Schott, Gaspar, Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet. , 1657

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="051/01/154.jpg" pagenum="123"/>
              terraneum P. Athanaſij Kircheri, ubi in Libro Centroſophico
                <lb/>
              fuſiſſimè pertractat hanc materiam. </s>
              <s>Lege præterea Joannem
                <lb/>
              Caramuelem in Cruce Sublimium ingeniorum. </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg222"/>
              Lex II. gra­
                <lb/>
              vium
                <expan abbr="de-ſcendentiũ">de­
                  <lb/>
                ſcendentium</expan>
              .</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg223"/>
                <emph type="italics"/>
              Numeri pa­
                <lb/>
              riter impa­
                <lb/>
              res ab unita­
                <lb/>
              te numera­
                <lb/>
              ti.
                <emph.end type="italics"/>
              </s>
            </p>
            <table>
              <row>
                <cell>Tempora</cell>
                <cell>Quadrata</cell>
                <cell>Spatia</cell>
              </row>
              <row>
                <cell>1</cell>
                <cell>1</cell>
                <cell>1</cell>
              </row>
              <row>
                <cell>2</cell>
                <cell>4</cell>
                <cell>3</cell>
              </row>
              <row>
                <cell>3</cell>
                <cell>9</cell>
                <cell>5</cell>
              </row>
              <row>
                <cell>4</cell>
                <cell>16</cell>
                <cell>7</cell>
              </row>
              <row>
                <cell>5</cell>
                <cell>25</cell>
                <cell>9</cell>
              </row>
              <row>
                <cell>6</cell>
                <cell>36</cell>
                <cell>11</cell>
              </row>
            </table>
            <p type="main">
              <s>
                <emph type="center"/>
              Leges aquæ naturali motu deſcendentis
                <lb/>
              & effluentis per tubos.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>SIt jam tubus ABCD, ſive ſemper, ſive non ſemper plenus,
                <lb/>
                <arrow.to.target n="marg224"/>
                <lb/>
              cujus foramen B;
                <expan abbr="tempuſq́ue">tempuſque</expan>
              in quo aqua ab A deſcendit
                <lb/>
              uſque ad B, dividatur in quinque æquales partes, in quarum
                <lb/>
              prima confecerit ſpatium A1; Dico, eandem aquam in ſe­
                <lb/>
              cunda parte temporis conficere ſpatium A4, in tertia parte
                <lb/>
                <arrow.to.target n="fig30"/>
                <lb/>
              A9, in quarta ſpatium A16, in quinta ſpatium A25;
                <lb/>
              atque adeo ſpatia æqualibus quinque temporibus
                <lb/>
              confecta, habere ſe ut quadrata quinque illorum
                <lb/>
              temporum, ut ex appoſitis utrimque numeris ap­
                <lb/>
              paret; ſeu velocitatem deſcenſus aquæ creſcere ſe­
                <lb/>
              cundùm progreſſionem numerorum imparium,
                <lb/>
              prout indicant numeri intra tubum notati; ſeu
                <lb/>
              ſpatia confecta habere duplicatam rationem illius,
                <lb/>
              quam habent tempora, ut apparet ſi conferas nu­
                <lb/>
              meros externos lateris AB, cum numeris lateris
                <lb/>
              CD. </s>
              <s>Ratio eſt, quia aqua gravis eſt, & intra tu­
                <lb/>
              bum naturali motu deſcendit, nullumque adeſt
                <lb/>
              impedimentum motus; ergo imitari debet leges aliorum gra­
                <lb/>
              vium naturali motu deſcendentium. </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg224"/>
                <emph type="italics"/>
              Leges aqua
                <lb/>
              naturali
                <lb/>
              motu de­
                <lb/>
              ſcendentis
                <lb/>
              per tubos.
                <emph.end type="italics"/>
              </s>
            </p>
            <figure id="id.051.01.154.1.jpg" xlink:href="051/01/154/1.jpg" number="50"/>
            <p type="main">
              <s>
                <emph type="center"/>
              Corollarium I.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>COlligitur hinc primò, Aquam è foramine B, tubi ſemper
                <lb/>
                <arrow.to.target n="marg225"/>
                <lb/>
              pleni, effluere tantâ velocitate, quantâ deſcendit ab A ad
                <lb/>
              B. </s>
              <s>Ratio eſt, quia ut ſupponitur, tantum effluit per B, quan­
                <lb/>
              tum influit per A, & è contrario tantum per A influit, quan­
                <lb/>
              tum per B effluit, & in deſcenſu ab A ad B nulla fit inter­
                <lb/>
              ruptio; ergo tam velociter effluit per B, quàm velociter de­
                <lb/>
              ſcendit ab A ad B. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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