Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4436" xml:space="preserve">
              <pb file="0178" n="178" rhead="FED. COMMANDINI"/>
            producantur. </s>
            <s xml:id="echoid-s4437" xml:space="preserve">Quoniam igitur pyramis ſecatur planis bafi
              <lb/>
            æquidiſtantibus, ſectiones ſimiles erunt: </s>
            <s xml:id="echoid-s4438" xml:space="preserve">atque erunt qua-
              <lb/>
              <note position="left" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">9. huius</note>
            drata, uel rectangula circa circulos, uel ellipſes deſcripta,
              <lb/>
            quemadmodum & </s>
            <s xml:id="echoid-s4439" xml:space="preserve">in ipſa baſi. </s>
            <s xml:id="echoid-s4440" xml:space="preserve">Sed cum circuli inter ſe eã
              <lb/>
            proportionem habeant, quam diametrorum quadrata:
              <lb/>
            </s>
            <s xml:id="echoid-s4441" xml:space="preserve">
              <note position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">2. duode-
                <lb/>
              cimi.</note>
            itemq; </s>
            <s xml:id="echoid-s4442" xml:space="preserve">ellipſes eam quam rectangula ex ipſarum diametris
              <lb/>
            conſtantia: </s>
            <s xml:id="echoid-s4443" xml:space="preserve">& </s>
            <s xml:id="echoid-s4444" xml:space="preserve">ſit circulus, uel ellipſis circa diametrum e f
              <lb/>
              <figure xlink:label="fig-0178-01" xlink:href="fig-0178-01a" number="133">
                <image file="0178-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0178-01"/>
              </figure>
              <note position="left" xlink:label="note-0178-03" xlink:href="note-0178-03a" xml:space="preserve">7. de co-
                <lb/>
              noidibus
                <lb/>
              & ſphæ-
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              roidibus</note>
            proportionalis inter circulos, uel ellipſes a b, c d; </s>
            <s xml:id="echoid-s4445" xml:space="preserve">erit re-
              <lb/>
            ctangulum e f etiam inter rectangula a b, c d proportio-
              <lb/>
            nale: </s>
            <s xml:id="echoid-s4446" xml:space="preserve">per rectangulum enim nunc breuitatis cauſa etiã ip-
              <lb/>
            ſum quadratum intelligemus. </s>
            <s xml:id="echoid-s4447" xml:space="preserve">quare ex iis, quæ proxime
              <lb/>
            dicta ſunt, pyramis baſim habens æqualem dictis rectangu
              <lb/>
            lis, & </s>
            <s xml:id="echoid-s4448" xml:space="preserve">altitudinem eandem, quam fruſtum a d, ipſi fruſto à
              <lb/>
            pyramide abſciſſo æqualis probabitur. </s>
            <s xml:id="echoid-s4449" xml:space="preserve">ut autem rectangu
              <lb/>
            lum c d ad rectangulũ e f, ita circulus, uel ellipſis c d a d e f
              <lb/>
            circulum, uel ellipſim: </s>
            <s xml:id="echoid-s4450" xml:space="preserve">componendoq; </s>
            <s xml:id="echoid-s4451" xml:space="preserve">ut rectangula c d,
              <lb/>
            e f, ad e f rectangulum, ita circuli, uel ellipſes e d, e f, ad e f:
              <lb/>
            </s>
            <s xml:id="echoid-s4452" xml:space="preserve">& </s>
            <s xml:id="echoid-s4453" xml:space="preserve">ut rectangulum e f ad rectangulum a b, ita cir culus, uel
              <lb/>
            cllipſis e f ad a b circulum, uel ellipſim. </s>
            <s xml:id="echoid-s4454" xml:space="preserve">ergo ex æquali, & </s>
            <s xml:id="echoid-s4455" xml:space="preserve">
              <lb/>
            componendo, utrectãgula c d, e f, a b ad ipſum a b, ita </s>
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