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

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="020/01/571.jpg" pagenum="14"/>
              dicolari GE, GF, le quali son la giusta misura del dipartirsi i due raggi, sono
                <lb/>
              fra loro uguali. </s>
              <s>D'onde, essendo i due triangoli EGC, FGC uguali è facile
                <lb/>
              concludere che i due angoli ECB, ACF debbon pure essere uguali. </s>
            </p>
            <p type="main">
              <s>Le due leggi, soggiunge ivi Dante essere dimostrate dall'
                <emph type="italics"/>
              esperienza
                <emph.end type="italics"/>
              e
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              dall'
                <emph type="italics"/>
              arte,
                <emph.end type="italics"/>
              ossia dal ragionamento, il qual ragionamento è quello che noi ab­
                <lb/>
              biamo ora spiegato dai versi del Poeta. </s>
              <s>Ma è facile vedere che anco qui,
                <lb/>
              come in Euclide a cui il Cantore de'citati versi tien d'occhio, tutto il fon­
                <lb/>
              damento è nel fatto sperimentale e poco o nulla nell'arte, la quale ancora
                <lb/>
              doveva essere attesa assai lungamente. </s>
            </p>
            <p type="main">
              <s>Non prima infatti del cominciar del secolo XVII si vide nel Keplero chi
                <lb/>
              tentasse di maneggiar quell'arte, invocando la Geometria applicata al moto
                <lb/>
              de'corpi, per dimostrar ciò che Euclide, e tutti gli altri Ottici dopo di lui,
                <lb/>
              avevano reputato geometricalmente indimostrabile. </s>
              <s>Quel
                <emph type="italics"/>
              nescio quid subtile
                <emph.end type="italics"/>
                <lb/>
              per cui s'erano l'Alhazen e Vitellione argomentati
                <emph type="italics"/>
              motum lucis oblique in­
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              cidentis componi ex motu perpendiculari et motu parallelo ad densi su­
                <lb/>
              perficiem
                <emph.end type="italics"/>
              (Paralipom. </s>
              <s>ad Vitell., Francof. </s>
              <s>1604, pag. </s>
              <s>84), parve al Keplero
                <lb/>
              esser uno spiraglio aperto alle nuove speranze d'ostetricare il primo parto
                <lb/>
              di quel connubio fra l'Ottica e la Meccanica, da'due commemorati Autori
                <lb/>
              felicemente iniziato. </s>
            </p>
            <p type="main">
              <s>La proposizione XIX formulata ne'Paralipomeni a Vitellione
                <emph type="italics"/>
              Repercus­
                <lb/>
              sus fit ad aequales angulos et eius quod oblique incidit ad latus alterum,
                <emph.end type="italics"/>
                <lb/>
              è quella stessa formulata tanti secoli prima nel suo I Teorema di Prospet­
                <lb/>
              tiva da Euclide, ma la dimostrazione è nel Matematico alemanno, dopo tanti
                <lb/>
              secoli, nuova, e a chi si diffidava di riuscir nella difficile impresa, si pre­
                <lb/>
              senta inaspettata. </s>
            </p>
            <p type="main">
              <s>Invocando dunque il Keplero il principio della composizion delle forze
                <lb/>
              applicato al moto della luce, così comincia e procede in quella sua dimo­
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              strazione: “ Cum quid oblique movetur ver­
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              sus superficiem, motus is componitur ex
                <lb/>
                <figure id="id.020.01.571.1.jpg" xlink:href="020/01/571/1.jpg" number="69"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 4.
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              perpendiculari et parallelo superficiei. </s>
              <s>Al
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              superficies tantum ei parti obiicitur, quae
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              est in se perpendicularis, non ei quae est
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              sibi parallelos. </s>
              <s>Quare nec impedit partem
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              sibi parallelon, sed palitur mobile resiliendo
                <lb/>
              pergere ad partem alteram sicut advenerat. </s>
              <s>
                <lb/>
              Sit CDF (fig. </s>
              <s>4) superficies, BD motus lu­
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              cis: continuetur BD in E, secans CDF in
                <lb/>
              D, et sit CDE aequalis CDA ” (ibi, pag. </s>
              <s>14). </s>
            </p>
            <p type="main">
              <s>La ragione di questa uguaglianza la dimostra il Keplero così argomen­
                <lb/>
              tando: Siccome il moto dalla parte D verso C non è impedito, ma è impe­
                <lb/>
              dito solo quello da C verso E, dunque il raggio riflesso AD deve serbar
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              quella medesima inclinazione verso la superficie riflettente CD secondo la
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              quale procederebbe il raggio BDE quando non fosse impedito. </s>
              <s>In altre pa­
                <lb/>
              role, deve esser CDE=CDA. </s>
              <s>Ma perchè CDE è uguale a BDF “ ergo (con-</s>
            </p>
          </chap>
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