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

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              <s>
                <pb xlink:href="020/01/2873.jpg" pagenum="498"/>
              quadrato AC revoluto circa AD, ad rotundum a trilineo ABCF circa AD, est,
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              ex eadem Centrobaryca, in ratione composita quadrati AC ad trilineum ABCF,
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              hoc est in ratione 14 ad 3 proxime, vel 42 ad 9, et ex ratione distantiae IK
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              ad distantiam GL eorum centrorum gravitatis I, G ab axe AD. </s>
              <s>Sed cylin­
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              drus ad rotundum est ut 3 ad 1, vel ut 42 ad 14; ergo 42 ad 14 rationem
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              habet compositam ex ratione 42 ad 9, et ex ratione earumdem distantiarum
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              IK, GL. </s>
              <s>Sed 42 ad 14 habet queque rationem compositam ex 42 ad 9, et
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              ex 9 ad 14, et ex his prima ratio est ea, quae inter quadratum et trilineum;
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              ergo secunda ratio inter 9 et 14 erit ratio distantiarum IK, GL. </s>
              <s>Sed IK in­
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              venta est partium 9, qualium DB erit 18; ergo GL est earumdem 14. Sed
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              IK ad GL est ut DI ad DG, ergo etiam DI ad DG est ut 9 ad 14. Sed DI
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              inventa est earumdem partium 12+51/70, si fiat ergo ut 9 ad 14, ita 12+51/70
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              ad aliam, quae est 19+4/5 totidem partium, erit ipsa DG, ad quam radius
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              DB erit ut 18 ad 19+4/5, vel ut 90 ad 99, vel ut 10 ad 11, quod erat se­
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              cundo ostendendum ” (ibid., fol. </s>
              <s>18). </s>
            </p>
            <p type="main">
              <s>“ PROPOSITIO V. —
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              Centrum gravitatis G, in eadem figura, trilinei
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              ABCF sic dividit rectam FD iungentem eius verticem F, et centrum D
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              sui arcus ABC, ut tota FD ad DG sit quam proxime ut 9 ad 7. — In­
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              super ipsum centrum gravitatis G trilinei AGCF sic dividit eius axem
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              FD, ut pars FG ad F, ad partem GB ad B, sit quam proxime ut 22
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              ad 7, vel ut circuli periferia ad diametrum. </s>
              <s>”
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>“ Et primo, cum sit IK 9 et GL 14, sitque DI 12+51/70, cumque ut
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              IK ad GL ita sit DI ad DG; erit DG 19+28/35. Sed tota DF est 25+16/35,
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              ergo DF ad DG erit ut 25+16/35 ad 19+28/35, vel ut 891 ad 693, vel ut
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              99 ad 77, vel ut 9 ad 7. Et convertendo, DG, ad DF ut 7 ad 9, quocirca
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              centrum gravitatis trilinei ABCF distat a centro D sui ipsius per distantiam
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              DG, ad quam tota diameter FD quadrati circumscripti proprio quadranti sit
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              quam proxime ut 9 ad 7. ” </s>
            </p>
            <p type="main">
              <s>“ Secundo, cumque DB ad DG sit quam proxime ut 10 ad 11, et DG
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              ad DF, ex nuper ostensis, quam proxime ut 7 ad 9, vel ut 11 ad 14+1/7;
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              tres DB, DG, DF erunt ut 10, 11, 14+1/7, vel ut 70, 77, 99. Quare ipsa­
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              rum differentiae BG, GF erunt ut hi numeri 7, 22, adeoque centrum gra­
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              vitatis G trilinei ABCF secat sic eius axem FB, ut pars ad F, ad partem
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              ad B, sit quam proxime ut 22 ad 7, vel ut circuli periferia ad suam dia­
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              metrum. </s>
              <s>” </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              “ Scholium.
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              — Propterea cum qualium partium DB ponitur 10, ta­
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              lium DE sit quam proxime 6, et DI 7+1/14, et DB 10, et DG 11, et DF
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              14+2/14; ipsae DE, DI, DB, DG, DF erunt ut hi numeri 84, 99, 140,
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              154, 198. Et, cum DE, DB, DG sint ut 84, 140, 154, in minimis terminis
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              essent ut 6, 10, 11 ” (ibid., fol. </s>
              <s>19). </s>
            </p>
            <p type="main">
              <s>Termineremo questo breve ordine di proposizioni baricentriche con una
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              relativa alla Cicloide, e che senza dubbio è posteriore al trattato wallisiano
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                <emph type="italics"/>
              De centro gravitatis,
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              supponendovisi la rettificazion della curva, pubblicata
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              quivi dal Matematico inglese nella seconda parte della proposizione XXII, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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