Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4801" xml:space="preserve">
              <pb o="40" file="0191" n="191" rhead="DE CENTRO GRAVIT. SOLID."/>
            eſſe pun ctum g. </s>
            <s xml:id="echoid-s4802" xml:space="preserve">Sequitur ergo uticoſahedri centrum gra
              <lb/>
            uitatis fit idem, quodipſius ſphæræ centrum.</s>
            <s xml:id="echoid-s4803" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4804" xml:space="preserve">Sit dodecahedrum a ſin ſphæra deſignatum, ſitque ſphæ
              <lb/>
            ræ centrum m. </s>
            <s xml:id="echoid-s4805" xml:space="preserve">Dico m centrum eſſe grauitatis ipſius do-
              <lb/>
            decahedri. </s>
            <s xml:id="echoid-s4806" xml:space="preserve">Sit enim pentagonum a b c d e una ex duode-
              <lb/>
            cim baſibus ſolidi a f: </s>
            <s xml:id="echoid-s4807" xml:space="preserve">& </s>
            <s xml:id="echoid-s4808" xml:space="preserve">iuncta a m producatur ad ſphæræ
              <lb/>
            ſuperficiem. </s>
            <s xml:id="echoid-s4809" xml:space="preserve">cadetin angulum ipſi a oppoſitum; </s>
            <s xml:id="echoid-s4810" xml:space="preserve">quod col-
              <lb/>
            ligitur ex decima ſeptima propoſitione tertiidecimilibri
              <lb/>
            elementorum. </s>
            <s xml:id="echoid-s4811" xml:space="preserve">cadat in f. </s>
            <s xml:id="echoid-s4812" 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:id="echoid-s4813" xml:space="preserve">cadent hæ in alios angulos baſis, quæ ipſi a b c d
              <lb/>
            baſi opponitur. </s>
            <s xml:id="echoid-s4814" 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/>
              <figure xlink:label="fig-0191-01" xlink:href="fig-0191-01a" number="142">
                <image file="0191-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0191-01"/>
              </figure>
            na dictorum circulorũ; </s>
            <s xml:id="echoid-s4815" xml:space="preserve">ad
              <lb/>
            circulum quidem a b c d e
              <lb/>
            perpendicularis m n: </s>
            <s xml:id="echoid-s4816" xml:space="preserve">& </s>
            <s xml:id="echoid-s4817" xml:space="preserve">ad
              <lb/>
            circulum f g h K l ipſa m o,
              <lb/>
              <note position="right" xlink:label="note-0191-01" xlink:href="note-0191-01a" xml:space="preserve">corol. pri
                <lb/>
              mæ ſphæ
                <lb/>
              ricorum
                <lb/>
              Theod.</note>
            erunt puncta n o circulorũ
              <lb/>
            centra: </s>
            <s xml:id="echoid-s4818" xml:space="preserve">& </s>
            <s xml:id="echoid-s4819" xml:space="preserve">lineæ m n, m o in
              <lb/>
            ter ſe æquales: </s>
            <s xml:id="echoid-s4820" xml:space="preserve">quòd circu-
              <lb/>
            li æquales ſint. </s>
            <s xml:id="echoid-s4821" xml:space="preserve">Eodem mo
              <lb/>
              <note position="right" xlink:label="note-0191-02" xlink:href="note-0191-02a" xml:space="preserve">6. primi
                <lb/>
              phærico
                <lb/>
              rum.</note>
            do, quo ſupra, demonſtrabi
              <lb/>
            mus lineas m n, m o in unã
              <lb/>
            atque eandem lineam con-
              <lb/>
            uenire. </s>
            <s xml:id="echoid-s4822" xml:space="preserve">ergo cum puncta n o ſint centra circulorum, con-
              <lb/>
            ſtat ex prima huius & </s>
            <s xml:id="echoid-s4823" xml:space="preserve">pentagonorũ grauitatis eſſe centra:
              <lb/>
            </s>
            <s xml:id="echoid-s4824" xml:space="preserve">idcircoq; </s>
            <s xml:id="echoid-s4825" xml:space="preserve">m n, m o pyramidum a b c d e m, ſ g h _K_ l m axes. </s>
            <s xml:id="echoid-s4826" xml:space="preserve">
              <lb/>
            ponatur a b c d e m pyramidis grauitatis centrum p: </s>
            <s xml:id="echoid-s4827" xml:space="preserve">& </s>
            <s xml:id="echoid-s4828" xml:space="preserve">py
              <lb/>
            ramidis f g h
              <emph style="sc">K</emph>
            l m ipſum q centrum. </s>
            <s xml:id="echoid-s4829" xml:space="preserve">erunt p m, m q æqua-
              <lb/>
            les, & </s>
            <s xml:id="echoid-s4830" xml:space="preserve">punctum m grauitatis centrum magnitudinis, quæ
              <lb/>
            ex ipſis pyramidibus conſtat. </s>
            <s xml:id="echoid-s4831" xml:space="preserve">eodẽ modo probabitur qua-
              <lb/>
            rumlibet pyramidum, quæ è regione opponuntur, </s>
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