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

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        <body>
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            <p type="main">
              <s>
                <pb xlink:href="020/01/2701.jpg" pagenum="326"/>
              versionem rationis, duplicando antecedentia, dividendo, et postea facta re­
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              ductione. </s>
              <s>Per constructionem est recta PO ad OM ut sex quadrata BE, cum
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              quadrato EG, ad duplum quadrati FG. Componendo, PM ad OM erit ut sex
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              quadrata BE, cum quadrato EG et duplo quadrati FG, ad duplum quadrati
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              FG. </s>
              <s>Duplicando antecedentia, FM, ad MO, erit ut 12 quadrata BE, cum
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              2EG+4FG, ad 2FG. </s>
              <s>Per conversionem rationis, MF ad FO ut 12BE+
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              2EG+4FG ad 12BE+2EG+2FG. </s>
              <s>Duplicando antecedentia, EF ad
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              FO ut 24BE+4EG+8FG, ad 12BE+2EG+2FG. Dividendo, EO
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              ad OF ut 12BE+2EG+6FG ad 12BE+2EG+2FG. ” </s>
            </p>
            <p type="main">
              <s>“ Sed quoniam rectangulum AGD quadrato BE est aequale, erit diffe­
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              rentia quadratorum AF, BE. </s>
              <s>Ergo potest fieri reductio talis, mutato prius
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              quadrato EG cum quadratis EF, FG. </s>
              <s>Sic EO ad OF est ut 12BE+2EF+
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              8FG, ad 12BE+2EF+4FG. Vel, facta reductione, EO ad OF est ut
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              4BE+2EF+8AF ad 8BE+2EF+4AF. Vel, facta ultima re­
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              ductione, EO ad OF est ut quadratum BC, cum duobus EF duobusque AD,
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              ad 2BC+2EF+uno AD,
                <expan abbr="q.">que</expan>
              e. </s>
              <s>d. </s>
              <s>” (ibid., fol. </s>
              <s>39). </s>
            </p>
            <p type="main">
              <s>Notabile fra tutte le altre passate è questa proposizione, non solo riguar­
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              data in sè stessa, ma nel suo processo dimostrativo, che offre il primo esem­
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              pio, dato dal Torricelli nella Scuola galileiana, per tentar di vincere la ritrosia
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              contro i metodi analitici, ritrovati tanto utili allora dai Matematici francesi. </s>
              <s>
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              Se ne compiacque il Nostro non poco, e annunziando il teorema a Miche­
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              langiolo Ricci, il di 7 Marzo 1642, pochi giorni dopo averlo dimostrato, gli
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              diceva: “ Giacchè V. S. studia Luca Valerio, eccogli una proposizione, che
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              ne abbraccia molte di Luca Valerio. </s>
              <s>Giudichi V. S. chi la porti meglio o egli
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              o io. </s>
              <s>Se sarà un frusto di sfera ABCD (nella preced. </s>
              <s>figura) tagliato co'piani
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              paralleli AD, BC, o passino per il centro sì o no, o l'intraprendano sì o no,
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              e sia l'asse del frusto EF, e centro di gravità O; sarà la retta EO alla retta
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              OF come il quadrato AB, con due quadrati EF, e due quadrati DC, ad un
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              quadrato DC, con due quadrati EF, e due quadrati AB. </s>
              <s>Se V. S. la comu­
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              nica al sig. </s>
              <s>Raffaello (Magiotti) so certo che l'avrà cara, perchè sui libri non
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              la troverà portata a questo modo ” (ivi, T. XL, fol. </s>
              <s>100). </s>
            </p>
            <p type="main">
              <s>Un anno dopo, dando la medesima notizia al Cavalieri si compiaceva di
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              fargli notare che il suo processo era molto più spedito che quello di Luca Va­
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              lerio, “ ed è, soggiungeva, universale, o sia intrapreso il centro o no. </s>
              <s>Insomma
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              a me pare che, per via degli indivisibili, si trovino, oltre le innumerabili e
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              maravigliose di V. P., anco tuttavia delle conclusioni da non sprezzarsi, e
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              che, se io le trovassi in altri, mi parrebbero speciose. </s>
              <s>Come dunque questa
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              dottrina non è da stimarsi? </s>
              <s>Se costoro ammettessero le conclusioni per belle,
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              come credo che bisogni concedere, converrà pur anco approvare le dottrine:
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              ovvero, se lodano le conclusioni e non le dottrine, almeno doveranno mo­
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              strare che ve ne siano delle false, ma credo che dureranno fatica ” (ivi,
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              fol. </s>
              <s>123). </s>
            </p>
            <p type="main">
              <s>Fra i
                <emph type="italics"/>
              Problemi proposti ai Matematici di Francia
                <emph.end type="italics"/>
              era notato anche
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              quello del centro di gravità nel frusto sferico, e, dopo averlo enumerato, sog-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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