Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo
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          <pb o="43" file="0097" n="97" rhead="DE I _IS_ QVAE VEH. IN AQVA."/>
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        <div xml:id="echoid-div182" type="section" level="1" n="56">
          <head xml:id="echoid-head61" xml:space="preserve">DEMONSTRATIO QVARTAE PARTIS.</head>
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            <s xml:id="echoid-s2560" xml:space="preserve">HABEAT rurſum portio ad humidum in grauitate
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            proportionem quidem maiorem, quàm quadratum f p ad
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            quadratum b d; </s>
            <s xml:id="echoid-s2561" xml:space="preserve">minorem uero, quàm quadratum x o ad
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            b d quadratum: </s>
            <s xml:id="echoid-s2562" xml:space="preserve">& </s>
            <s xml:id="echoid-s2563" xml:space="preserve">quam proportionem habet portio ad
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            humidum in grauitate, eandem habeat quadratum, quod
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            fit à linea ψ ad quadratum b d. </s>
            <s xml:id="echoid-s2564" xml:space="preserve">erit ψ maior, quàm f p, & </s>
            <s xml:id="echoid-s2565" xml:space="preserve">mi
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            nor, quàm x o. </s>
            <s xml:id="echoid-s2566" xml:space="preserve">aptetur ergo quæ dam rectalinea i u inter
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            portiones a u q l, a x d interiecta, quæ ſit æqualis ψ, & </s>
            <s xml:id="echoid-s2567" xml:space="preserve">ipſi
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            b d æquidiſtans: </s>
            <s xml:id="echoid-s2568" xml:space="preserve">occurratq; </s>
            <s xml:id="echoid-s2569" xml:space="preserve">reliquæ ſectioni in y. </s>
            <s xml:id="echoid-s2570" xml:space="preserve">rurſus
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            u y dupla ipſius y i demonſtrabitur, ſicuti demonſtrata eſt
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            o g ipſius g x dupla. </s>
            <s xml:id="echoid-s2571" xml:space="preserve">ducatur autem ab u linea u ο, quæ ſe
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            ctionem a u q l in u contingat: </s>
            <s xml:id="echoid-s2572" xml:space="preserve">& </s>
            <s xml:id="echoid-s2573" xml:space="preserve">iuncta a i ad q produca
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            tur. </s>
            <s xml:id="echoid-s2574" xml:space="preserve">eodem modo oſtendemus lineam a i ipſi i q æqualem
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            eſſe: </s>
            <s xml:id="echoid-s2575" xml:space="preserve">& </s>
            <s xml:id="echoid-s2576" xml:space="preserve">a q ipſi
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              <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a" number="63">
                <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0097-01"/>
              </figure>
            u ω æquidiſtan-
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            tem. </s>
            <s xml:id="echoid-s2577" xml:space="preserve">Demon-
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            ſtrãdum eſt por
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            tionem in humi
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            dum demiſſam,
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            ĩclinatãq; </s>
            <s xml:id="echoid-s2578" xml:space="preserve">adeo,
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            ut baſis ipſius
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            non contingat
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            humidũ, ita con
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            ſiſtere, ut baſis
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            in humidũ ma-
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            gis demergatur
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            quam ut in uno
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            puncto eius ſu-
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            perficiem cõtin
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            gat. </s>
            <s xml:id="echoid-s2579" xml:space="preserve">Demittatur enim in humidum, ut dictum eſt; </s>
            <s xml:id="echoid-s2580" xml:space="preserve">& </s>
            <s xml:id="echoid-s2581" xml:space="preserve">iaceat
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            primo ſic inclinata, ut baſis nullo modo contingat ſuperfi-
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            ciem humidi. </s>
            <s xml:id="echoid-s2582" xml:space="preserve">ſecta autem ipſa plano per axem ad </s>
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