Archimedes, Archimedis De insidentibvs aqvae

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              <pb file="0028" n="28" rhead="DE INSIDENTIBVS AQV AE"/>
            rectanguli coni quæ quidem K, h, æquediſtanter ipſi a, l, quo autem p, i,
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            æquediſtanter dy imetro ſecta ipſa K, ***. </s>
            <s xml:id="echoid-s392" xml:space="preserve">Quæ autem a s, æquediſtanter
              <lb/>
            contingenti ſecundum p. </s>
            <s xml:id="echoid-s393" xml:space="preserve">neceſſarium eſt ipſam p, i, autem
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            eandem proportionem habere ad p, h, quam habet quæ n, ***, ad ***, o,
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            maiorem proportionem demonſtratum eſt enim hoc perſumpta. </s>
            <s xml:id="echoid-s394" xml:space="preserve">Quæ au
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            tem ***, h, _est_ æmyolia ipſius ***, o, & </s>
            <s xml:id="echoid-s395" xml:space="preserve">quæ i, h. </s>
            <s xml:id="echoid-s396" xml:space="preserve">Ergo aut æmyolia eſt ip-
              <lb/>
            ſius h, p, aut maior quàm æmyolia quæ ergo p, h, ipſius h, i, aut dupla _est_,
              <lb/>
            aut minor quàm dupla. </s>
            <s xml:id="echoid-s397" xml:space="preserve">Sit autem quæ p, t, ipſius t, i, dupla. </s>
            <s xml:id="echoid-s398" xml:space="preserve">Centrum er
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            go grauitatis eius quod in humido _est_ ſignum t, & </s>
            <s xml:id="echoid-s399" xml:space="preserve">copulata quæ t, f, edu
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            catur, & </s>
            <s xml:id="echoid-s400" xml:space="preserve">ſit centrum grauitatis eius quòd extra humidum g, & </s>
            <s xml:id="echoid-s401" xml:space="preserve">a, b, ip
              <lb/>
            ſi n, o, recta quę b, r. </s>
            <s xml:id="echoid-s402" xml:space="preserve">Quoniam igitur est quæ quidem p, i, æ quedistanter
              <lb/>
            dyametro n, o, quæ autem b, r, perpendicularis ſuper dyametrum. </s>
            <s xml:id="echoid-s403" xml:space="preserve">Quæ
              <lb/>
            autem f, b, æqualis ei quæ uſque ad axem palam quòd quę t, r, educta
              <lb/>
            æquales angulos ad contingentem ſectionem apol. </s>
            <s xml:id="echoid-s404" xml:space="preserve">ſecundum p, quare
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            & </s>
            <s xml:id="echoid-s405" xml:space="preserve">ad a, s, & </s>
            <s xml:id="echoid-s406" xml:space="preserve">ad ſuperficiem aquæ ductis autem per t, g, ęquediſtanter ip
              <lb/>
            ſif, b, erunt & </s>
            <s xml:id="echoid-s407" xml:space="preserve">ipſe perpendiculares ad ſuperficiem aquæ, & </s>
            <s xml:id="echoid-s408" xml:space="preserve">magnitudo
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              <figure xlink:label="fig-0028-01" xlink:href="fig-0028-01a" number="23">
                <image file="0028-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0028-01"/>
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