Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
431
431 		432
432
433
433 		434
434
435
435 		436
436
437
437 		438
438
439
439 		440
440
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/438.jpg" pagenum="410"/>
                    <arrow.to.target n="note439"/>
                  ſterior proportionalis ſit motui Nodorum in Circulo, erit area
                    <lb/>
                  prior proportionalis motui Nodorum in Ellipſi.
                    <emph type="italics"/>
                  Q.E.D.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note438"/>
                  LIBER
                    <lb/>
                  TERTIUS.</s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note439"/>
                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  Igitur cum, in data Nodorum poſitione, ſumma omnium
                    <lb/>
                  arearum
                    <emph type="italics"/>
                  pDdm,
                    <emph.end type="italics"/>
                  quo tempore Luna pergit a Quadratura ad lo­
                    <lb/>
                  cum quemvis
                    <emph type="italics"/>
                  m,
                    <emph.end type="italics"/>
                  ſit area
                    <emph type="italics"/>
                  mpQEd,
                    <emph.end type="italics"/>
                  quæ ad Ellipſeos tangentem
                    <lb/>
                    <emph type="italics"/>
                  QE
                    <emph.end type="italics"/>
                  terminatur; & ſumma omnium arearum illarum, in revolu­
                    <lb/>
                  tione integra, ſit area Ellipſeos totius: motus mediocris Nodorum
                    <lb/>
                  in Ellipſi erit ad motum mediocrem Nodorum in Circulo, ut El­
                    <lb/>
                  lipſis ad Circulum; id eſt, ut
                    <emph type="italics"/>
                  Ta
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  TA,
                    <emph.end type="italics"/>
                  ſeu 69 ad 70. Et
                    <lb/>
                  propterea, cum motus mediocris horarius Nodorum in Circulo
                    <lb/>
                  ſit ad 16″. </s>
                  <s>35′. </s>
                  <s>16
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>36
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ut
                    <emph type="italics"/>
                  AZqu.
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ATqu.
                    <emph.end type="italics"/>
                  ſi capiatur angu­
                    <lb/>
                  lus 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>ad angulum 16″. </s>
                  <s>35′. </s>
                  <s>16
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>36
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ut 69 ad 70,
                    <lb/>
                  erit motus mediocris horarius Nodorum in Ellipſi ad 16″. </s>
                  <s>21′. </s>
                  <s>
                    <lb/>
                  3
                    <emph type="sup"/>
                  iv
                    <emph.end type="sup"/>
                  . </s>
                  <s>30
                    <emph type="sup"/>
                  v
                    <emph.end type="sup"/>
                  . </s>
                  <s>ut
                    <emph type="italics"/>
                  AZq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  ATq
                    <emph.end type="italics"/>
                  ; hoc eſt, ut quadratum ſinus diſtantiæ
                    <lb/>
                  Nodi a Sole ad quadratum Radii. </s>
                </p>
                <p type="main">
                  <s>Cæterum Luna, radio ad Terram ducto, aream velocius deſcri­
                    <lb/>
                  bit in Syzygiis quam in Quadraturis, & eo nomine tempus in Sy­
                    <lb/>
                  zygiis contrahitur, in Quadraturis producitur; & una cum tem­
                    <lb/>
                  pore motus Nodorum augetur ac diminuitur. </s>
                  <s>Erat autem mo­
                    <lb/>
                  mentum areæ in Quadraturis Lunæ ad ejus momentum in Syzygiis
                    <lb/>
                  ut 10973 ad 11073, & propterea momentum mediocre in Octan­
                    <lb/>
                  tibus eſt ad exceſſum in Syzygiis, defectumQ.E.I. Quadraturis, ut
                    <lb/>
                  numerorum ſemiſumma 11023 ad eorundem ſemidifferentiam 50.
                    <lb/>
                  Unde cum tempus Lunæ in ſingulis Orbis particulis æqualibus ſit
                    <lb/>
                  reciproce ut ipſius velocitas, erit tempus mediocre in Octantibus
                    <lb/>
                  ad exceſſum temporis in Quadraturis, ac defectum in Syzygiis, ab
                    <lb/>
                  hac cauſa oriundum, ut 11023 ad 50 quam proxime. </s>
                  <s>Pergendo
                    <lb/>
                  autem a Quadraturis ad Syzygias, invenio quod exceſſus momen­
                    <lb/>
                  torum areæ in locis ſingulis, ſupra momentum minimum in Qua­
                    <lb/>
                  draturis, ſit ut quadratum ſinus diſtantiæ Lunæ a Quadraturis
                    <lb/>
                  quam proxime; & propterea differentia inter momentum in loco
                    <lb/>
                  quocunque & momentum mediocre in Octantibus, eſt ut diffe­
                    <lb/>
                  rentia inter quadratum ſinus diſtantiæ Lunæ a Quadraturis &
                    <lb/>
                  quadratum ſinus graduum 45, ſeu ſemiſſem quadrati Radii; &
                    <lb/>
                  incrementum temporis in locis ſingulis inter Octantes & Quadra­
                    <lb/>
                  turas, & decrementum ejus inter Octantes & Syzygias, eſt in ea­
                    <lb/>
                  dem ratione. </s>
                  <s>Motus autem Nodorum, quo tempore Luna per­
                    <lb/>
                  currit ſingulas Orbis particulas æquales, acceleratur vel retardatur
                    <lb/>
                  in duplicata ratione temporis. </s>
                  <s>Eſt enim motus iſte, dum Luna </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum