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

Table of figures

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            <p type="caption">
              <s>
                <pb xlink:href="020/01/2763.jpg" pagenum="388"/>
                <emph type="italics"/>
              Ergo,
                <emph.end type="italics"/>
              dice il Torricelli,
                <emph type="italics"/>
              ut totum locum ad totum,
                <emph.end type="italics"/>
              cioè
                <emph type="italics"/>
              ut totum OB ad
                <lb/>
              totum BP, ita dimidium EB ad dimidium BH, vel EI ad IH, vel HL
                <lb/>
              ad LE reciproce. </s>
              <s>Ergo L centrum gravitatis est loci ”
                <emph.end type="italics"/>
              (ibid., fol 115). </s>
            </p>
            <p type="main">
              <s>Queste cose premesse e dimostrate, vuole il Torricelli che le condizioni
                <lb/>
              dell'equilibrio della catena, parte disposta sul piano comunqu e inclinato MB,
                <lb/>
              e parte sul piano BN, siano quelle medesime, che se si tenesse sospesa per
                <lb/>
              i punti estremi A, e C liberamente pendula. </s>
              <s>La supposizione fatta dal Disce­
                <lb/>
              polo è senza dubbio non meno arbitraria di quell'altra fatta dal Maestro, ma
                <lb/>
              è certo che, come dal concedersi a Galileo che gli anelli sian discesi nella
                <lb/>
              catena insaccata, secondo la ragion de'momenti, che avrebbe ciascuno di essi
                <lb/>
              in romper l'asta, nella quale si supponessero orizontalmente infilati, resta
                <lb/>
              legittimamente dimostrato che quella tal saccaia è in figura di parabola; così,
                <lb/>
              dal concedere al Torricelli quella sua ipotesi già detta, si vien pur legittima­
                <lb/>
                <figure id="id.020.01.2763.1.jpg" xlink:href="020/01/2763/1.jpg" number="757"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 252.
                <lb/>
              mente alla medesima conclusione, premesso il
                <lb/>
              seguente
                <emph type="italics"/>
              Lemma,
                <emph.end type="italics"/>
              relativo alle proprietà di
                <lb/>
              certe linee, con premeditata intenzione tirate
                <lb/>
              intorno, e dentro alla Parabola. </s>
            </p>
            <p type="main">
              <s>“ Sia la parabola ABC (fig. </s>
              <s>252), il cui
                <lb/>
              asse BH, ed ordinatamente applicata AC, e,
                <lb/>
              presa BD uguale a BH, tirinsi AD, CD, che
                <lb/>
              saranno tangenti. </s>
              <s>Preso poi qualunque punto
                <lb/>
              E, tirisi l'altra tangente FEG; dimostreremo
                <lb/>
              più cose: ” </s>
            </p>
            <p type="main">
              <s>“ Per i punti F, E, G tirinsi parallele
                <lb/>
              all'asse FM, NP, IL, e si prolunghi AD, che
                <lb/>
              concorra con LG in I, e si tiri AP parallela
                <lb/>
              a FE. </s>
              <s>Perchè si è preso nella parabola un punto E, e la EP parallela al­
                <lb/>
              l'asse, e la AP parallela alla tangente FE, e la AF tangente in A; saranno
                <lb/>
              uguali PE, EN, e però saranno uguali AF, FN fra le stesse parallele. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Perchè poi l'angolo ADC è diviso bifariam dalla HD, e la GI paral­
                <lb/>
              lela alla HD, saranno uguali GD, DI. ” </s>
            </p>
            <p type="main">
              <s>“ Perchè CG ad AF ha proporzione subdupla di GL a FM, sarà, come
                <lb/>
              CG ad AF, così GE ad EF, ovvero IN ad NF. </s>
              <s>Ma perchè i conseguenti AF,
                <lb/>
              NF sono uguali, saranno uguali gli antecedenti CG, NI. </s>
              <s>Ed aggiunta la co­
                <lb/>
              mune DG sarà CD, ovvero AD, uguale alle NI, DG. </s>
              <s>E levata la comune ND,
                <lb/>
              sarà AN uguale alle ID, DG, e però la metà AF uguale alla metà DG. ”
                <lb/>
                <figure id="id.020.01.2763.2.jpg" xlink:href="020/01/2763/2.jpg" number="758"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 253.</s>
            </p>
            <p type="main">
              <s>“ Stante questo, dico che anco FE sarà uguale
                <lb/>
              ad OG. S'è mostrato che GE a EF sta come CG
                <lb/>
              ad AF, ovvero come FD a DG, ovvero FO ad OG,
                <lb/>
                <emph type="italics"/>
              ob angulum D bifariam sectum.
                <emph.end type="italics"/>
              Come dunque GE
                <lb/>
              ad EF, così FO ad OG. </s>
              <s>E componendo, GF ad FE,
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              come FG a GO, e così sono uguali FE, GO. ” </s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE XV. —
                <emph type="italics"/>
              Siano i due centri
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              primarii A, B
                <emph.end type="italics"/>
              (fig. </s>
              <s>253)
                <emph type="italics"/>
              e sia mossa la catena,
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
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