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

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            <p type="caption">
              <s>
                <pb xlink:href="020/01/2013.jpg" pagenum="256"/>
              o momento parte sul piano BC, e parte sul BD. </s>
              <s>Cerca con che proporzione
                <lb/>
              sian divisi questi momenti in differenti inclinazioni di piano, e variandosi
                <lb/>
              l'angolo DBC da acuto a retto e da retto a ottuso ” (MSS. Gal. </s>
              <s>Disc., T.
                <lb/>
              CXIII, fol. </s>
              <s>30 a tergo). </s>
            </p>
            <p type="main">
              <s>Non molto tempo dopo lasciava così in un altro foglio il Viviani stesso
                <lb/>
              abbozzato quel che cercando aveva trovato: “ Sia la sfera A, nella mede­
                <lb/>
              sima figura, che posi nell'angolo de'due piani DB, BC. e sia DC orizzon­
                <lb/>
              tale, BE perpendicolare, e DG parallela ad EB, ed EF a CB. </s>
              <s>Dico il mo­
                <lb/>
              mento gravitativo di A sopra CB, al gravitativo sopra DB, stare come DB
                <lb/>
              ad EF,
                <emph type="italics"/>
              vel ad BG, vel ut EII ad EI parallelae ipsis planis, vel ut EL
                <lb/>
              ad EM perpendiculares iisdem planis,
                <emph.end type="italics"/>
              cioè come i seni retti de'comple­
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              menti delle inclinazioni de'piani. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Poichè il gravitativo sopra BC al totale sta come EC a CB, ovvero
                <lb/>
              come DE ad EF, ed il totale, al gravitativo sopra DB, sta come BD a DE;
                <lb/>
              così
                <emph type="italics"/>
              ex aequo in ratione perturbata,
                <emph.end type="italics"/>
              come il gravitativo sopra BC, al gra­
                <lb/>
              vitativo sopra DB, così la DB alla EF. </s>
              <s>Ma EF è uguale a GB, però il gravi­
                <lb/>
              tativo al gravitativo sta come DB a BG, ovvero EH ad HB
                <emph type="italics"/>
              vel ad EI. </s>
              <s>Sed
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              duetis perpendicularibus EL, EM, triangula EHL, EIM fiunt similia, et
                <lb/>
              propterea, ut EH ad EI, ita EL ad EM, quae sunt sinus recti comple­
                <lb/>
              mentarum angulorum ECB, EDB elevationum ”
                <emph.end type="italics"/>
              (ivi, fol. </s>
              <s>18). </s>
            </p>
            <p type="main">
              <s>Ecco messa così dallo stesso Viviani a partito la dottrina dei moti equi­
                <lb/>
              pollenti, ma quale argomento somministrava per rispondere al Vanni? </s>
              <s>Nuovo
                <lb/>
              era senza dubbio e bello il meccanico teorema che le pressioni si compar­
                <lb/>
              tono sui due piani proporzionalmente ai coseni degli angoli delle elevazioni,
                <lb/>
              ma qual'è la terza linea che rappresenta la pressione totale, proporzional­
                <lb/>
              mente comparabile con le due trovate pressioni parziali? </s>
              <s>Noi sappiamo es­
                <lb/>
              sere quella terza linea la EB, diagonale del parallelogrammo EIBH, ma il
                <lb/>
              Viviani avversava questa dottrina, reputandola falsa, perchè, non essendo
                <lb/>
              l'angolo EIB retto, non potevano i moti per EI e per IB essere eguali a
                <lb/>
              quello fatto per EB, che non è ipotenusa, come EI e IB non sono cateti;
                <lb/>
              nè perciò alla potenza di quella si può dire uguale la somma delle potenze
                <lb/>
              di questi. </s>
              <s>Essendo però così, come Galileo insegnava nel teorema II Dei
                <lb/>
              proietti, ben comprendeva il Viviani che, tutt'altro che confutare, anzi si
                <lb/>
              confermava l'obiezione del Vanni, per cui a risolverla, tentando altra via,
                <lb/>
              disputavasi intanto in Roma intorno al modo di computare i momenti. </s>
              <s>Non
                <lb/>
              vuol di quelle dispute passarsi la nostra Storia, ma prima di dir di loro
                <lb/>
              giova veder quel che se ne pensasse in proposito dai Matematici stranieri. </s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              IV.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Aveva il Vanni stesso mandato il suo
                <emph type="italics"/>
              Specimen
                <emph.end type="italics"/>
              agli eruditi di Lipsia,
                <lb/>
              che lo inserirono ne'loro atti di Novembre dell'anno 1684, con la ri­
                <lb/>
              sposta, nella quale, benchè si affermasse non essere assurdo che i momenti </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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