Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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page |< < (11) of 213 > >|
DE CENTRO GRA VIT. SOLID.
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              <pb o="11" file="0133" n="133" rhead="DE CENTRO GRA VIT. SOLID."/>
            & </s>
            <s xml:space="preserve">per o ducatur o p ad k m ipſi h g æquidiſtans. </s>
            <s xml:space="preserve">Itaque li
              <lb/>
            nea h m bifariã uſque eò diuidatur, quoad reliqua ſit pars
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            quædam q m, minor o p. </s>
            <s xml:space="preserve">deinde h m, m g diuidantur in
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            partes æ quales ipſi m q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per diuiſiones lineæ ipſi m K
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            æ quidiſtantes ducantur. </s>
            <s xml:space="preserve">puncta uero, in quibus hæ trian-
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            gulorum latera ſecant, coniungantur ductis lineis r s, t u,
              <lb/>
              <anchor type="figure" xlink:label="fig-0133-01a" xlink:href="fig-0133-01"/>
            x y; </s>
            <s xml:space="preserve">quæ baſi g h æquidiſtabunt. </s>
            <s xml:space="preserve">Quoniam enim lineæ g z,
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            h α ſunt æ quales: </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">æquales g m, m h: </s>
            <s xml:space="preserve">ut m g ad g z,
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            ita erit m h, ad h α: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo, ut m z ad z g, ita m α ad
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            α h. </s>
            <s xml:space="preserve">Sed ut m z ad z g, ita k r ad r g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut m α ad α h, ita k s
              <lb/>
              <anchor type="note" xlink:label="note-0133-01a" xlink:href="note-0133-01"/>
            ad s h. </s>
            <s xml:space="preserve">quare ut κ r ad r g, ita k s ad s h. </s>
            <s xml:space="preserve">æ quidiſtant igitur
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              <anchor type="note" xlink:label="note-0133-02a" xlink:href="note-0133-02"/>
            inter ſe ſe r s, g h. </s>
            <s xml:space="preserve">eadem quoque ratione demonſtrabimus
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              <anchor type="note" xlink:label="note-0133-03a" xlink:href="note-0133-03"/>
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