Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s2409" xml:space="preserve">
              <pb file="0092" n="92" rhead="ARCHIMEDIS"/>
            quia o g ipſius g x eſt dupla. </s>
            <s xml:id="echoid-s2410" xml:space="preserve">Sit p h dupla h t: </s>
            <s xml:id="echoid-s2411" xml:space="preserve">& </s>
            <s xml:id="echoid-s2412" xml:space="preserve">iun-
              <lb/>
            cta h κ ad ω producatur. </s>
            <s xml:id="echoid-s2413" xml:space="preserve">erit totius quidem portionis cen
              <lb/>
            trum grauitatis k; </s>
            <s xml:id="echoid-s2414" xml:space="preserve">partis eius, quæ intra humidum h; </s>
            <s xml:id="echoid-s2415" xml:space="preserve">eius
              <lb/>
            uero, quæ extra humidum in linea κ ω, quod ſit ω. </s>
            <s xml:id="echoid-s2416" xml:space="preserve">Itaque
              <lb/>
            demonſtrabitur
              <lb/>
              <figure xlink:label="fig-0092-01" xlink:href="fig-0092-01a" number="58">
                <image file="0092-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0092-01"/>
              </figure>
            ſimiliter & </s>
            <s xml:id="echoid-s2417" xml:space="preserve">k z ad
              <lb/>
            humidi ſuperſi-
              <lb/>
            ciem perpẽdicu-
              <lb/>
            laris, & </s>
            <s xml:id="echoid-s2418" xml:space="preserve">quæ per
              <lb/>
            puncta h ω æqui-
              <lb/>
            diſtantes ipſi κ z
              <lb/>
            ducuntur. </s>
            <s xml:id="echoid-s2419" xml:space="preserve">quare
              <lb/>
            nõ manebit por
              <lb/>
            tio, ſed inclinabi
              <lb/>
            tur, donec baſis
              <lb/>
            ipſius in uno pũ
              <lb/>
            cto contingat ſu
              <lb/>
            perficiem humi-
              <lb/>
            di: </s>
            <s xml:id="echoid-s2420" xml:space="preserve">atque ita con
              <lb/>
            ſiſtet. </s>
            <s xml:id="echoid-s2421" xml:space="preserve">nam in por
              <lb/>
            tionibus æquali-
              <lb/>
            bus a o q l, a p m l, ductæ erunt ab extremitatibus baſium
              <lb/>
            a q, a m, quæ æquales portiones abſcindunt: </s>
            <s xml:id="echoid-s2422" xml:space="preserve">etenim a o q
              <lb/>
            ipſi a p m, utin ſuperioribus æqualis demonſtrabitur. </s>
            <s xml:id="echoid-s2423" xml:space="preserve">ergo
              <lb/>
              <note position="left" xlink:label="note-0092-01" xlink:href="note-0092-01a" xml:space="preserve">E</note>
            æquales faciunt acutos angulos a q, a m cum diametris ba
              <lb/>
            ſium: </s>
            <s xml:id="echoid-s2424" xml:space="preserve">quòd anguli ad χ & </s>
            <s xml:id="echoid-s2425" xml:space="preserve">n æquales ſint. </s>
            <s xml:id="echoid-s2426" xml:space="preserve">quare ſi ducta
              <lb/>
            h k ad ω producatur, erit totius portionis grauitatis cen-
              <lb/>
            trum k; </s>
            <s xml:id="echoid-s2427" xml:space="preserve">partis eius, quæ in humido h; </s>
            <s xml:id="echoid-s2428" xml:space="preserve">at eius, quæ extra
              <lb/>
            humidum in linea h κ; </s>
            <s xml:id="echoid-s2429" xml:space="preserve">quod ſit ω: </s>
            <s xml:id="echoid-s2430" xml:space="preserve">& </s>
            <s xml:id="echoid-s2431" xml:space="preserve">h k ad humidi ſuper-
              <lb/>
            ficiem perpendicularis. </s>
            <s xml:id="echoid-s2432" xml:space="preserve">per eaſdem igitur rectas lineas,
              <lb/>
            quod quidem in humido eſt, ſurſum, & </s>
            <s xml:id="echoid-s2433" xml:space="preserve">quod extra humi-
              <lb/>
            dum deorſum feretur. </s>
            <s xml:id="echoid-s2434" xml:space="preserve">quare manebit portio, cuius baſis
              <lb/>
            humidi ſuperficiem in uno puncto continget: </s>
            <s xml:id="echoid-s2435" xml:space="preserve">& </s>
            <s xml:id="echoid-s2436" xml:space="preserve">axis cum
              <lb/>
            ipſa angulum faciet æqualem angulo χ. </s>
            <s xml:id="echoid-s2437" xml:space="preserve">Similiter demon-
              <lb/>
              <note position="left" xlink:label="note-0092-02" xlink:href="note-0092-02a" xml:space="preserve">F</note>
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