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

Table of figures

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="020/01/2715.jpg" pagenum="340"/>
              omnes simul armillae aequales omnibus simul circulis, hoc est solidum va­
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              siforme sphaericum aequale cylindro praedicto, quod etc. </s>
              <s>” (MSS. Gal. </s>
              <s>Disc.,
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              T. XXX, fol. </s>
              <s>18-25). </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              VIII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Il trattatello elegante della stereometria e della baricentrica dei solidi
                <lb/>
              vasiformi, di cui abbiamo dal manoscritto torricelliano scelto i teoremi prin­
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              cipali, s'incontrava in qualche parte nelle medesime cose dimostrate da al­
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              tri, come dal Commandino, dal Valerio e dal Galileo; ma il Torricelli faceva
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              notare che le sue dimostrazioni procedevano in modo nuovo, e che si face­
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              vano derivare da principii più generali, comprendenti in una somma unità
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              i vari casi particolari. </s>
              <s>Si compiaceva di ciò molto a ragione il Nostro, perchè
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              il merito della novità non consisteva semplicemente nel compendiare, o nel
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              ridurre a maggior facilità le cose da trattarsi, ma nel premostrare ai Mate­
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              matici quel vigore potente, che si verrebbe a infondere nella Scienza dal li­
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              bero uso dell'analisi, applicata al Metodo degli indivisibili in quel che si
                <lb/>
              chiamerebbe poi Calcolo differenziale. </s>
              <s>Un esempio di ciò l'aveva lo stesso
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              Torricelli dato a proposito del centro di gravità nella sfera, comunque ella
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              venisse ridotta o in segmenti o in frusti, e lo udimmo poco fa quasi com­
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              passionare il Valerio, per non essersi accorto che la fatica del ritessere tante
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              volte il viaggio potevasi risparmiare movendo a dirittura dal suo primo prin­
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              cipio. </s>
              <s>Un altro simile incomodo, di divagar nei particolari senz'aver ricono­
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              sciuta la generalità, nella quale potevano tutti esser compresi, ebbe a notarla
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              nell'argomento del centro di gravità dei solidi conoidali, intorno a che il
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              Valerio e Galileo avevano sudato tanto, per dimostrare alcune proposizioni, ri­
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              maste ne'loro libri come membra sparse e inerti, perchè non ricongiunte a
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              quel principio, che avrebbe dovuto in esse far refluire la vita. </s>
            </p>
            <p type="main">
              <s>Nel numero dei Problemi, proposti e passati scambievolmente tra i ma­
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              tematici di Francia, il Torricelli racconta di aver messo anche questo: “ Se
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              sarà il solido CFAHD (fig. </s>
              <s>208), nato dalla rivoluzione di una sezione conica,
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              o sia perabola o iperbola o porzione di circolo, ovvero di ellisse, e sia tirato il
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                <figure id="id.020.01.2715.1.jpg" xlink:href="020/01/2715/1.jpg" number="713"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 208.
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              piano FH parallelo alla base CD, e che seghi per
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              mezzo l'asse nel punto E; chiameremo il cerchio
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              FH media sezione, e intorno a ciò si dimostrarono
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              e si proposero i due teoremi seguenti: I. </s>
              <s>Il solido
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              predetto, al suo cono inscritto, sarà come una sua
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              base, con quattro medie sezioni, e due sue basi. </s>
              <s>
                <lb/>
              II. </s>
              <s>Ma facendosi come una base, con due medie
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              sezioni, a due medie sezioni, così la retta AO alla
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              OB; sarà il punto O centro di gravità di quel tale solido. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Nella prima di queste due enunciazioni sta compendiata ùna gran </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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