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

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="020/01/2722.jpg" pagenum="347"/>
                <foreign lang="grc">π</foreign>
              AE.EF; dunque
                <emph type="italics"/>
              lunula integra est aequalis armillae unius rectanguli
                <lb/>
              AEF,
                <emph.end type="italics"/>
              come l'Autore dianzi diceva. </s>
            </p>
            <p type="main">
              <s>Chiamato C il circolo dal diametro FD, ed L al solito la lunula,
                <lb/>
              avremo dunque L:C=AE.EF:DE2. </s>
              <s>Dividendo, sarà L—C:C=
                <lb/>
              AE.EF—DE2:DE2=AE.ED—DE2:DE2=ED(AE—DE):DE2=
                <lb/>
              ED.DA:DE2. </s>
              <s>Chiamisi ora C′ un altro circulo qualunque, di raggio OS:
                <lb/>
              avremo C′:C=OS2:DE2, e di qui L—C:C′=ED.DA:CB2, e sostituito
                <lb/>
              DE=DF/2, L—C:C′=FD.DA/2:OS2. </s>
              <s>Ma L—C rappresenta la lunula
                <lb/>
              perforata dal circolo DF, e C′ il circolo assunto, dunque si conferma di qui
                <lb/>
              la verità del lemma torricelliano. </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Lemma II.
                <emph.end type="italics"/>
              — Perforatae lunulae, quales ante dicebamus, sunt inter
                <lb/>
              se ut rectangula sub diametris demptorum circulorum contenta. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Esto etc.: erit
                <lb/>
                <figure id="id.020.01.2722.1.jpg" xlink:href="020/01/2722/1.jpg" number="720"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 215.
                <lb/>
              ergo lunula perforata
                <lb/>
              AMP (fig. </s>
              <s>215), ad cir­
                <lb/>
              culum FH, ut rectan­
                <lb/>
              gulum ABC ad qua­
                <lb/>
              dratum FI. </s>
              <s>Sed circu­
                <lb/>
              lus FH, ad lunulam
                <lb/>
              perforatam EOR, est ut
                <lb/>
              quadratum FI ad re­
                <lb/>
              ctangulum EFI; ergo
                <lb/>
              ex aequo lunula perfo­
                <lb/>
              rata AMP, ad lunulam perforatam EOR, est ut rectangulum ABC ad rectan­
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              gulum EFI, sive, sumptis duplis, ut rectangulum ABD ad rectangulum EFH ”
                <lb/>
              (ibid.). </s>
            </p>
            <p type="main">
              <s>Premessi i quali due lemmi, passa il Torricelli a dimostrare, in una sua
                <lb/>
              prima proposizione, che, tolti dal frusto conico i due coni designati dal Ricci,
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              quel che riman del solido uguaglia una sferoide, la quale dimostra, in un'al­
                <lb/>
                <figure id="id.020.01.2722.2.jpg" xlink:href="020/01/2722/2.jpg" number="721"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 216.
                <lb/>
              tra proposizione, risolversi in quel terzo
                <lb/>
              cono, dallo stesso Ricci designato per me­
                <lb/>
              dio proporzionale tra gli altri due. </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Proposizione prima.
                <emph.end type="italics"/>
              — “ Si a seg­
                <lb/>
              mento conico demantur duo coni, aeque
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              alti cum segmento, et super utraque ipsius
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              basi constituti, reliquum solidum erit ae­
                <lb/>
              quale sphaeroidi cuidam, eamdem cum
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              segmento conico altitudinem habenti. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Esto segmentum coni ABCD (fig. </s>
              <s>216), cuius axis EF, et ab ipso de­
                <lb/>
              mantur duo coni ABD, BDC, etc. </s>
              <s>Ponatur quadratum PH duplum quadrati
                <lb/>
              GH, et per PO intelligatur planum oppositis basibus parallelum: eritque lu­
                <lb/>
              nula perforata PO, demptis circulis PH, HO, aequalis circulo, cuius radius
                <lb/>
              GH, ob constructionem, et ex demonstratis ” (ibid., fol. </s>
              <s>48). </s>
            </p>
          </chap>
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