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

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          <chap>
            <pb xlink:href="020/01/3480.jpg" pagenum="441"/>
            <p type="main">
              <s>
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              “ Corollarium II.
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              — In prismate basis triangularis ICD ordinatae DA,
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              EO exhibent velocitates superficierum supremarum ID, PR, dum vas esina­
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              nitur ” (ibid., fol. </s>
              <s>116). </s>
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            <p type="main">
              <s>Lieto di così fatti progressi il Viviani sentì nascersi la curiosità di ritro­
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              vare la scala, per la quale scendono dentro il cono i livelli dell'acqua, che
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              si versa per la troncata punta rivolta in basso. </s>
              <s>Al Grandi, che aveva tro­
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              vato in questi manoscritti essere la detta scala nelle ordinatamente applicate
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              a una iperbola cubica del secondo grado, fu facile cosa confermarne la ve­
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              rità, concludendola immediatamente dai principii idrodinamici già dimostrati. </s>
              <s>
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              Se infatti è ABC, nella figura 222, il triangolo genitore del vaso, dentro il
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              quale siano le velocità dei livelli in AC, DE ordinatamente rappresentate
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              dalle linee AC, DL; abbiamo, per la XXII di questo,
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              AC:DL=DE2.√AB:AC2.√BD. </s>
              <s>
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              E perchè, per la similitudine de'triangoli, DE2:AC2=BD2:AB2, sarà
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              AC:DL=BD2.√AB:AB2.√BD. </s>
              <s>E quadrando,
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              AC2:DL2=BD4.AB:AB4.BD=BD3:AB3,
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              ond'è veramente, come il Grandi stesso concludeva, nel corollario V della
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              citata proposizione XXII del suo trattato del Movimento delle acque, la scala
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                <figure id="id.020.01.3480.1.jpg" xlink:href="020/01/3480/1.jpg" number="1121"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 222.
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              delle velocità del liquido, fluente
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              per l'apice di un vaso conico, una
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              iperbola cubica del secondo gra­
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              do. (Raccolta d'Autori cit., T. III,
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              pag. </s>
              <s>91). </s>
            </p>
            <p type="main">
              <s>Il Viviani però, che non sa­
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              peva ancora sotto quale aspetto gli
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              si presenterebbe la verità, rimasta
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              agli occhi dei Matematici tuttavia
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              nascosta; non ha la mano così
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              franca e spedita, nello svilupparle
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              il geloso velo dalla faccia divina. </s>
              <s>
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              Ma riconosciuto appena il mistero,
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              quasi a modo di epigrafe solen­
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              nemente commemorativa del fatto,
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              scrive in linea, che seconda la concavità della disegnata curva PCL,
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              Hyper­
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              bola, in qua quadrata ordinatarum sunt ut cubi abscissarum reciproce,
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              et punctum B est omnium centrum, asymptoti vero BA, BM
                <emph.end type="italics"/>
              (MSS. Gal. </s>
              <s>
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              Disc., T. CXVII, fol. </s>
              <s>9). Il calcolo, che si concludeva in questa iscrizione, è
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              al solito avvolto come i passi di chi è incerto dove sarà per riuscire. </s>
              <s>Tali
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              poi, quali noi le riferiamo in modo analitico, sono del detto calcolo le tracce,
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              rimasteci nel manoscritto, il quale comincia dal comandare che, dopo le DE,
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              DF, DG, sian prese le tre continue proporzionali DH, DI, DL. </s>
            </p>
            <p type="main">
              <s>È per la XXII di questo,
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              V
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              ,AC:
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              V
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              .DE=DG.DE2:DF.DG2, e </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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