Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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        <div xml:id="echoid-div226" type="section" level="1" n="75">
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            <s xml:id="echoid-s3694" xml:space="preserve">
              <pb file="0146" n="146" rhead="FED. COMMANDINI"/>
            partes d. </s>
            <s xml:id="echoid-s3695" xml:space="preserve">in pyramide igitur inſcripta erit quædam figura,
              <lb/>
            ex priſinatibus æqualem altitudinem habentibus cóſtans,
              <lb/>
            ad partes e: </s>
            <s xml:id="echoid-s3696" xml:space="preserve">& </s>
            <s xml:id="echoid-s3697" xml:space="preserve">altera circumſcripta ad partes d. </s>
            <s xml:id="echoid-s3698" xml:space="preserve">Sed unum-
              <lb/>
            quodque eorum priſmatum, quæ in figura inſcripta conti-
              <lb/>
            nentur, æquale eſt priſmati, quod ab eodem fit triangulo in
              <lb/>
            figura circumſcripta: </s>
            <s xml:id="echoid-s3699" xml:space="preserve">nam priſma p q priſmati p o eſt æ-
              <lb/>
            quale; </s>
            <s xml:id="echoid-s3700" xml:space="preserve">priſma s t æquale priſmati s r; </s>
            <s xml:id="echoid-s3701" xml:space="preserve">priſma x y priſmati
              <lb/>
            x u; </s>
            <s xml:id="echoid-s3702" xml:space="preserve">priſma η θ priſinati η z; </s>
            <s xml:id="echoid-s3703" xml:space="preserve">priſina μ ν priſmati μ λ; </s>
            <s xml:id="echoid-s3704" xml:space="preserve">priſ-
              <lb/>
            ma ρ σ priſmati ρ π; </s>
            <s xml:id="echoid-s3705" xml:space="preserve">& </s>
            <s xml:id="echoid-s3706" xml:space="preserve">priſma φ χ priſinati φ τ æquale. </s>
            <s xml:id="echoid-s3707" xml:space="preserve">re-
              <lb/>
            linquitur ergo, ut circumſcripta figura exuperet inſcriptã
              <lb/>
            priſmate, quod baſim habet a b c triangulum, & </s>
            <s xml:id="echoid-s3708" xml:space="preserve">axem e f.
              <lb/>
            </s>
            <s xml:id="echoid-s3709" xml:space="preserve">Illud uero minus eſt ſolida magnitudine propoſita. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">Eadȩ
              <lb/>
            ratione inſcribetur, & </s>
            <s xml:id="echoid-s3711" xml:space="preserve">circumſcribetur ſolida figura in py-
              <lb/>
            ramide, quæ quadrilateram, uel plurilaterã baſim habeat.</s>
            <s xml:id="echoid-s3712" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div227" type="section" level="1" n="76">
          <head xml:id="echoid-head83" xml:space="preserve">PROBLEMA II. PROPOSITIO XI.</head>
          <p>
            <s xml:id="echoid-s3713" xml:space="preserve">
              <emph style="sc">Dato</emph>
            cono, fieri poteſt, ut figura ſolida in-
              <lb/>
            ſcribatur, & </s>
            <s xml:id="echoid-s3714" xml:space="preserve">altera circumſcribatur ex cylindris
              <lb/>
            æqualem habentibus altitudinem, ita ut circum-
              <lb/>
            ſcripta ſuperet inſcriptam, magnitudine, quæ ſo-
              <lb/>
            lida magnitudine propoſita ſit minor.</s>
            <s xml:id="echoid-s3715" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3716" xml:space="preserve">SIT conus, cuius axis b d: </s>
            <s xml:id="echoid-s3717" xml:space="preserve">& </s>
            <s xml:id="echoid-s3718" xml:space="preserve">ſecetur plano per axem
              <lb/>
            ducto, ut ſectio ſit triangulum a b c: </s>
            <s xml:id="echoid-s3719" xml:space="preserve">intelligaturq; </s>
            <s xml:id="echoid-s3720" xml:space="preserve">cylin-
              <lb/>
            drus, qui baſim eandem, & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">eundem axem habeat. </s>
            <s xml:id="echoid-s3722" xml:space="preserve">Hoc igi-
              <lb/>
            tur cylindro continenter bifariam ſecto, relinquetur cylin
              <lb/>
            drus minor ſolida magnitudine propoſita. </s>
            <s xml:id="echoid-s3723" xml:space="preserve">Sit autem is cy
              <lb/>
            lindrus, qui baſim habet circulum circa diametrum a c, & </s>
            <s xml:id="echoid-s3724" xml:space="preserve">
              <lb/>
            axem d e. </s>
            <s xml:id="echoid-s3725" xml:space="preserve">Itaque diuidatur b d in partes æquales ipſi d e
              <lb/>
            in punctis f g h _K_lm: </s>
            <s xml:id="echoid-s3726" xml:space="preserve">& </s>
            <s xml:id="echoid-s3727" xml:space="preserve">per ea ducantur plana conum ſe-
              <lb/>
            cantia; </s>
            <s xml:id="echoid-s3728" xml:space="preserve">quæ baſi æquidiſtent. </s>
            <s xml:id="echoid-s3729" xml:space="preserve">erunt ſectiones circuli, cen-
              <lb/>
            tra in axi habentes, ut in primo libro conicorum, </s>
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