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="020/01/2706.jpg" pagenum="331"/>
              non meno splendide e nuove. </s>
              <s>Dalla V del III del Cavalieri si concludeva es­
                <lb/>
              sere la scodella esterna uguale al cono, o fosse il cilindro circoscritto alla
                <lb/>
              sfera, o alla sferoide, cosicchè in questo caso, togliendosi la scodella stessa,
                <lb/>
              rimaneva l'emisferoide ignuda, della quale potevasi, con la nota regola del­
                <lb/>
              l'VIII degli Equiponderanti, ritrovare il baricentro, conoscendosi quello del
                <lb/>
              tutto e di una sua parte. </s>
              <s>La proporzione stereometrica poi tra l'una e l'al­
                <lb/>
              tro, cioè tra l'emisferoide e il cono inscritto, era nota per la XXIX di Ar­
                <lb/>
              chimede nel libro
                <emph type="italics"/>
              De conoid. </s>
              <s>et sphaer.,
                <emph.end type="italics"/>
              ma il Torricelli, per far prova della
                <lb/>
              superiorità del metodo degl'indivisibili verso l'antico, e per mostrare con
                <lb/>
              quanto maravigliosa facilità e speditezza si potesse giungere a quelle mede­
                <lb/>
              sime conclusioni, alle quali si giungeva pure dai matematici seguaci del Si­
                <lb/>
              racusano, ma per vie tanto aspre e affannose; si applicò a dimostrare, con
                <lb/>
              aggressioni nuove, che l'emisfero o l'emisferoide è doppia del cono inscritto,
                <lb/>
              premettendo tre lemmi alla proposizione. </s>
            </p>
            <p type="main">
              <s>Il primo è compreso nella VI archimedea
                <emph type="italics"/>
              De conoid. </s>
              <s>et sphaer.,
                <emph.end type="italics"/>
              nella
                <lb/>
              quale si dimostra che l'ellisse sta al circolo come il rettangolo sotto gli assi
                <lb/>
              sta al quadrato del diametro; d'onde si deriva che, se uno degli assi è uguale
                <lb/>
              al diametro, come suppone il Torricelli, l'ellisse sta al circolo come l'altro
                <lb/>
              asse al diametro, secondo che il Torricellì stesso proponevasi di dimostrare,
                <lb/>
              benchè in un modo del tutto nuovo. </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Lemma I.
                <emph.end type="italics"/>
              — Omnis ellipsis, ad circulum qui habeat diametrum ae­
                <lb/>
              quale alteri axium ellipseos, eam habet proportionem, quam alter, nempe
                <lb/>
              inaequalis axis, ad circuli diametrum. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Esto ellipsis ABC (fig. </s>
              <s>192), circulus ADC, et sit axis ellipsis AC ae­
                <lb/>
              qualis diametro circuli AC. </s>
              <s>Sitque alter axis BH: dico
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                <figure id="id.020.01.2706.1.jpg" xlink:href="020/01/2706/1.jpg" number="697"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 192.
                <lb/>
              ellipsim ad circulum esse ut BH ad HD. </s>
              <s>Ducatur enim
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              ordinatim EF, ubicumque, et erit quadratum EF, ad qua­
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              dratum BH, ut rectangulum AFC, ad rectangulum AHC. </s>
              <s>
                <lb/>
              Sed etiam quadratum IF, ad quadratum DH, est ut re­
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              ctangulum AFC ad rectangulum AHC; ergo quadratum
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              EF, ad quadratum BH, est ut quadratum IF ad quadra­
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              tum DH. </s>
              <s>Ergo et lineae sunt proportionales. </s>
              <s>Et, permu­
                <lb/>
              tando, EF ad FI est ut BH ad HD, et hoc semper. </s>
              <s>Propterea erunt omnes
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              antecedentes simul, ad omnes simul consequentes, ut una antecedentium ad
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              unam consequentium, nempe ellipsis ABC, ad circulum ADC, ut BH ad HD ”
                <lb/>
              (idid., fol. </s>
              <s>172). </s>
            </p>
            <p type="main">
              <s>Segue l'altro lemma, che, trapassando dal circolo e dall'ellisse alla sfera
                <lb/>
              e allo sferoide, procede per gl'indivisibili in modo analogo al primo. </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Lemma II.
                <emph.end type="italics"/>
              — Omnis sphaerois, ad sphaeram, quae habeat maximum
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              circulum aequalem maximo circulo sphaeroidis, est ut axis ad axem. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Esto sphaerois ABC (fig. </s>
              <s>193) sphaera vero ADC quales dictae sunt:
                <lb/>
              maximus utriusque circulus sit AHCL. </s>
              <s>Dico sphaeroidem ad sphaeram esse
                <lb/>
              ut axis BE ad axem ED. </s>
              <s>Secetur enim utraque per centrum E, plano HBL
                <lb/>
              ad diametrum AC erecto, et iterum altero plano MFN, ipsi HBL parallelo </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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