Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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