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="051/01/179.jpg" pagenum="148"/>
                <arrow.to.target n="fig38"/>
                <lb/>
              bet, ſive ſecunda, aut media. </s>
              <s>
                <lb/>
              Deinde ductâ rectâ AB, aga­
                <lb/>
              tur illi ex C parallela CD,
                <lb/>
              occurrensipſi AE productæ,
                <lb/>
              in D; eritque ED tertia
                <lb/>
              proportionalis quæſita. </s>
            </p>
            <figure id="id.051.01.179.1.jpg" xlink:href="051/01/179/1.jpg" number="67"/>
            <p type="main">
              <s>
                <emph type="center"/>
              Annotatio.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              SI duæ datæſint nimis longæ, ſervetur id, quod diximus in Annota­
                <lb/>
              tione Propoſitionis quartæ præcedentis.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              Propoſitio VII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              Datis tribus numeris, invenire quartum pro­
                <lb/>
              portionalem.
                <emph.end type="center"/>
                <lb/>
                <arrow.to.target n="marg256"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg256"/>
                <emph type="italics"/>
              Numeris
                <lb/>
              tribus datis
                <lb/>
              quartum
                <lb/>
              proportiona­
                <lb/>
              lem inveni­
                <lb/>
              re.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>UTere Regulâ proportionum apud Arithmeticos notiſſima,
                <lb/>
              quam Auteam vocant; & habebis intentum. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              Propoſitio VIII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              Datis tribus rectia lineis, quartam propor­
                <lb/>
              tionaleminvenirc.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg257"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg257"/>
                <emph type="italics"/>
              Lineis tri­
                <lb/>
              bus datis,
                <lb/>
                <expan abbr="quartã">quartam</expan>
              pro­
                <lb/>
              portiona­
                <lb/>
              lem inveni­
                <lb/>
              re.
                <emph.end type="italics"/>
              </s>
            </p>
            <figure id="id.051.01.179.2.jpg" xlink:href="051/01/179/2.jpg" number="68"/>
            <p type="main">
              <s>SInt tres lineæ rectæ, AB, BC,
                <lb/>
              AD, quibus invenienda ſit
                <lb/>
              quarta. proportionalis, ad
                <lb/>
              quàm ſit tertia AD, ut eſt
                <lb/>
              prima AB, ad ſecundam BC. </s>
              <s>
                <lb/>
                <expan abbr="Diſponãtur">Diſponantur</expan>
              primæ duæ, AB,
                <lb/>
              BC, ſecundùm lineam
                <expan abbr="rectã">rectam</expan>
                <lb/>
              quæ ſit AC; tertia verò AD,
                <lb/>
              cum prima AB, faciatangulum A quemcunque: deinde ex B
                <lb/>
              ad D ducatur recta BD, cui per C ducatur parallela CE, oc­
                <lb/>
              currens rectæ AD productæ, in E puncto. </s>
              <s>Dico, DE, eſſe
                <lb/>
              quartam proportionalem. </s>
              <s>Demonſtrationem vide apud
                <lb/>
              Euclidem lib. 6. Propoſit. 12. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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