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="039/01/338.jpg" pagenum="310"/>
                    <lb/>
                    <arrow.to.target n="note286"/>
                    <emph type="center"/>
                  LEMMA IV.
                    <emph.end type="center"/>
                    <lb/>
                  </s>
                </p>
                <p type="margin">
                  <s>
                    <margin.target id="note286"/>
                  DE MOTU
                    <lb/>
                  CORPORUM</s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cylindri, qui ſecundum longitudinem ſuam uniformiter progreditur,
                    <lb/>
                  reſiſtentia ex aucta vel diminuta ejus longitudine non mutatur;
                    <lb/>
                  ideoque eadem eſt cum reſiſtentia Circuli eadem diametro de­
                    <lb/>
                  ſcripti & eadem velocitate ſecundum lineam rectam plano ip­
                    <lb/>
                  ſius perpendicularem progredientis.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam latera Cylindri motui ejus minime opponuntur: & Cy­
                    <lb/>
                  lindrus, longitudine ejus in infinitum diminuta, in Circulum
                    <lb/>
                  vertitur.
                    <lb/>
                    <emph type="center"/>
                  PROPOSITIO XXXVII. THEOREMA XXIX.
                    <emph.end type="center"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>
                    <emph type="italics"/>
                  Cylindri, qui in fluide compreſſo infinito & non elaſtico ſecundum
                    <lb/>
                  longitudinem ſuam uniformiter progreditur, reſiſtentia quæ ori­
                    <lb/>
                  tur a magnitudine ſectionis tranſverſæ, eſt ad vim qua totus
                    <lb/>
                  ejus motus interea dum quadruplum longitudinis ſuæ deſcribit,
                    <lb/>
                  vel tolli poſſit vel generari, ut denſitas Medii ad denſitatem
                    <lb/>
                  Cylindri quamproxime.
                    <emph.end type="italics"/>
                    <lb/>
                  </s>
                </p>
                <p type="main">
                  <s>Nam ſi vas
                    <emph type="italics"/>
                  ABDC
                    <emph.end type="italics"/>
                  fundo ſuo
                    <emph type="italics"/>
                  CD
                    <emph.end type="italics"/>
                  ſuperficiem aquæ ſtagnan­
                    <lb/>
                  tis tangat, & aqua ex hoc vaſe per ca­
                    <lb/>
                    <figure id="id.039.01.338.1.jpg" xlink:href="039/01/338/1.jpg" number="189"/>
                    <lb/>
                  nalem Cylindricum
                    <emph type="italics"/>
                  EFTS
                    <emph.end type="italics"/>
                  horizonti
                    <lb/>
                  perpendicularem in aquam ſtagnantem
                    <lb/>
                  effluat, locetur autem Circellus
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ho­
                    <lb/>
                  rizonti parallelus ubivis in medio ca­
                    <lb/>
                  nalis, & producatur
                    <emph type="italics"/>
                  CA
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  K,
                    <emph.end type="italics"/>
                  ut ſit
                    <lb/>
                    <emph type="italics"/>
                  AK
                    <emph.end type="italics"/>
                  ad
                    <emph type="italics"/>
                  CK
                    <emph.end type="italics"/>
                  in duplicata ratione quam
                    <lb/>
                  habet exceſſus orificii canalis
                    <emph type="italics"/>
                  EF
                    <emph.end type="italics"/>
                  ſupra
                    <lb/>
                  circellum
                    <emph type="italics"/>
                  PQ
                    <emph.end type="italics"/>
                  ad circulum
                    <emph type="italics"/>
                  AB
                    <emph.end type="italics"/>
                  : mani­
                    <lb/>
                  feſtum eſt (per Caſ.5, Caſ.6, & Cor. 1.
                    <lb/>
                  Prop.XXXVI.) quod velocitas aquæ tran­
                    <lb/>
                  ſeuntis per ſpatium annulare inter cir­
                    <lb/>
                  cellum & latera vaſis, ea erit quam aqua
                    <lb/>
                  cadendo & caſu ſuo deſcribendo altitudinem
                    <emph type="italics"/>
                  KC
                    <emph.end type="italics"/>
                  vel
                    <emph type="italics"/>
                  IG
                    <emph.end type="italics"/>
                  acquirere
                    <lb/>
                  poteſt. </s>
                </p>
              </subchap2>
            </subchap1>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum