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

Table of figures

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="020/01/2754.jpg" pagenum="379"/>
              ovvero IL, poichè, se il peso è come EC, ovvero EI, sarà in EI come IL,
                <lb/>
              e però la forza IL lo agguaglierà. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Corollario I.
                <emph.end type="italics"/>
              — Di qui si ricava che le strade più oblique dei monti
                <lb/>
              sono tanto più agevoli, quanto la IL è minore della CD, ovvero la IM della
                <lb/>
              CE, essendo simili CED, IML. ” </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Corollario II.
                <emph.end type="italics"/>
              — Però, quando l'angolo IEB sarà gradi 30, allora la
                <lb/>
              salita per EI sarà la metà più agevole, che per EC, essendo il sino IM di
                <lb/>
              gradi 30 la metà del sino toto EC: ovvero inferisci che la fatica della salita
                <lb/>
              sarà come i sini degli angoli, che farà la strada con la orizontale. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Corollario III.
                <emph.end type="italics"/>
              — I pesi dei corpi nostri, e delle cose che porteremo,
                <lb/>
              saranno per le strade EC, EI come CD, IL, ovvero, come CE, IM, che sono
                <lb/>
              i sini suddetti ” (ivi, T. XXXIII, fol. </s>
              <s>87). </s>
            </p>
            <p type="main">
              <s>Questa proposizione la dicemmo semplicemente illustrativa del Teorema
                <lb/>
              meccanico, la dimostrativa del quale è la prima del trattato stampato, la
                <lb/>
              quale si conduce dal celebre principio che due pesi stanno allora fra loro in
                <lb/>
              equilibrio, quando congiunti insieme, a rimoverli dalla loro prima stazione,
                <lb/>
              il centro di gravità rimane sulla medesima linea orizontale. </s>
              <s>Condizioni di un
                <lb/>
              tale equilibrio si dimostra esser che i pesi abbiano omologa proporzione con
                <lb/>
              le lunghezze dei piani inclinati: che, se varia l'inclinazione, i pesi stessi ne­
                <lb/>
              cessariamente si muovono, e il Torricelli investiga così qual via si farebbe
                <lb/>
              dal comun centro di gravità nel moto. </s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE IV. —
                <emph type="italics"/>
              Si plana AB, BC
                <emph.end type="italics"/>
              (fig. </s>
              <s>239)
                <emph type="italics"/>
              fuerint utcumque
                <lb/>
              inclinata, et gravia A, C aequalia, aequaliterque a puncto B remota; erit
                <lb/>
              AC via centri gravitatis. </s>
              <s>”
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Venerint enim in D et E, et erunt aequales AD, CE: dico centrum
                <lb/>
              esse F. </s>
              <s>Agatur EH parallela ipsi BD: erit, ut CB ad BA, ita CE ad EH,
                <lb/>
                <figure id="id.020.01.2754.1.jpg" xlink:href="020/01/2754/1.jpg" number="744"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 239.
                <lb/>
              vel DA ad EH. Sed, cum CB, BA sint aequales, erunt
                <lb/>
              DA, EH aequales, et erunt parallelae. </s>
              <s>Quare EF, FD
                <lb/>
              aequales erunt. </s>
              <s>Ergo etc. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Scholium.
                <emph.end type="italics"/>
              — Quando vero gravia non sint ae­
                <lb/>
              qualia, aptentur gravia ita, ut sit ut grave A ad grave
                <lb/>
              C, ita AB ad BC, et erit iterum AC via centri. </s>
              <s>Mo­
                <lb/>
              veantur usque in D et E: eruntque DA, CE aequales. </s>
              <s>
                <lb/>
              At grave A, ad grave C, est ut AB ad BC, vel HE
                <lb/>
              ad EC, vel HE ad AD, vel FE ad FD reciproce; est
                <lb/>
              ergo F centrum ” (ivi, T, XXXVII, fol. </s>
              <s>72). </s>
            </p>
            <p type="main">
              <s>Vedremo, nel seguente trattato
                <emph type="italics"/>
              De momentis,
                <emph.end type="italics"/>
              an­
                <lb/>
              che più spiegatamente condotta questa proposizione, che
                <lb/>
              sarà premessa per lemma ad altre proposizioni, ma per ora, proseguendo il
                <lb/>
              divisato ordine nostro, raccoglieremo le poche cose seguenti, relative alle pro­
                <lb/>
              porzioni che passano tra le velocità e i tempi de'mobili nei piani inclinati,
                <lb/>
              quasi fragrante mazzolino di fiori, di che la Meccanica severa non sdegnerà
                <lb/>
              ornarsene il seno. </s>
            </p>
            <p type="main">
              <s>“ PROPOSIZIONE V. —
                <emph type="italics"/>
              Si duo circuli se se in infimo puncto tangant,
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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