Caverni, Raffaello, Storia del metodo sperimentale in Italia, 1891-1900

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="020/01/2712.jpg" pagenum="337"/>
              ticem inclusae parabolae, sed EF ubicumque, dummodo utranque parabolam
                <lb/>
              secet; dico esse ut EG ad CD, ita CD ad GF. </s>
              <s>Ponatur enim AH latus rectum
                <lb/>
              commune, et erit, ob parabolam, rectangulum
                <lb/>
                <figure id="id.020.01.2712.1.jpg" xlink:href="020/01/2712/1.jpg" number="706"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 201.
                <lb/>
              HAB aequale quadrato BE. </s>
              <s>Si ergo ab aequa­
                <lb/>
              libus aequalia demas, nempe rectangulum sub
                <lb/>
              AH, CB, ex rectangulo HAB, et quadratum
                <lb/>
              BG ex quadrato BE, quae remanent aequalia
                <lb/>
              erunt, nempe rectangulum HAC, sive quadra­
                <lb/>
              tum CD, et rectangulum EGF. </s>
              <s>Quare erit ut
                <lb/>
              EG ad CD, ita CD ad GF,
                <expan abbr="q.">que</expan>
              e. </s>
              <s>d. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE XLI. —
                <emph type="italics"/>
              Si fuerint duae
                <lb/>
              parabolae aequales circa communem axem, et convertatur figura, erit
                <lb/>
              solidum vasiforme descriptum aequale cylindro, eamdem basim cum so­
                <lb/>
              lido, eamdemque altitudinem habenti. </s>
              <s>”
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Sint circa communem axem AB, uti in praeced. </s>
              <s>figura, duae para­
                <lb/>
              bolae aequales DE, GC hoc est quarum latera recta sint aequalia, et ductis
                <lb/>
              ordinatim CD, BE, quarum CD tangat inclusam parabolam, BE vero secet,
                <lb/>
              convertatur figura circa axem AB. </s>
              <s>Dico solidum vasiforme, descriptum a
                <lb/>
              quadrilineo EDCG, aequale esse cylindro, cuius basis sit circulus circa DO,
                <lb/>
              altitudo vero CB. ” </s>
            </p>
            <p type="main">
              <s>“ Cum enim, per lemma praecedens, in continua ratione sint EG, DC,
                <lb/>
              GF, erit, per lemma I, armilla, ex linea EG descripta, aequalis circulo ex
                <lb/>
              DC, hoc est ex BH, et hoc semper. </s>
              <s>Ergo omnes simul armillae, hoc est so­
                <lb/>
                <figure id="id.020.01.2712.2.jpg" xlink:href="020/01/2712/2.jpg" number="707"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 202.
                <lb/>
              lidum vasiforme parabolicum, aequales
                <lb/>
              erunt omnibus simul circulis, hoc est cy­
                <lb/>
              lindro HDOL,
                <expan abbr="q.">que</expan>
              e. </s>
              <s>d. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Lemma III.
                <emph.end type="italics"/>
              — Si recta linea AB
                <lb/>
              (fig. </s>
              <s>202) secetur inaequaliter bis in C
                <lb/>
              et D, ponaturque BE aequalis ipsi CA; erit rectangulum ADB, partium scili­
                <lb/>
              cet minus inaequalium, aequale duobus simul rectangulis, nempe ACB, par­
                <lb/>
              tium magis inaequalium, et rectangulo CDE sub intermediis sectionibus. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Secetur AB bifariam in I, et erunt aequales
                <lb/>
                <figure id="id.020.01.2712.3.jpg" xlink:href="020/01/2712/3.jpg" number="708"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 203.
                <lb/>
              ipsae etiam IC, IE. Sed, cum rectangulum ADB, si­
                <lb/>
              mul cum quadrato DI, aequale sit quadrato AI; item,
                <lb/>
              rectangulum ACB, cum quadrato CI, eidem quadrato
                <lb/>
              AI aequale sit; erunt rectangulum ADB, cum qua­
                <lb/>
              drato DI, aequalia rectangulo ACB cum quadrato CI. </s>
              <s>
                <lb/>
              Commune auferatur quadratum DI, erit reliquum
                <lb/>
              rectangulum ADB aequale reliquis duobus rectan­
                <lb/>
              gulis ACB, et CDE. </s>
              <s>Si enim demas, ex quadralo CI,
                <lb/>
              quadratum DI, spatium quod relinquitur est rectan­
                <lb/>
              gulum CDE. </s>
              <s>Ergo constat propositum. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Lemma IV.
                <emph.end type="italics"/>
              — Si fuerint circa communem
                <lb/>
              axem AB (fig. </s>
              <s>203), et circa idem contrum C, duo </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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