Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
181
181 		182
182
183
183 		184
184
185
185 		186
186
187
187 		188
188
189
189 		190
190
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <pb xlink:href="039/01/183.jpg" pagenum="155"/>
                <p type="main">
                  <s>
                    <emph type="center"/>
                  PROPOSITIO LXV. THEOREMA XXV.
                    <emph.end type="center"/>
                    <lb/>
                    <arrow.to.target n="note131"/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note131"/>
                  LIBER
                    <lb/>
                  PRIMUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corpora plura, quorum Vires decreſcunt in duplicata ratione di­
                    <lb/>
                  ſtantiarum ab eorundem centris, moveri poſſe inter ſe in El­
                    <lb/>
                  lipſibus; & radiis ad umbilicos ductis areas deſcribere tempo­
                    <lb/>
                  ribus proportionales quam proxime.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>In Propoſitione ſuperiore demonſtratus eſt caſus ubi motus plu­
                    <lb/>
                  res peraguntur in Ellipſibus accurate. </s>
                  <s>Quo magis recedit Lex vi­
                    <lb/>
                  rium a Lege ibi poſita, eo magis corpora perturbabunt mutuos
                    <lb/>
                  motus; neque fieri poteſt ut corpora, ſecundum Legem hic poſitam
                    <lb/>
                  ſe mutuo trahentia, moveantur in Ellipſibus accurate, niſi ſervando
                    <lb/>
                  certam proportionem diſtantiarum ab invicem. </s>
                  <s>In ſequentibus au­
                    <lb/>
                  tem caſibus non multum ab Ellipſibus errabitur. </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  1. Pone corpora plura minora circa maximum aliquod ad
                    <lb/>
                  varias ab eo diſtantias revolvi, tendantque ad ſingula vires abſolu­
                    <lb/>
                  tæ proportionales iiſdem corporibus. </s>
                  <s>Et quoniam omnium com­
                    <lb/>
                  mune gravitatis centrum (per Legum Corol. </s>
                  <s>quartum) vel quie­
                    <lb/>
                  ſcit vel movetur uniformiter in directum, fingamus corpora mi­
                    <lb/>
                  nora tam parva eſſe, ut corpus maximum nunquam diſtet ſenſibi­
                    <lb/>
                  liter ab hoc centro: & maximum illud vel quieſcet vel movebitur
                    <lb/>
                  uniformiter in directum, abſque errore ſenſibili; minora autem re­
                    <lb/>
                  volventur circa hoc maximum in Ellipſibus, atque radiis ad idem
                    <lb/>
                  ductis deſcribent areas temporibus proportionales; niſi quatenus
                    <lb/>
                  errores inducuntur, vel per errorem maximi a communi illo gravi­
                    <lb/>
                  tatis centro, vel per actiones minorum corporum in ſe mutuo. </s>
                  <s>Di­
                    <lb/>
                  minui autem poſſunt corpora minora uſQ.E.D.nec error iſte & ac­
                    <lb/>
                  tiones mutuæ ſint datis quibuſvis minores, atque adeo donec Orbes
                    <lb/>
                  cum Ellipſibus quadrent, & areæ reſpondeant temporibus, abſque
                    <lb/>
                  errore qui non ſit minor quovis dato.
                    <emph type="italics"/>
                  q.E.O.
                    <emph.end type="italics"/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cas.
                    <emph.end type="italics"/>
                  2. Fingamus jam Syſtema corporum minorum modo jam
                    <lb/>
                  deſcripto circa maximum revolventium, aliudve quodvis duorum
                    <lb/>
                  circum ſe mutuo revolventium corporum Syſtema progredi unifor­
                    <lb/>
                  miter in directum, & interea vi corporis alterius longe maximi &
                    <lb/>
                  ad magnam diſtantiam ſiti urgeri ad latus. </s>
                  <s>Et quoniam æquales
                    <lb/>
                  vires acceleratrices, quibus corpora ſecundum lineas parallelas ur­
                    <lb/>
                  gentur, non mutant ſitus corporum ad invicem, ſed ut Syſtema
                    <lb/>
                  totum, ſervatis partium motibus inter ſe, ſimul transferatur effici­
                    <lb/>
                  unt: manifeſtum eſt quod, ex attractionibus in corpus maximum, </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum