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

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            <p type="main">
              <s>
                <pb xlink:href="020/01/2707.jpg" pagenum="332"/>
              ubicumque. </s>
              <s>Eritque, per praecedens lemma, ellipsis HBL, ad circulum HDL,
                <lb/>
                <figure id="id.020.01.2707.1.jpg" xlink:href="020/01/2707/1.jpg" number="698"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 193.
                <lb/>
              ut BE ad ED. </s>
              <s>Sed etiam ellipsis MFN est
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              ad circulum MIN ut FG ad GI, sive ut BE
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              ad ED, et sic semper. </s>
              <s>Propterea erunt
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              omnes simul antecedentes, ad omnes con­
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              sequentes simul, ut una ad unum, nempe
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              ut ellipsis HBL ad circulum HDL, sive ut
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              axis BE ad axem ED ” (ibid., fol. </s>
              <s>173). </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Lemma III.
                <emph.end type="italics"/>
              — Sphaeroides inter
                <lb/>
              se sunt ut solida parallelepipeda, quorum
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              bases sunt quadrata diametrorum, altitu­
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              dines vero longitudines axium. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>“ Sint sphaeroides ABC, DEF (fig. </s>
              <s>194)
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              quarum axes BG, EH, diametri vero AC,
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              DF. </s>
              <s>Dico sphaeroidem ABC, ad sphaeroidem
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                <figure id="id.020.01.2707.2.jpg" xlink:href="020/01/2707/2.jpg" number="699"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 194.
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              DEF, esse ut solidum parallelepipedum, basi
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              quadrato AC, altitudine vero BG, ad solidum
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              parallelepipedum, basi quadrato DF, altitudine
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              vero EH. </s>
              <s>Concipiatur enim, in utraque sphae­
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              roide, sphaera aequalis diametri AIC, DOF. </s>
              <s>Erit­
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              que sphaerois ABC, ad sphaeram AIC, ut recta
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              BG ad GI, per praecedens, sive, ut solidum
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              basiquadrato GI, altitudine BG, ad cubum GI. </s>
              <s>Sphaera vero AIC, ad sphae­
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              ram DOF, est ut cubus GI ad cubum HO, et denique sphaera DOF, ad
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              sphaeroidem DEF, est ut cubus HO ad solidum parallelepipedum, basi qua­
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              drato HO, altitudine vero HE. </s>
              <s>Ergo ex aequo patet propositum. </s>
              <s>Sumptis
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              vero quadruplis, erit sphaerois ABC ad DEF ut solidum basi quadrato AC,
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              altitudine BG, ad solidnm basiquadrato DF. altitudine EH,
                <expan abbr="q.">que</expan>
              e. </s>
              <s>d. </s>
              <s>” (ibid.,
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              fol. </s>
              <s>174). </s>
            </p>
            <p type="main">
              <s>Con l'aiuto de'quali tre lemmi passa il Torricelli finalmente a dimo­
                <lb/>
                <figure id="id.020.01.2707.3.jpg" xlink:href="020/01/2707/3.jpg" number="700"/>
              </s>
            </p>
            <p type="caption">
              <s>Figura 195.
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              strar la proposizione, che dice:
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              Hemisphaerium, sive
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              hemisphaeroides dupla est coni inscripti.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Esto hemisphaerum sive hemisphaeroides ABC
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              (fig. </s>
              <s>195), cuius axis BD, et applicata ex puncto E
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              medio axis sit FEH, conus inscriptus ABC. </s>
              <s>Jam osten­
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              dimus solidum reliquum, dempto cono ABC, aequale
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              esse sphaeroidi cuidam, cuius axis sit BD, maximus
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              vero circulus sit aequalis armillae FG, nempe cuius
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              radius I medius sit inter FG, GH. ” </s>
            </p>
            <p type="main">
              <s>“ Jam ratio sphaeroidis ABCO, ad sphaeroidem
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              cuius radius est I, axis vero BD, est, per praecedens lemma, ut solidum ba­
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              siquadrato I, altitudine BE. </s>
              <s>Ergo rationem habet compositam ex ratione
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              quadrati AD, ad quadratum I, sive ad rectangulum FGH, nempe ut 4 ad 2,
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              et ex ratione altitudinis DB ad BE, nempe 2 ad 1. Ergo sphaerois ABCO, </s>
            </p>
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