Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/376.jpg" pagenum="348"/>
                    <arrow.to.target n="note356"/>
                  diſtinguatur Fluidum in Orbes innumeros concentricos ejuſdem
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                  craſſitudinis. </s>
                  <s>Finge autem Orbes illos eſſe ſolidos; & quoniam
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                  homogeneum eſt Fluidum, impreſſiones contiguorum Orbium in
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                  ſe mutuo factæ, erunt (per Hypotheſin) ut eorum tranſlationes
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                  ab invicem & ſuperficies contiguæ in quibus impreſſiones fiunt. </s>
                  <s>
                    <lb/>
                  Si impreſſio in Orbem aliquem major eſt vel minor ex parte con­
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                  cava quam ex parte convexa; prævalebit impeſſio fortior, & velo­
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                  citatem Orbis vel accelerabit vel retardabit, prout in eandem regi­
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                  onem cum ipſius motu vel in contrariam dirigitur. </s>
                  <s>Proinde ut
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                  Orbis unuſquiſQ.E.I. motu ſuo perſeveret uniformiter, debebunt
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                  impreſſiones ex parte utraque ſibi invicem æquari, & fieri in re­
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                  giones contrarias. </s>
                  <s>Unde cum impreſſiones ſint ut contiguæ ſu­
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                  perficies & harum tranſlationes ab invicem; erunt tranſlationes
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                  inverſe ut ſuperficies, hoc eſt, inverſe ut quadrata diſtantiarum ſu­
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                  perficierum à centro. </s>
                  <s>Sunt autem differentiæ motuum angularium
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                  circa axem ut hæ tranſlationes applicatæ ad diſtantias, ſive ut
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                  tranſlationes directe & diſtantiæ inverſe; hoc eſt (conjunctis ra­
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                  tionibus) ut cubi diſtantiarum inverſe. </s>
                  <s>Quare ſi ad rectæ infi­
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                  nitæ
                    <emph type="italics"/>
                  SABCDEQ
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                  partes ſingulas erigantur perpendicula
                    <emph type="italics"/>
                  Aa,
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                  Bb, Cc, Dd, Ee,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>ipſarum
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                  SA, SB, SC, SD, SE,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>
                    <lb/>
                  cubis reciproce proportionalia, erunt ſummæ differentiarum, hoc
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                  eſt, motus toti angulares, ut reſpondentes ſummæ linearum
                    <emph type="italics"/>
                  Aa,
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                  Bb, Cc, Dd, Ee
                    <emph.end type="italics"/>
                  : id eſt (ſi ad conſtituendum Medium uniformi­
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                  ter fluidum, numerus Orbium augeatur & latitudo minuatur in in­
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                  finitum) ut areæ Hyperbolicæ his ſummis analogæ
                    <emph type="italics"/>
                  AaQ, BbQ,
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                  CcQ, DdQ, EeQ,
                    <emph.end type="italics"/>
                  &c. </s>
                  <s>Et tempora periodica motibus angu­
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                  laribus reciproce proportionalia, erunt etiam his areis reciproce
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                  proportionalia. </s>
                  <s>Eſt igitur tempus periodicum Orbis cujuſvis
                    <lb/>
                    <emph type="italics"/>
                  DIO
                    <emph.end type="italics"/>
                  reciproce ut area
                    <emph type="italics"/>
                  DdQ,
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                  hoc eſt, (per notas Curvarum
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                  quadraturas) directe ut quadratum diſtantiæ
                    <emph type="italics"/>
                  SD.
                    <emph.end type="italics"/>
                  Id quod vo­
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                  lui primo demonſtrare. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note356"/>
                  DE MOTU
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                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. A centro Sphæræ ducantur infinitæ rectæ quam pluri­
                    <lb/>
                  mæ, quæ cum axe datos contineant angulos, æqualibus differen­
                    <lb/>
                  tiis ſe mutuo ſuperantes; & his rectis circa axem revolutis concipe
                    <lb/>
                  Orbes in annulos innumeros ſecari; & annulus unuſquiſque habe­
                    <lb/>
                  bit annulos quatuor ſibi contiguos, unum interiorem, alterum ex­
                    <lb/>
                  teriorem & duos laterales. </s>
                  <s>Attritu interioris & exterioris non
                    <lb/>
                  poteſt annulus unuſquiſque, niſi in motu juxta legem caſus primi
                    <lb/>
                  facto, æqualiter & in partes contrarias urgeri. </s>
                  <s>Patet hoc ex de­
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                  monſtratione caſus primi. </s>
                  <s>Et propterea annulorum ſeries quælibet </s>
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