Newton, Isaac, Philosophia naturalis principia mathematica, 1713

Table of figures

< >
< >
page |< < of 524 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <subchap1>
              <subchap2>
                <p type="main">
                  <s>
                    <pb xlink:href="039/01/342.jpg" pagenum="314"/>
                    <lb/>
                    <arrow.to.target n="note290"/>
                  tium
                    <emph type="italics"/>
                  HG,
                    <emph.end type="italics"/>
                  deſcribendum a Cylindro
                    <lb/>
                    <figure id="id.039.01.342.1.jpg" xlink:href="039/01/342/1.jpg" number="191"/>
                    <lb/>
                  cadente dum velocitatem ſuam ac­
                    <lb/>
                  quirit, ut
                    <emph type="italics"/>
                  HG
                    <emph.end type="italics"/>
                  ad 1/2
                    <emph type="italics"/>
                  AB.
                    <emph.end type="italics"/>
                  Sint etiam
                    <lb/>
                    <emph type="italics"/>
                  CF
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  DF
                    <emph.end type="italics"/>
                  arcus alii duo Para­
                    <lb/>
                  bolici, axe
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  & latere recto
                    <lb/>
                  quod ſit prioris lateris recti qua­
                    <lb/>
                  druplum deſcripti; & convolutione figuræ circum axem
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ge­
                    <lb/>
                  neretur ſolidum cujus media pars
                    <emph type="italics"/>
                  ABDC
                    <emph.end type="italics"/>
                  ſit Cylindrus de quo
                    <lb/>
                  agimus, & partes extremæ
                    <emph type="italics"/>
                  ABE
                    <emph.end type="italics"/>
                  &
                    <emph type="italics"/>
                  CDF
                    <emph.end type="italics"/>
                  contineant partes fluidi
                    <lb/>
                  inter ſe quieſcentes & in corpora duo rigida concretas, quæ Cy­
                    <lb/>
                  lindro utrinque tanquam caput & cauda adhæreant. </s>
                  <s>Et ſolidi
                    <lb/>
                    <emph type="italics"/>
                  EACFDB,
                    <emph.end type="italics"/>
                  ſecundum longitudinem axis ſui
                    <emph type="italics"/>
                  FE
                    <emph.end type="italics"/>
                  in partes ver­
                    <lb/>
                  ſus
                    <emph type="italics"/>
                  E
                    <emph.end type="italics"/>
                  progredientis, reſiſtentia ea erit quamproxime quam in hac
                    <lb/>
                  Propoſitione deſcripſimus, id eſt, quæ rationem illam habet ad
                    <lb/>
                  vim qua totus Cylindri motus, interea dum longitudo 4
                    <emph type="italics"/>
                  AC
                    <emph.end type="italics"/>
                  motu
                    <lb/>
                  illo uniformiter continuato deſcribatur, vel tolli poſſit vel generari,
                    <lb/>
                  quam denſitas Fluidi habet ad denſitatem Cylindri quamproxime.
                    <lb/>
                  Et hac vi Reſiſtentia minor eſſe non poteſt quam in ratione 2 ad 3,
                    <lb/>
                  per Corol. 7. Prop. XXXVI.
                    <lb/>
                    <emph type="center"/>
                  LEMMA V.
                    <emph.end type="center"/>
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note290"/>
                  DE MOTU
                    <lb/>
                  CORPORUM.</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Si Cylindrus, Sphæra & Sphærois, quorum latitudines ſunt æqua­
                    <lb/>
                  les, in medio canalis Cylindrici ita locentur ſucceſſive ut eo­
                    <lb/>
                  rum axes cum axe canalis coincidant: hæc corpora fluxum
                    <lb/>
                  aquæ per canalem æqualiter impedient.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam ſpatia inter Canalem & Cylindrum, Sphæram, & Sphæroi­
                    <lb/>
                  dem per quæ aqua tranſit, ſunt æqualia: & aqua per æqualia ſpa­
                    <lb/>
                  tia æqualiter tranſit.
                    <lb/>
                    <emph type="center"/>
                  LEMMA VI.
                    <emph.end type="center"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Iiſdem poſitis, corpora prædicta æqualiter urgentur ab aqua per
                    <lb/>
                  canalem fluente.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>Patet per Lemma v & Motus Legem tertiam. </s>
                  <s>Aqua utique &
                    <lb/>
                  corpora in ſe mutuo æqualiter agunt. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum