Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/439.jpg" pagenum="411"/>
                  percurrit
                    <emph type="italics"/>
                  PM,
                    <emph.end type="italics"/>
                  (cæteris paribus) ut
                    <emph type="italics"/>
                  ML,
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  ML
                    <emph.end type="italics"/>
                  eſt in dupli­
                    <lb/>
                    <arrow.to.target n="note440"/>
                  cata ratione temporis. </s>
                  <s>Quare motus Nodorum in Syzygiis, eo
                    <lb/>
                  tempore confectus quo Luna datas Orbis particulas percurrit, di­
                    <lb/>
                  minuitur in duplicata ratione numeri 11073 ad numerum 11023;
                    <lb/>
                  eſtQ.E.D.crementum ad motum reliquum ut 100 ad 10973, ad
                    <lb/>
                  motum vero totum ut 100 ad 11073 quam proxime. </s>
                  <s>Decre­
                    <lb/>
                  mentum autem in locis inter Octantes & Syzygias, & incremen­
                    <lb/>
                  tum in locis inter Octantes & Quadraturas, eſt quam proxime ad
                    <lb/>
                  hoc decrementum, ut motus totus in locis illis ad motum totum
                    <lb/>
                  in Syzygiis & differentia inter quadratum ſinus diſtantiæ Lunæ a
                    <lb/>
                  Quadratura & ſemiſſem quadrati Radii ad ſemiſſem quadrati Ra­
                    <lb/>
                  dii, conjunctim. </s>
                  <s>Unde ſi Nodi in Quadraturis verſentur, & ca­
                    <lb/>
                  piantur loca duo æqualiter ab Octante hinc inde diſtantia, & alia
                    <lb/>
                  duo a Syzygia & Quadratura iiſdem intervallis diſtantia, deque
                    <lb/>
                  decrementis motuum in locis duobus inter Syzygiam & Octantem,
                    <lb/>
                  ſubducantur incrementa motuum in locis reliquis duobus, quæ
                    <lb/>
                  ſunt inter Octantem & Quadraturam; decrementum reliquum
                    <lb/>
                  æquale erit decremento in Syzygia: uti rationem ineunti facile
                    <lb/>
                  conſtabit. </s>
                  <s>ProindeQ.E.D.crementum mediocre, quod de Nodo­
                    <lb/>
                  rum motu mediocri ſubduci debet, eſt pars quarta decrementi in
                    <lb/>
                  Syzygia. </s>
                  <s>Motus totus horarius Nodorum in Syzygiis (ubi Luna
                    <lb/>
                  radio ad Terram ducto aream tempori proportionalem deſcribere
                    <lb/>
                  ſupponebatur) erat 32″. </s>
                  <s>42′. </s>
                  <s>7
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>Et decrementum motus Nodo­
                    <lb/>
                  rum, quo tempore Luna jam velocior deſcribit idem ſpatium,
                    <lb/>
                  diximus eſſe ad hunc motum ut 100 ad 11073; adeoQ.E.D.cre­
                    <lb/>
                  mentum illud eſt 17′. </s>
                  <s>43
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>11
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  , cujus pars quarta 4′. </s>
                  <s>25
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>48
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  ,
                    <lb/>
                  motui horario mediocri ſuperius invento 16″. </s>
                  <s>21′. </s>
                  <s>3
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>30
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ſub­
                    <lb/>
                  ducta, relinquit 16″. </s>
                  <s>16′. </s>
                  <s>37
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>42
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>motum mediocrem horarium
                    <lb/>
                  correctum. </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note440"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="main">
                  <s>Si Nodi verſantur extra Quadraturas, & ſpectentur loca bina a
                    <lb/>
                  Syzygiis hinc inde æqualiter diſtantia; ſumma motuum Nodo­
                    <lb/>
                  rum, ubi Luna verſatur in his locis, erit ad ſummam motuum,
                    <lb/>
                  ubi Luna in iiſdem locis & Nodi in Quadraturis verſantur, ut
                    <lb/>
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ATqu.
                    <emph.end type="italics"/>
                  Et decrementa motuum, a cauſis jam expo­
                    <lb/>
                  ſitis oriunda, erunt ad invicem ut ipſi motus, adeoque motus reli­
                    <lb/>
                  qui erunt ad invicem ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ATqu.
                    <emph.end type="italics"/>
                  & motus mediocres
                    <lb/>
                  ut motus reliqui. </s>
                  <s>Eſt itaque motus mediocris horarius correctus,
                    <lb/>
                  in dato quocunque Nodorum ſitu, ad 16″. </s>
                  <s>16′. </s>
                  <s>37
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>42
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ut.
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                    <lb/>
                  ad
                    <emph type="italics"/>
                  ATqu.
                    <emph.end type="italics"/>
                  ; id eſt, ut quadratum ſinus diſtantiæ Nodorum a Sy­
                    <lb/>
                  zygiis ad quadratum Radii. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
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