Newton, Isaac, Philosophia naturalis principia mathematica, 1713

List of thumbnails

< >
341
341 		342
342
343
343 		344
344
345
345 		346
346
347
347 		348
348
349
349 		350
350
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/341.jpg" pagenum="313"/>
                    <lb/>
                  ſemel, & ratione
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq-PQq
                    <emph.end type="italics"/>
                  bis, & ratione denſitatis
                    <lb/>
                    <arrow.to.target n="note289"/>
                  Medii ad denſitatem Cylindri.
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note289"/>
                  LIBER
                    <lb/>
                  SECUNDUS.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Corol.
                    <emph.end type="italics"/>
                  3. Iiſdem poſitis, & quod longitudo L ſit ad quadru­
                    <lb/>
                  plum longitudinis Cylindri in ratione quæ componitur ex ratione
                    <lb/>
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  -1/2
                    <emph type="italics"/>
                  PQq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                  ſemel, & ratione
                    <emph type="italics"/>
                  EFq-PQq
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  EFq
                    <emph.end type="italics"/>
                    <lb/>
                  bis: reſiſtentia Cylindri erit ad vim qua totus ejus motus, interea
                    <lb/>
                  dum longitudinem L deſcribit, vel tolli poſſit vel generari, ut
                    <lb/>
                  denſitas Medii ad denſitatem Cylindri.
                    <lb/>
                    <emph type="center"/>
                    <emph type="italics"/>
                  Scholium.
                    <emph.end type="italics"/>
                    <emph.end type="center"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>In hac Propoſitione reſiſtentiam inveſtigavimus quæ oritur a
                    <lb/>
                  ſola magnitudine tranſverſæ ſectionis Cylindri, neglecta reſiſtentiæ
                    <lb/>
                  parte quæ ab obliquitate motuum oriri poſſit. </s>
                  <s>Nam quemadmo­
                    <lb/>
                  dum in caſu primo Propoſitionis XXXVI, obliquitas motuum qui­
                    <lb/>
                  bus partes aquæ in vaſe, undique convergebant in foramen
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                    <lb/>
                  impedivit effluxum aquæ illius per foramen: ſic in hac Propoſiti­
                    <lb/>
                  one, obliquitas motuum quibus partes aquæ ab anteriore Cylindri
                    <lb/>
                  termino preſſæ, cedunt preſſioni & undiQ.E.D.vergunt, retardat eo­
                    <lb/>
                  rum tranſitum per loca in circuitu termini illius antecedentis ver­
                    <lb/>
                  ſus poſteriores partes Cylindri, efficitque ut fluidum ad majorem
                    <lb/>
                  diſtantiam commoveatur & reſiſtentiam auget, idQ.E.I. ea fere
                    <lb/>
                  ratione qua effluxum aquæ e vaſe diminuit, id eſt, in ratione du­
                    <lb/>
                  plicata 25 ad 21 circiter. </s>
                  <s>Et quemadmodum, in Propoſitionis illius
                    <lb/>
                  caſu primo, effecimus ut partes aquæ perpendiculariter & maxima
                    <lb/>
                  copia tranſirent per foramen
                    <emph type="italics"/>
                  EF,
                    <emph.end type="italics"/>
                  ponendo quod aqua omnis in
                    <lb/>
                  vaſe quæ in circuitu cataractæ congelata fuerat, & cujus motus
                    <lb/>
                  obliquus erat & inutilis, maneret ſine motu: ſic in hac Propoſi­
                    <lb/>
                  tione, ut obliquitas motuum tollatur, & partes aquæ motu maxime
                    <lb/>
                  directo & breviſſimo cedentes facillimum præbeant tranſitum Cy­
                    <lb/>
                  lindro, & ſola maneat reſiſtentia quæ oritur a magnitudine ſecti­
                    <lb/>
                  onis tranſverſæ, quæQ.E.D.minui non poteſt niſi diminuendo dia­
                    <lb/>
                  metrum Cylindri, concipiendum eſt quod partes fluidi quarum
                    <lb/>
                  motus ſunt obliqui & inutiles & reſiſtentiam creant, quieſcant in­
                    <lb/>
                  ter ſe ad utrumque Cylindri ter­
                    <lb/>
                    <figure id="id.039.01.341.1.jpg" xlink:href="039/01/341/1.jpg" number="190"/>
                    <lb/>
                  minum, & cohæreant & Cylindro
                    <lb/>
                  jungantur. </s>
                  <s>Sit
                    <emph type="italics"/>
                  ABCD
                    <emph.end type="italics"/>
                  rectan­
                    <lb/>
                  gulum, & ſint
                    <emph type="italics"/>
                  AE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  BE
                    <emph.end type="italics"/>
                  arcus
                    <lb/>
                  duo Parabolici axe
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  deſcripti,
                    <lb/>
                  latere autem recto quod ſit ad ſpa-</s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum