Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
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              <pb file="0174" n="174" rhead="FED. COMMANDINI"/>
            per f planum baſibus æquidiſtans ducatur, ut ſit ſectio cir
              <lb/>
            culus, uel ellipſis circa diametrum f g. </s>
            <s xml:space="preserve">Dico ſectionem a b
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            ad ſectionem f g eandem proportionem habere, quam f g
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            ad ipſam c d. </s>
            <s xml:space="preserve">Simili enim ratione, qua ſupra, demonſtrabi-
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            tur quadratum a b ad quadratum f g ita eſſe, ut quadratũ
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            f g ad c d quadratum. </s>
            <s xml:space="preserve">Sed circuli inter ſe eandem propor-
              <lb/>
              <anchor type="note" xlink:label="note-0174-01a" xlink:href="note-0174-01"/>
            tionem habent, quam diametrorum quadrata. </s>
            <s xml:space="preserve">ellipſes au-
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            tem circa a b, f g, c d, quæ ſimiles ſunt, ut oſten dimus in cõ-
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            mentariis in principium libri Archimedis de conoidibus,
              <lb/>
            & </s>
            <s xml:space="preserve">ſphæroidibus, eam habẽt proportionem, quam quadrar
              <lb/>
            ta diametrorum, quæ eiuſdem rationis ſunt, ex corollaio-
              <lb/>
            ſeptimæ propoſitionis eiuſdem li-
              <lb/>
              <anchor type="figure" xlink:label="fig-0174-01a" xlink:href="fig-0174-01"/>
            bri. </s>
            <s xml:space="preserve">ellipſes enim nunc appello ip-
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            ſa ſpacia ellipſibus contenta. </s>
            <s xml:space="preserve">ergo
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            circulus, uel ellipſis a b ad circulũ,
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            uel ellipſim f g eam proportionem
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            habet, quam circulus, uel ellipſis
              <lb/>
            f g ad circulum uel ellipſim c d.
              <lb/>
            </s>
            <s xml:space="preserve">quod quidem facienduni propo-
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            ſuimus.</s>
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          </p>
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            <note position="left" xlink:label="note-0174-01" xlink:href="note-0174-01a" xml:space="preserve">2. duode
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            cimi</note>
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              <image file="0174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0174-01"/>
            </figure>
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        <div type="section" level="1" n="90">
          <head xml:space="preserve">THEOREMA XX. PROPOSITIO XXV.</head>
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              <emph style="sc">Qvodlibet</emph>
            fruſtum pyramidis, uel coni,
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            uel coni portionis ad pyramidem, uel conum, uel
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            coni portionem, cuius baſis eadem eſt, & </s>
            <s xml:space="preserve">æqualis
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            altitudo, eandem proportionẽ habet, quam utræ
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            que baſes, maior, & </s>
            <s xml:space="preserve">minor ſimul ſumptæ vnà cũ
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            ea, quæ inter ipſas ſit proportionalis, ad baſim ma
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            iorem.</s>
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Impressum