <lb/>
                    <emph type="italics"/>
                  SABCDEQ
                    <emph.end type="italics"/>
                  partes ſin­
                    <lb/>
                    <figure id="id.039.01.374.1.jpg" xlink:href="039/01/374/1.jpg" number="201"/>
                    <lb/>
                  gulas erigantur perpendicula
                    <lb/>
                    <emph type="italics"/>
                  Aa, Bb, Cc, Dd, Ee,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>
                    <lb/>
                  ipſarum
                    <emph type="italics"/>
                  SA, SB, SC, SD,
                    <lb/>
                  SE,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>quadratis reciproce
                    <lb/>
                  proportionalia, & per ter­
                    <lb/>
                  minos perpendicularium du­
                    <lb/>
                  ci intelligatur linea curva
                    <lb/>
                  Hyperbolica; erunt ſummæ
                    <lb/>
                  differentiarum, hoc eſt, mo­
                    <lb/>
                  tus toti angulares, ut re­
                    <lb/>
                  ſpondentes ſummæ linearum
                    <lb/>
                    <emph type="italics"/>
                  Aa, Bb, Cc, Dd, Ee
                    <emph.end type="italics"/>
                  : id
                    <lb/>
                  eſt, ſi ad conſtituendum Me­
                    <lb/>
                  dium uniformiter fluidum, Orbium numerus augeatur & latitudo
                    <lb/>
                  minuatur in infinitum, ut areæ Hyperbolicæ his ſummis analogæ
                    <lb/>
                    <emph type="italics"/>
                  AaQ, BbQ, CcQ, DdQ, EeQ,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Et tempora motibus an­
                    <lb/>
                  gularibus reciproce proportionalia, erunt etiam his areis reciproce
                    <lb/>
                  proportionalia. </s>
                  <s>Eſt igitur tempus periodicum particulæ cujuſvis
                    <lb/>
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  reciproce ut area
                    <emph type="italics"/>
                  DdQ,
                    <emph.end type="italics"/>
                  hoc eſt, (per notas Curvarum qua­
                    <lb/>
                  draturas) directe ut diſtantia
                    <emph type="italics"/>
                  SD. Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note354"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc motus angulares particularum fluidi ſunt reci­
                    <lb/>
                  proce ut ipſarum diſtantiæ ab axe cylindri, & velocitates abſo­
                    <lb/>
                  lutæ ſunt æquales. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  2. Si fluidum in vaſe cylindrico longitudinis infinitæ con­
                    <lb/>
                  tineatur, & cylindrum alium interiorem contineat, revolvatur
                    <lb/>
                  autem cylindrus uterque circa axem communem, ſintque revolu-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
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