Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb o="16" file="0144" n="144" rhead="FED. COMMANDINI"/>
          <p>
            <s xml:id="echoid-s3635" xml:space="preserve">SIT pyramis, cuius baſis triangulum a b c; </s>
            <s xml:id="echoid-s3636" xml:space="preserve">axis d e: </s>
            <s xml:id="echoid-s3637" xml:space="preserve">& </s>
            <s xml:id="echoid-s3638" xml:space="preserve">
              <lb/>
            ſecetur plano baſi æquidiſtante; </s>
            <s xml:id="echoid-s3639" xml:space="preserve">quod ſectionẽ faciat f g h;
              <lb/>
            </s>
            <s xml:id="echoid-s3640" xml:space="preserve">occurratq; </s>
            <s xml:id="echoid-s3641" xml:space="preserve">axi in puncto k. </s>
            <s xml:id="echoid-s3642" xml:space="preserve">Dico f g h triangulum eſſe, ipſi
              <lb/>
            a b c ſimile; </s>
            <s xml:id="echoid-s3643" xml:space="preserve">cuius grauitatis centrum eſt K. </s>
            <s xml:id="echoid-s3644" xml:space="preserve">Quoniã enim
              <lb/>
              <note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">16. unde
                <lb/>
              cimi</note>
            duo plana æquidiſtantia a b c, f g h ſecantur à plano a b d;
              <lb/>
            </s>
            <s xml:id="echoid-s3645" xml:space="preserve">communes eorum ſectiones a b, f g æquidiſtantes erunt: </s>
            <s xml:id="echoid-s3646" xml:space="preserve">& </s>
            <s xml:id="echoid-s3647" xml:space="preserve">
              <lb/>
            eadem ratione æquidiſtantes ipſæ b c, g h: </s>
            <s xml:id="echoid-s3648" xml:space="preserve">& </s>
            <s xml:id="echoid-s3649" xml:space="preserve">c a, h f. </s>
            <s xml:id="echoid-s3650" xml:space="preserve">Quòd
              <lb/>
            cum duæ lineæ f g, g h, duabus a b, b c æquidiſtent, nec
              <lb/>
            ſintin eodem plano; </s>
            <s xml:id="echoid-s3651" xml:space="preserve">angulus ad g æqualis eſt angulo ad
              <lb/>
              <note position="left" xlink:label="note-0144-02" xlink:href="note-0144-02a" xml:space="preserve">10. undeci
                <lb/>
              mi.</note>
            b: </s>
            <s xml:id="echoid-s3652" xml:space="preserve">& </s>
            <s xml:id="echoid-s3653" xml:space="preserve">ſimiliter angulus ad h angulo ad c: </s>
            <s xml:id="echoid-s3654" xml:space="preserve">angulusq; </s>
            <s xml:id="echoid-s3655" xml:space="preserve">ad f ei,
              <lb/>
            qui ad a eſt æqualis. </s>
            <s xml:id="echoid-s3656" xml:space="preserve">triangulum igitur f g h ſimile eſt tri-
              <lb/>
            angulo a b c. </s>
            <s xml:id="echoid-s3657" xml:space="preserve">At uero punctum k centrum eſſe grauita-
              <lb/>
            tis trianguli f g h hoc modo oſtendemus. </s>
            <s xml:id="echoid-s3658" xml:space="preserve">Ducantur pla-
              <lb/>
            na per axem, & </s>
            <s xml:id="echoid-s3659" xml:space="preserve">per lineas d a, d b, d c: </s>
            <s xml:id="echoid-s3660" xml:space="preserve">erunt communes ſe-
              <lb/>
              <note position="left" xlink:label="note-0144-03" xlink:href="note-0144-03a" xml:space="preserve">16. unde-
                <lb/>
              cimi</note>
            ctiones f K, a e æquidiſtantes: </s>
            <s xml:id="echoid-s3661" xml:space="preserve">pariterq; </s>
            <s xml:id="echoid-s3662" xml:space="preserve">k g, e b; </s>
            <s xml:id="echoid-s3663" xml:space="preserve">& </s>
            <s xml:id="echoid-s3664" xml:space="preserve">k h, e c:
              <lb/>
            </s>
            <s xml:id="echoid-s3665" xml:space="preserve">quare angulus k f h angulo e a c; </s>
            <s xml:id="echoid-s3666" xml:space="preserve">& </s>
            <s xml:id="echoid-s3667" xml:space="preserve">angulus k f g ipſi e a b
              <lb/>
              <note position="left" xlink:label="note-0144-04" xlink:href="note-0144-04a" xml:space="preserve">10. unde-
                <lb/>
              cimi</note>
            eſt æqualis. </s>
            <s xml:id="echoid-s3668" xml:space="preserve">Eadem ratione
              <lb/>
              <figure xlink:label="fig-0144-01" xlink:href="fig-0144-01a" number="98">
                <image file="0144-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0144-01"/>
              </figure>
            anguli ad g angulis ad b: </s>
            <s xml:id="echoid-s3669" xml:space="preserve">& </s>
            <s xml:id="echoid-s3670" xml:space="preserve">
              <lb/>
            anguli ad h iis, qui ad c æ-
              <lb/>
            quales erunt. </s>
            <s xml:id="echoid-s3671" xml:space="preserve">ergo puncta
              <lb/>
            e _K_ in triangulis a b c, f g h
              <lb/>
            ſimiliter ſunt poſita, per ſe-
              <lb/>
            xtam poſitionem Archime-
              <lb/>
            dis in libro de centro graui-
              <lb/>
            tatis planorum. </s>
            <s xml:id="echoid-s3672" xml:space="preserve">Sed cum e
              <lb/>
            ſit centrum grauitatis trian
              <lb/>
            guli a b c, erit ex undecíma
              <lb/>
            propoſitione eiuſdem libri,
              <lb/>
            & </s>
            <s xml:id="echoid-s3673" xml:space="preserve">K trianguli f g h grauita
              <lb/>
            tis centrum. </s>
            <s xml:id="echoid-s3674" xml:space="preserve">id quod demonſtrare oportebat. </s>
            <s xml:id="echoid-s3675" xml:space="preserve">Non aliter
              <lb/>
            in ceteris pyramidibus, quod propoſitum eſt demonſtra-
              <lb/>
            bitur.</s>
            <s xml:id="echoid-s3676" xml:space="preserve"/>
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