Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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page |< < (43) of 213 > >|
DE I _IS_ QVAE VEH. IN AQVA.
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        <div type="section" level="1" n="55">
          <pb o="43" file="0097" n="97" rhead="DE I _IS_ QVAE VEH. IN AQVA."/>
        </div>
        <div type="section" level="1" n="56">
          <head xml:space="preserve">DEMONSTRATIO QVARTAE PARTIS.</head>
          <p>
            <s xml:space="preserve">HABEAT rurſum portio ad humidum in grauitate
              <lb/>
            proportionem quidem maiorem, quàm quadratum f p ad
              <lb/>
            quadratum b d; </s>
            <s xml:space="preserve">minorem uero, quàm quadratum x o ad
              <lb/>
            b d quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet portio ad
              <lb/>
            humidum in grauitate, eandem habeat quadratum, quod
              <lb/>
            fit à linea ψ ad quadratum b d. </s>
            <s xml:space="preserve">erit ψ maior, quàm f p, & </s>
            <s xml:space="preserve">mi
              <lb/>
            nor, quàm x o. </s>
            <s xml:space="preserve">aptetur ergo quæ dam rectalinea i u inter
              <lb/>
            portiones a u q l, a x d interiecta, quæ ſit æqualis ψ, & </s>
            <s xml:space="preserve">ipſi
              <lb/>
            b d æquidiſtans: </s>
            <s xml:space="preserve">occurratq; </s>
            <s xml:space="preserve">reliquæ ſectioni in y. </s>
            <s xml:space="preserve">rurſus
              <lb/>
            u y dupla ipſius y i demonſtrabitur, ſicuti demonſtrata eſt
              <lb/>
            o g ipſius g x dupla. </s>
            <s xml:space="preserve">ducatur autem ab u linea u ο, quæ ſe
              <lb/>
            ctionem a u q l in u contingat: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a i ad q produca
              <lb/>
            tur. </s>
            <s xml:space="preserve">eodem modo oſtendemus lineam a i ipſi i q æqualem
              <lb/>
            eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q ipſi
              <lb/>
              <anchor type="figure" xlink:label="fig-0097-01a" xlink:href="fig-0097-01"/>
            u ω æquidiſtan-
              <lb/>
            tem. </s>
            <s xml:space="preserve">Demon-
              <lb/>
            ſtrãdum eſt por
              <lb/>
            tionem in humi
              <lb/>
            dum demiſſam,
              <lb/>
            ĩclinatãq; </s>
            <s xml:space="preserve">adeo,
              <lb/>
            ut baſis ipſius
              <lb/>
            non contingat
              <lb/>
            humidũ, ita con
              <lb/>
            ſiſtere, ut baſis
              <lb/>
            in humidũ ma-
              <lb/>
            gis demergatur
              <lb/>
            quam ut in uno
              <lb/>
            puncto eius ſu-
              <lb/>
            perficiem cõtin
              <lb/>
            gat. </s>
            <s xml:space="preserve">Demittatur enim in humidum, ut dictum eſt; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iaceat
              <lb/>
            primo ſic inclinata, ut baſis nullo modo contingat ſuperfi-
              <lb/>
            ciem humidi. </s>
            <s xml:space="preserve">ſecta autem ipſa plano per axem ad humidi</s>
          </p>
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