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="020/01/2713.jpg" pagenum="338"/>
              ellipses similes, nempe ut DC ad CE, ita BC ad CF; ordinatimque ducantur
                <lb/>
              FH tangens, et IL secans inclusam ellipsim; dico ita esse IM ad HF, ut HF
                <lb/>
              ad ML. ” </s>
            </p>
            <p type="main">
              <s>“ Est enim quadratum IN, ad quadratum DC, ut rectangulum BNA, ad
                <lb/>
              rectangulum BCA: hoc est, ut quadratum BC. </s>
              <s>Sed DC quadratum, ad qua­
                <lb/>
              dratum CE, est ut quadratum BC ad CF, et quadratum CE, ad quadratum
                <lb/>
              MN, est ut quadratum CF ad rectangulum ONF; quare ex aequo erit qua­
                <lb/>
              dratum IN, ad quadratùm MN, ut rectangulum BNA, ad rectangulum FNO. ” </s>
            </p>
            <p type="main">
              <s>“ Iterum, quadratum idem IN, ad quadratum HF, est ut rectangulum
                <lb/>
              idem BNA, ad rectangulum BFA. </s>
              <s>Quare erit quadratum IN, ad duo simul
                <lb/>
              quadrata MN, HF, ut rectangulum BNA, ad duo simul rectangula FNO, BFA. </s>
              <s>
                <lb/>
              Sed rectangulum BNA, per lemma praecedens, duobus dictis rectangulis ae­
                <lb/>
              quale est; ergo et quadratum IN duobus simul quadratis MN, HF aequale
                <lb/>
              erit. </s>
              <s>Si ergo ab aequalibus commune auferas quadratum MN, reliquum re­
                <lb/>
              ctangulum IML aequale erit reliquo quadrato HF. </s>
              <s>Propterea patet propo­
                <lb/>
              situm. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE XLII. —
                <emph type="italics"/>
              Si fuerint circa communem axem CB, in
                <lb/>
              eadem figura, et circa idem centrum C, duo ellipses similes, et converta­
                <lb/>
              tur figura circa axem; erit solidum vasiforme, factum a revolutione qua­
                <lb/>
              drilinei DHFE, aequale cylindro eamdem ipso basi, eamdemque altitudinem
                <lb/>
              habenti. </s>
              <s>”
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Intelligatur enim super basi HP cylindrus HQ, et planum DR ad axem
                <lb/>
              erectum. </s>
              <s>Erunt itaque, per lemma praecedens, DE, HF, ER in continua ra­
                <lb/>
              tione. </s>
              <s>Quare, per Lemma I, erit armilla ex DE descripta aequalis circulo ex
                <lb/>
              HF, vel ex CS, et hoc semper. </s>
              <s>Quare erunt omnes simul armillae aequa­
                <lb/>
              les omnibus simul circulis, nempe solidum vasiforme ellipticum aequale cy­
                <lb/>
              lindro. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE XLIII. —
                <emph type="italics"/>
              Si intra parallelogrammum rectangulum
                <lb/>
              ABCD
                <emph.end type="italics"/>
              (fig. </s>
              <s>204)
                <emph type="italics"/>
              sit quadrans ellipsis DB, et convertatur figura circa al­
                <lb/>
              terutrum vel AB vel AD; erit solidum vasiforme, factum a trilineo BDC,
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.020.01.2713.1.jpg" xlink:href="020/01/2713/1.jpg" number="709"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 204.
                <lb/>
                <emph type="italics"/>
              acquale cono CAH eamdem ipsi basim, eamdemque
                <lb/>
              altitudinem habenti. </s>
              <s>”
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Agatur enim planum EF ad axem erectum,
                <lb/>
              ponaturque BO axis integrae ellipsis. </s>
              <s>Quadratum EI,
                <lb/>
              vel DA, ad quadratum LI, est ut quadratum BA,
                <lb/>
              ad rectangulum BIO. </s>
              <s>Quadratum iterum EI, vel CB.
                <lb/>
              ad quadratum MI, est ut quadratum BA, ad qua­
                <lb/>
              dratum IA. </s>
              <s>Quare erit idem quadratum EI, ad duo
                <lb/>
              simul quadrata LI, MI, ut quadratum BA, ad duo
                <lb/>
              simul spatia: rectangulum scilicet BIO et quadra­
                <lb/>
              tum IA. </s>
              <s>Sed quadratum BA aequale est dictis duo­
                <lb/>
              bus spatiis, ergo et quadratum EI aequale erit duo­
                <lb/>
              bus quadratis LI, MI. </s>
              <s>Dempto autem communi quadrato LI, erit reliquum
                <lb/>
              rectangulum ELF aequale quadrato MI. </s>
              <s>Constat igitur, per Lemma I, armil-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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