Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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          <p>
            <s xml:space="preserve">
              <pb o="40" file="0191" n="191" rhead="DE CENTRO GRAVIT. SOLID."/>
            eſſe pun ctum g. </s>
            <s xml:space="preserve">Sequitur ergo uticoſahedri centrum gra
              <lb/>
            uitatis fit idem, quodipſius ſphæræ centrum.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0190-01" xlink:href="note-0190-01a" xml:space="preserve">13. primi</note>
            <note position="left" xlink:label="note-0190-02" xlink:href="note-0190-02a" xml:space="preserve">14. primi</note>
            <figure xlink:label="fig-0190-01" xlink:href="fig-0190-01a">
              <image file="0190-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0190-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Sit dodecahedrum a ſin ſphæra deſignatum, ſitque ſphæ
              <lb/>
            ræ centrum m. </s>
            <s xml:space="preserve">Dico m centrum eſſe grauitatis ipſius do-
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            decahedri. </s>
            <s xml:space="preserve">Sit enim pentagonum a b c d e una ex duode-
              <lb/>
            cim baſibus ſolidi a f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a m producatur ad ſphæræ
              <lb/>
            ſuperficiem. </s>
            <s xml:space="preserve">cadetin angulum ipſi a oppoſitum; </s>
            <s xml:space="preserve">quod col-
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            ligitur ex decima ſeptima propoſitione tertiidecimilibri
              <lb/>
            elementorum. </s>
            <s xml:space="preserve">cadat in f. </s>
            <s xml:space="preserve">at ſi ab aliis angulis b c d e per cẽ
              <lb/>
            trum itidem lineæ ducantur ad ſuperficiem ſphæræ in pun
              <lb/>
            cta g h k l; </s>
            <s xml:space="preserve">cadent hæ in alios angulos baſis, quæ ipſi a b c d
              <lb/>
            baſi opponitur. </s>
            <s xml:space="preserve">tranſeant ergo per pentagona a b c d e,
              <lb/>
            f g h K l plana ſphæram ſecantia, quæ facient ſectiones cir-
              <lb/>
            culos æquales inter ſe ſe poſtea ducantur ex centro ſphæræ
              <lb/>
            m perpen diculares ad pla-
              <lb/>
              <anchor type="figure" xlink:label="fig-0191-01a" xlink:href="fig-0191-01"/>
            na dictorum circulorũ; </s>
            <s xml:space="preserve">ad
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            circulum quidem a b c d e
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            perpendicularis m n: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad
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            circulum f g h K l ipſa m o,
              <lb/>
              <anchor type="note" xlink:label="note-0191-01a" xlink:href="note-0191-01"/>
            erunt puncta n o circulorũ
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            centra: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">lineæ m n, m o in
              <lb/>
            ter ſe æquales: </s>
            <s xml:space="preserve">quòd circu-
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            li æquales ſint. </s>
            <s xml:space="preserve">Eodem mo
              <lb/>
              <anchor type="note" xlink:label="note-0191-02a" xlink:href="note-0191-02"/>
            do, quo ſupra, demonſtrabi
              <lb/>
            mus lineas m n, m o in unã
              <lb/>
            atque eandem lineam con-
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            uenire. </s>
            <s xml:space="preserve">ergo cum puncta n o ſint centra circulorum, con-
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            ſtat ex prima huius & </s>
            <s xml:space="preserve">pentagonorũ grauitatis eſſe centra:
              <lb/>
            </s>
            <s xml:space="preserve">idcircoq; </s>
            <s xml:space="preserve">m n, m o pyramidum a b c d e m, ſ g h _K_ l m axes. </s>
            <s xml:space="preserve">
              <lb/>
            ponatur a b c d e m pyramidis grauitatis centrum p: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">py
              <lb/>
            ramidis f g h
              <emph style="sc">K</emph>
            l m ipſum q centrum. </s>
            <s xml:space="preserve">erunt p m, m q æqua-
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            les, & </s>
            <s xml:space="preserve">punctum m grauitatis centrum magnitudinis, quæ
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            ex ipſis pyramidibus conſtat. </s>
            <s xml:space="preserve">eodẽ modo probabitur qua-
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            rumlibet pyramidum, quæ è regione opponuntur, centrũ</s>
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