Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
391
391
392
392
393
393
394
394
395
395
396
396
397
397
398
398
399
399
400
400
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/398.jpg" pagenum="370"/>
                    <lb/>
                    <arrow.to.target n="note376"/>
                  PROPOSITIO VIII. THEOREMA VIII.
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note376"/>
                  DE MUNDI
                    <lb/>
                  SYSTEMATE</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Globorum duorum in ſe mutuo gravitantium materia undique,
                    <lb/>
                  in regionibus quæ à centris æqualiter diſtant, homogenea ſit:
                    <lb/>
                  erit pondus Globi alterutrius in alterum reciproce ut quadra­
                    <lb/>
                  tum diſtantiæ inter centra.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>Poſtquam inveniſſem gravitatem in Planetam totum oriri &
                    <lb/>
                  componi ex gravitatibus in partes; & eſſe in partes ſingulas reci­
                    <lb/>
                  proce proportionalem quadratis diſtantiarum a partibus: dubita­
                    <lb/>
                  bam an reciproca illa proportio duplicata obtineret accurate in vi
                    <lb/>
                  tota ex viribus pluribus compoſita, an vero quam proxime. </s>
                  <s>Nam
                    <lb/>
                  fieri poſſet ut proportio, quæ in majoribus diſtantiis ſatis accu­
                    <lb/>
                  rate obtineret, prope ſuperficiem Planetæ ob inæquales particu­
                    <lb/>
                  larum diſtantias & ſitus diſſimiles, notabiliter erraret. </s>
                  <s>Tandem
                    <lb/>
                  vero, per Prop. LXXV. & LXXVI. Libri primi & ipſarum Corol­
                    <lb/>
                  laria, intellexi veritatem Propoſitionis de qua hic agitur.
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  1. Hinc inveniri & inter ſe comparari poſſunt pondera
                    <lb/>
                  corporum in diverſos Planetas. </s>
                  <s>Nam pondera corporum æqua­
                    <lb/>
                  lium circum Planetas in circulis revolventium ſunt (per Corol. 2.
                    <lb/>
                  Prop. IV. Lib.I.) ut diametri circulorum directe & quadrata tem­
                    <lb/>
                  porum periodieorum inverſe; & pondera ad ſuperficies Planeta­
                    <lb/>
                  rum, aliaſve quaſvis a centro diſtantias, majora ſunt vel minora
                    <lb/>
                  (per hanc Propoſitionem) in duplicata ratione diſtantiarum in­
                    <lb/>
                  verſa. Sic ex temporibus periodicis Veneris circum Solem die­
                    <lb/>
                  rum 224 & horarum 16 1/4, Satellitis extimi circumjovialis circum
                    <lb/>
                  Jovem dierum 16 & horarum (16 1/15), Satellitis Hugeniani circum
                    <lb/>
                  Saturnum dierum 15 & horarum 22 2/3, & Lunæ circum Terram
                    <lb/>
                  dierum 27, hor. 7. min. 43, collatis cum diſtantia mediocri Vene­
                    <lb/>
                  ris a Sole & cum elongationibus maximis heliocentricis Satellitis
                    <lb/>
                  extimi circumjovialis a centro Jovis 8′. 21 1/2″, Satellitis Hugeniani
                    <lb/>
                  a centro Saturni 3′. 20″, & Lunæ a Terra 10′, computum ineundo
                    <lb/>
                  inveni quod corporum æqualium & a Sole, Jove, Saturno ac Terra
                    <lb/>
                  æqualiter diſtantium pondera in Solem, Jovem, Saturnum ac Ter­
                    <lb/>
                  ram forent ad invicem ut 1, (1/1033), (1/2411), & (1/227512) reſpective. </s>
                  <s>Eſt enim
                    <lb/>
                  parallaxis Solis ex obſervationibus noviſſimis quaſi 10″, &
                    <emph type="italics"/>
                  Hal­
                    <lb/>
                  leius
                    <emph.end type="italics"/>
                  noſter per emerſiones Jovis & Satellitum e parte obſcura
                    <lb/>
                  </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>