Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <p>
            <s xml:id="echoid-s4353" xml:space="preserve">
              <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:id="echoid-s4354" xml:space="preserve">Dico ſectionem a b
              <lb/>
            ad ſectionem f g eandem proportionem habere, quam f g
              <lb/>
            ad ipſam c d. </s>
            <s xml:id="echoid-s4355" xml:space="preserve">Simili enim ratione, qua ſupra, demonſtrabi-
              <lb/>
            tur quadratum a b ad quadratum f g ita eſſe, ut quadratũ
              <lb/>
            f g ad c d quadratum. </s>
            <s xml:id="echoid-s4356" xml:space="preserve">Sed circuli inter ſe eandem propor-
              <lb/>
              <note position="left" xlink:label="note-0174-01" xlink:href="note-0174-01a" xml:space="preserve">2. duode
                <lb/>
              cimi</note>
            tionem habent, quam diametrorum quadrata. </s>
            <s xml:id="echoid-s4357" xml:space="preserve">ellipſes au-
              <lb/>
            tem circa a b, f g, c d, quæ ſimiles ſunt, ut oſten dimus in cõ-
              <lb/>
            mentariis in principium libri Archimedis de conoidibus,
              <lb/>
            & </s>
            <s xml:id="echoid-s4358" xml:space="preserve">ſphæroidibus, eam habẽt proportionem, quam quadrar
              <lb/>
            ta diametrorum, quæ eiuſdem rationis ſunt, ex corollaio-
              <lb/>
            ſeptimæ propoſitionis eiuſdem li-
              <lb/>
              <figure xlink:label="fig-0174-01" xlink:href="fig-0174-01a" number="128">
                <image file="0174-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0174-01"/>
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            bri. </s>
            <s xml:id="echoid-s4359" xml:space="preserve">ellipſes enim nunc appello ip-
              <lb/>
            ſa ſpacia ellipſibus contenta. </s>
            <s xml:id="echoid-s4360" xml:space="preserve">ergo
              <lb/>
            circulus, uel ellipſis a b ad circulũ,
              <lb/>
            uel ellipſim f g eam proportionem
              <lb/>
            habet, quam circulus, uel ellipſis
              <lb/>
            f g ad circulum uel ellipſim c d.
              <lb/>
            </s>
            <s xml:id="echoid-s4361" xml:space="preserve">quod quidem facienduni propo-
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            ſuimus.</s>
            <s xml:id="echoid-s4362" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div263" type="section" level="1" n="90">
          <head xml:id="echoid-head97" xml:space="preserve">THEOREMA XX. PROPOSITIO XXV.</head>
          <p>
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              <emph style="sc">Qvodlibet</emph>
            fruſtum pyramidis, uel coni,
              <lb/>
            uel coni portionis ad pyramidem, uel conum, uel
              <lb/>
            coni portionem, cuius baſis eadem eſt, & </s>
            <s xml:id="echoid-s4364" xml:space="preserve">æqualis
              <lb/>
            altitudo, eandem proportionẽ habet, quam utræ
              <lb/>
            que baſes, maior, & </s>
            <s xml:id="echoid-s4365" xml:space="preserve">minor ſimul ſumptæ vnà cũ
              <lb/>
            ea, quæ inter ipſas ſit proportionalis, ad baſim ma
              <lb/>
            iorem.</s>
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