Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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              <pb o="15" file="0041" n="41" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _quare per o ductaipſi al æquidiſtans cadet extra ſectionem ex 17._
              <lb/>
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            <s xml:id="echoid-s854" xml:space="preserve">_primi conicorum: </s>
            <s xml:id="echoid-s855" xml:space="preserve">& </s>
            <s xml:id="echoid-s856" xml:space="preserve">cum b p producta coibit inſra p. </s>
            <s xml:id="echoid-s857" xml:space="preserve">ergò & </s>
            <s xml:id="echoid-s858" xml:space="preserve">per-_
              <lb/>
            _pendicularis ducta per b cum eadem infra b coibit, at que inter b &_</s>
            <s xml:id="echoid-s859" xml:space="preserve">
              <lb/>
            _p neceſſario cadet. </s>
            <s xml:id="echoid-s860" xml:space="preserve">multo autem magis illud idem ſequetur, ſi pona-_
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            _mus pf ipſa om maiorem eſſe._</s>
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          <p>
            <s xml:id="echoid-s862" xml:space="preserve">Et quoniam p f quidem æquidiſtans eſt diametro, htau
              <lb/>
              <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">H</note>
            tem ad diametrum perpendicularis; </s>
            <s xml:id="echoid-s863" xml:space="preserve">& </s>
            <s xml:id="echoid-s864" xml:space="preserve">rh æqualis ei, quæ
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            uſque ad axem, ducta linea ab r ad e, & </s>
            <s xml:id="echoid-s865" xml:space="preserve">producta angulos
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            rectos facere cum linea ſectionem in p contingente.</s>
            <s xml:id="echoid-s866" xml:space="preserve">]
              <lb/>
            _Hoc ſuperius à nobis demonſtratum eſt in ſecundam buin
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            s._</s>
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          <head xml:id="echoid-head32" xml:space="preserve">PROPOSITIO V.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
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            leuior humido axem habuerit maiorem, quàm
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            ſeſquialterum eius, quæ uſque ad axem; </s>
            <s xml:id="echoid-s869" xml:space="preserve">ſi ad hu-
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            midum in grauitate non maiorem proportionẽ
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            habeat, quàm exceſſus, quo quadratum quod ſit
              <lb/>
            ab axe maius eſt quadrato, quod ab exceſſu, quo
              <lb/>
            axis maior eſt, quàm ſeſquialter eius, quæ uſque
              <lb/>
            ad axem, ad quadratum, quod ab axe: </s>
            <s xml:id="echoid-s870" xml:space="preserve">demiſſa in
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            humidum, ita ut baſis ipſius tota ſit in humido;
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            </s>
            <s xml:id="echoid-s871" xml:space="preserve">& </s>
            <s xml:id="echoid-s872" xml:space="preserve">poſita inclinata non manebit inclinata, ſed re-
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            ſtituetur ita, ut axis ipſius ſecundum perpendi-
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            cularem fiat.</s>
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          <p>
            <s xml:id="echoid-s874" xml:space="preserve">DEMITTATVR enim in humidum portio aliqna,
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            qualis dicta eſt: </s>
            <s xml:id="echoid-s875" xml:space="preserve">& </s>
            <s xml:id="echoid-s876" xml:space="preserve">ſit baſis ipſius tota in humido. </s>
            <s xml:id="echoid-s877" xml:space="preserve">Secta au-
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            tem ipſa plano per axem, recto ad ſuperſiciem humidi, erit
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            ſectio rectanguli coniſectio, quæ ſit apol: </s>
            <s xml:id="echoid-s878" xml:space="preserve">axis </s>
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