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

Table of figures

< >
< >
page |< < of 3504 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="020/01/2107.jpg" pagenum="350"/>
            <p type="main">
              <s>
                <emph type="center"/>
              III.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>Chi, dalle nuove aure menato, s'asside nella mirabile navicella a cor­
                <lb/>
              rere questo lucido mare aperto da Galileo, s'accorge che una vela, benchè
                <lb/>
              rimanga alquanto più sotto alla maestra, è nondimeno la più frequente nel­
                <lb/>
              l'opera, e in render agile il corso forse la più efficace di tutte le altre. </s>
              <s>È
                <lb/>
              facile agli studiosi della Scienza meccanica, vogliam dire passando al senso
                <lb/>
              proprio dal figurato, accorgersi che, nella massima parte dei teoremi gali­
                <lb/>
              leiani, chi conduce innanzi le dimostrazioni, e più efficacemente le volge alla
                <lb/>
              loro final conclusione, è la legge dei tempi, che si passano dal mobile in
                <lb/>
              percorrer due spazi ugualmente diretti. </s>
              <s>Abbiamo veduto per quali vie lun­
                <lb/>
              ghe e tortuose fosse dovuto passar Galileo, prima di giungere, nella sopra
                <lb/>
              trascritta proposizione VII, a quella conclusione, che ora invece vedeva scen­
                <lb/>
              dere per corollario immediato dal principio dinamico, sentenziosamente da
                <lb/>
              lui stesso formulato in queste parole: “ Momenta velocitatum cadentis ex
                <lb/>
              sublimi sunt inter se ut radices distantiarum peractarum, nempe in subdu­
                <lb/>
              pla ratione illarum ” (MSS. Gal., P. V, T. II, fol. </s>
              <s>164 a tergo). </s>
            </p>
            <p type="main">
              <s>Di qui è che, avendo le velocità la medesima proporzione dei tempi, se
                <lb/>
              cada il mobile da A in B (fig. </s>
              <s>172) o da A in C, per due spazi diversi, ma se­
                <lb/>
              condo la medesima linea AL diretti, avremo T.oAB:T.oAC=√AB:√AC=
                <lb/>
              AB:√AB.AC, che è quel che appunto proponevasi di dimostrar Galileo
                <lb/>
                <figure id="id.020.01.2107.1.jpg" xlink:href="020/01/2107/1.jpg" number="363"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 172.
                <lb/>
              stesso, co'principii statici, nella detta sua VII pro­
                <lb/>
              posizione. </s>
            </p>
            <p type="main">
              <s>Incomincia perciò questo secondo Libro, dietro
                <lb/>
              i principii dinamici riformato, dal dimostrare le pro­
                <lb/>
              prietà generali dei moti accelerati, per derivarne di
                <lb/>
              lì gli opportuni corollari. </s>
              <s>Ma non abbiamo trovate
                <lb/>
              scritte le proposizioni preparate a questo particolare
                <lb/>
              intento di servir come d'introduzione al nuovo trat­
                <lb/>
              tato. </s>
              <s>Forse, tutto in sollecitudine di ridurre intanto
                <lb/>
              alle forme più convenienti il teorema fondamentale
                <lb/>
              dei tempi, nelle oblique ugualmente elevate, propor­
                <lb/>
              zionali agli spazi; non attese Galileo a distendere
                <lb/>
              quelle prime dimostrazioni relative alle libere ca­
                <lb/>
              dute dei gravi, riserbandosi a farlo dopo che, dallo stesso ora detto fonda­
                <lb/>
              mentale, si sarebbe svolta la serie di tutti gli altri teoremi. </s>
              <s>Quando poi, per
                <lb/>
              ridursi sotto gli occhi compiuto il disegno del suo trattato, prese risoluzione
                <lb/>
              di porre a questa serie i primi termini tralasciati, era già venuto il Cava­
                <lb/>
              lieri a proporgli il suo Metodo degli indivisibili, secondo il quale condusse
                <lb/>
              Galileo stesso le proposizioni, che si ricopian dal Manoscritto, per ridurle
                <lb/>
              qui ne'primi ordini di questo secondo Libro, resa la ragione ai Lettori del
                <lb/>
              commesso anacronismo. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum