Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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                <p type="main">
                  <s>
                    <pb xlink:href="039/01/442.jpg" pagenum="414"/>
                    <arrow.to.target n="note443"/>
                  Curvam
                    <emph type="italics"/>
                  NeFn,
                    <emph.end type="italics"/>
                  area tota
                    <emph type="italics"/>
                  NeZ,
                    <emph.end type="italics"/>
                  quæ ſumma eſt omnium decre­
                    <lb/>
                  mentorum, reſpondebit decremento toti, quo tempore arcus
                    <emph type="italics"/>
                  AN
                    <emph.end type="italics"/>
                    <lb/>
                  percurritur; & area reliqua
                    <emph type="italics"/>
                  NAe
                    <emph.end type="italics"/>
                  reſpondebit motui reliquo, qui
                    <lb/>
                  verus eſt Nodi motus quo tempore arcus totus
                    <emph type="italics"/>
                  NA,
                    <emph.end type="italics"/>
                  per Solis &
                    <lb/>
                  Nodi conjunctos motus, percurritur. </s>
                  <s>Jam vero area ſemicirculi
                    <lb/>
                  eſt ad aream Figuræ
                    <emph type="italics"/>
                  NeFnT,
                    <emph.end type="italics"/>
                  per methodum Serierum infinita­
                    <lb/>
                  rum quæſitam, ut 793 ad 60 quamproxime. </s>
                  <s>Motus autem qui
                    <lb/>
                  reſpondet Circulo toti erat 19
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  49′. </s>
                  <s>3″. </s>
                  <s>55′; & propterea motus,
                    <lb/>
                  qui Figuræ
                    <emph type="italics"/>
                  NeFnT
                    <emph.end type="italics"/>
                  duplicatæ reſpondet, eſt 1
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  29′. </s>
                  <s>58″. </s>
                  <s>2′. </s>
                  <s>
                    <lb/>
                  Qui de motu priore ſubductus relinquit 18
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  19′. </s>
                  <s>5″. </s>
                  <s>53′. </s>
                  <s>motum
                    <lb/>
                  totum Nodi inter ſui ipſius Conjunctiones cum Sole; & hic mo­
                    <lb/>
                  tus de Solis motu annuo graduum 360 ſubductus, relinquit 341
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                    <lb/>
                  40′. </s>
                  <s>54″. </s>
                  <s>7′. </s>
                  <s>motum Solis inter eaſdem Conjunctiones. </s>
                  <s>Iſte au­
                    <lb/>
                  tem motus eſt ad motum annuum 360
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  ut Nodi motus jam in­
                    <lb/>
                  ventus 18
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  19′. </s>
                  <s>5″. </s>
                  <s>53′. </s>
                  <s>ad ipſius motum annuum, qui propterea
                    <lb/>
                  erit 19
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  18′. </s>
                  <s>1″. </s>
                  <s>23′. </s>
                  <s>Hic eſt motus medius Nodorum in anno
                    <lb/>
                  Sidereo. </s>
                  <s>Idem per Tabulas Aſtronomicas eſt 19
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  21′. </s>
                  <s>21″. </s>
                  <s>50′. </s>
                  <s>
                    <lb/>
                  Differentia minor eſt parte trecenteſima motus totius, & ab Or­
                    <lb/>
                  bis Lunaris Eccentricitate & Inclinatione ad planum Eclipticæ
                    <lb/>
                  oriri videtur. </s>
                  <s>Per Eccentricitatem Orbis motus Nodorum nimis
                    <lb/>
                  acceleratur, & per ejus Inclinationem viciſſim retardatur aliquan­
                    <lb/>
                  tulum, & ad juſtam velocitatem reducitur. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note443"/>
                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO XXXIII. PROBLEMA XIV.
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Invenire motum verum Nodorum Lunæ.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                  </s>
                </p>
                <p type="main">
                  <s>In tempore quod eſt ut area
                    <emph type="italics"/>
                  NTA-NdZ, (in Fig. </s>
                  <s>præced.)
                    <emph.end type="italics"/>
                    <lb/>
                  motus iſte eſt ut area
                    <emph type="italics"/>
                  NAeN,
                    <emph.end type="italics"/>
                  & inde datur. </s>
                  <s>Verum ob nimiam
                    <lb/>
                  calculi difficultatem, præſtat ſequentem Problematis conſtructio­
                    <lb/>
                  nem adhibere. </s>
                  <s>Centro
                    <emph type="italics"/>
                  C,
                    <emph.end type="italics"/>
                  intervallo quovis
                    <emph type="italics"/>
                  CD,
                    <emph.end type="italics"/>
                  deſcribatur
                    <lb/>
                  circulus
                    <emph type="italics"/>
                  BEFD.
                    <emph.end type="italics"/>
                  Producatur
                    <emph type="italics"/>
                  DC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  A,
                    <emph.end type="italics"/>
                  ut ſit
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                    <lb/>
                  ut motus medius ad ſemiſſem motus veri mediocris, ubi Nodi
                    <lb/>
                  ſunt in Quadraturis, (id eſt, ut 19
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  18′. </s>
                  <s>1″. </s>
                  <s>23′. </s>
                  <s>ad 19
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  49′. </s>
                  <s>
                    <lb/>
                  3″. </s>
                  <s>55′, atque adeo
                    <emph type="italics"/>
                  BC
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  ut motuum differentia 0
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  31′. </s>
                  <s>
                    <lb/>
                  2″. </s>
                  <s>32′, ad motum poſteriorem 19′
                    <emph type="sup"/>
                  gr.
                    <emph.end type="sup"/>
                  49. 3″. </s>
                  <s>55′) hoc eſt, ut
                    <lb/>
                  1 ad (38 1/10) dein per punctum
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ducatur infinita
                    <emph type="italics"/>
                  Gg,
                    <emph.end type="italics"/>
                  quæ tangat
                    <lb/>
                  circulum in
                    <emph type="italics"/>
                  D
                    <emph.end type="italics"/>
                  ; & ſi capiatur angulus
                    <emph type="italics"/>
                  BCE
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  BCF
                    <emph.end type="italics"/>
                  æqualis
                    <lb/>
                  duplæ diſtantiæ Solis a loco Nodi, per motum medium invento; </s>
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