Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                  <s>
                    <pb xlink:href="039/01/451.jpg" pagenum="423"/>
                  7, 8 & 9. Prop. </s>
                  <s>LXVI. Lib. </s>
                  <s>I. </s>
                  <s>Et hæ inæqualitates per eadem </s>
                </p>
                <p type="main">
                  <s>
                    <arrow.to.target n="note452"/>
                  Corollaria permagnæ ſunt, & Æquationem principalem Apogæi
                    <lb/>
                  generant, quam Semeſtrem vocabo. </s>
                  <s>Et Æquatio maxima Seme­
                    <lb/>
                  ſtris eſt 12
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  18′ circiter, quantum ex Obſervationibus colligere
                    <lb/>
                  potui.
                    <emph type="italics"/>
                  Horroxius
                    <emph.end type="italics"/>
                  noſter Lunam in Ellipſi circum Terram, in ejus
                    <lb/>
                  umbilico inferiore conſtitutam, revolvi primus ſtatuit.
                    <emph type="italics"/>
                  Halleius
                    <emph.end type="italics"/>
                    <lb/>
                  centrum Ellipſeos in Epicyclo locavit, cujus centrum uniformiter
                    <lb/>
                  revolvitur circum Terram. </s>
                  <s>Et ex motu in Epicyclo oriuntur in­
                    <lb/>
                  æqualitates jam dictæ in progreſſu & regreſſu Apogæi & quanti­
                    <lb/>
                  tate Eccentricitatis. </s>
                  <s>Dividi intelligatur diſtantia mediocris Lunæ
                    <lb/>
                  a Terra in partes 100000, & referat
                    <emph type="italics"/>
                  T
                    <emph.end type="italics"/>
                  Terram &
                    <emph type="italics"/>
                  TC
                    <emph.end type="italics"/>
                  Eccentri­
                    <lb/>
                  citatem mediocrem Lunæ partium 5505. Producatur
                    <emph type="italics"/>
                  TC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  B,
                    <emph.end type="italics"/>
                    <lb/>
                  ut ſit
                    <emph type="italics"/>
                  CB
                    <emph.end type="italics"/>
                  ſinus Æquationis maximæ Semeſtris 12
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  18′ ad ra­
                    <lb/>
                  dium
                    <emph type="italics"/>
                  TC,
                    <emph.end type="italics"/>
                  & circulus
                    <emph type="italics"/>
                  BDA
                    <emph.end type="italics"/>
                  centro
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  intervallo
                    <emph type="italics"/>
                  CB
                    <emph.end type="italics"/>
                  deſcriptus,
                    <lb/>
                  erit Epicyclus ille in quo centrum Orbis Lunaris locatur & ſe­
                    <lb/>
                  cundum ordinem literarum
                    <emph type="italics"/>
                  BDA
                    <emph.end type="italics"/>
                  revolvitur. </s>
                  <s>Capiatur angulus
                    <lb/>
                    <emph type="italics"/>
                  BCD
                    <emph.end type="italics"/>
                  æqualis duplo argumento annuo, ſeu duplæ diſtantiæ veri
                    <lb/>
                  loci Solis ab Apogæo Lunæ ſemel æquato, & erit
                    <emph type="italics"/>
                  CTD
                    <emph.end type="italics"/>
                  Æquatio
                    <lb/>
                    <figure id="id.039.01.451.1.jpg" xlink:href="039/01/451/1.jpg" number="220"/>
                    <lb/>
                  Semeſtris Apogæi Lunæ &
                    <emph type="italics"/>
                  TD
                    <emph.end type="italics"/>
                  Eccentricitas Orbis ejus in Apo­
                    <lb/>
                  gæum ſecundo æquatum tendens. </s>
                  <s>Habitis autem Lunæ motu
                    <lb/>
                  medio & Apogæo & Eccentricitate, ut & Orbis axe majore par­
                    <lb/>
                  tium 200000; ex his eruetur verus Lunæ locus in Orbe & di­
                    <lb/>
                  ſtantia ejus a Terra, idque per Methodos notiſſimas. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note452"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>In Perihelio Terræ, propter majorem vim Solis, centrum Or­
                    <lb/>
                  bis Lunæ velocius movetur circum centrum
                    <emph type="italics"/>
                  C
                    <emph.end type="italics"/>
                  quam in Aphelio,
                    <lb/>
                  idQ.E.I. triplicata ratione diſtantiæ Terræ a Sole inverſe. </s>
                  <s>Ob
                    <lb/>
                  Æquationem centri Solis in Argumento annuo comprehenſam, cen­
                    <lb/>
                  trum Orbis Lunæ velocius movetur in Epicyclo
                    <emph type="italics"/>
                  BDA
                    <emph.end type="italics"/>
                  in du­
                    <lb/>
                  plicata ratione diſtantiæ Terræ a Sole inverſe. </s>
                  <s>Ut idem adhuc
                    <lb/>
                  velocius moveatur in ratione ſimplici diſtantiæ inverſe; ab Orbis
                    <lb/>
                  centro
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  agatur recta
                    <emph type="italics"/>
                  DE
                    <emph.end type="italics"/>
                  verſus Apogæum Lunæ, ſeu rectæ
                    <lb/>
                    <emph type="italics"/>
                  TC
                    <emph.end type="italics"/>
                  parallela, & capiatur angulus
                    <emph type="italics"/>
                  EDF
                    <emph.end type="italics"/>
                  æqualis exceſſui Argu-</s>
                </p>
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