Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4213" xml:space="preserve">
              <pb o="29" file="0169" n="169" rhead="DE CENTRO GRAVIT. SOLID."/>
            l h eandem habet proportionem, quam e m ad m k, uideli-
              <lb/>
            cet triplam. </s>
            <s xml:id="echoid-s4214" xml:space="preserve">quare linea l m ipſam e f ſecabit in puncto g:
              <lb/>
            </s>
            <s xml:id="echoid-s4215" xml:space="preserve">etenim e g ad g f eſt, ut el ad l h. </s>
            <s xml:id="echoid-s4216" xml:space="preserve">præterea quoniam h k, l m
              <lb/>
            æquidiſtant, erunt triangula h e f, l e g ſimilia: </s>
            <s xml:id="echoid-s4217" xml:space="preserve">itemq; </s>
            <s xml:id="echoid-s4218" xml:space="preserve">inter
              <lb/>
            ſe ſimilia f e k, g e m: </s>
            <s xml:id="echoid-s4219" xml:space="preserve">& </s>
            <s xml:id="echoid-s4220" xml:space="preserve">ut e fad e g, ita h fad l g: </s>
            <s xml:id="echoid-s4221" xml:space="preserve">& </s>
            <s xml:id="echoid-s4222" xml:space="preserve">ita f _K_ ad
              <lb/>
            g m. </s>
            <s xml:id="echoid-s4223" xml:space="preserve">ergo uth fadlg, ita f k ad g m: </s>
            <s xml:id="echoid-s4224" xml:space="preserve">& </s>
            <s xml:id="echoid-s4225" xml:space="preserve">permutando uth f
              <lb/>
            ad f _K_, ita l g ad g m. </s>
            <s xml:id="echoid-s4226" xml:space="preserve">ſed cum h ſit centrum trianguli a b d; </s>
            <s xml:id="echoid-s4227" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s4228" xml:space="preserve">K triãguli b c d: </s>
            <s xml:id="echoid-s4229" xml:space="preserve">punctũ uero f totius quadrilateri a b c d
              <lb/>
            centrum: </s>
            <s xml:id="echoid-s4230" xml:space="preserve">erit ex 8. </s>
            <s xml:id="echoid-s4231" xml:space="preserve">Archimedis de centro grauitatis plano
              <lb/>
            rum h fad f
              <emph style="sc">K</emph>
            , ut triangulum b c d ad triangulum a b d: </s>
            <s xml:id="echoid-s4232" xml:space="preserve">ut
              <lb/>
            autem b c d triangulum ad triangulum a b d, ita pyramis
              <lb/>
            b c d e ad pyramidem a b d e. </s>
            <s xml:id="echoid-s4233" xml:space="preserve">ergo
              <lb/>
              <figure xlink:label="fig-0169-01" xlink:href="fig-0169-01a" number="124">
                <image file="0169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0169-01"/>
              </figure>
            linea lg ad g m erit, ut pyramis
              <lb/>
            b c d e ad pyramidé a b d e. </s>
            <s xml:id="echoid-s4234" xml:space="preserve">ex quo
              <lb/>
            ſequitur, ut totius pyramidis
              <lb/>
            a b c d e punctum g ſit grauitatis
              <lb/>
            centrum. </s>
            <s xml:id="echoid-s4235" xml:space="preserve">Rurſus ſit pyramis ba-
              <lb/>
            ſim habens pentagonum a b c d e:
              <lb/>
            </s>
            <s xml:id="echoid-s4236" xml:space="preserve">& </s>
            <s xml:id="echoid-s4237" xml:space="preserve">axem f g: </s>
            <s xml:id="echoid-s4238" xml:space="preserve">diuidaturq; </s>
            <s xml:id="echoid-s4239" xml:space="preserve">axis in pũ
              <lb/>
            cto h, ita ut fh ad h g triplam habe
              <lb/>
            at proportionem. </s>
            <s xml:id="echoid-s4240" xml:space="preserve">Dico h grauita-
              <lb/>
            tis centrũ eſſe pyramidis a b c d e f. </s>
            <s xml:id="echoid-s4241" xml:space="preserve">
              <lb/>
            iungatur enim e b: </s>
            <s xml:id="echoid-s4242" xml:space="preserve">intelligaturq; </s>
            <s xml:id="echoid-s4243" xml:space="preserve">
              <lb/>
            pyramis, cuius uertex f, & </s>
            <s xml:id="echoid-s4244" xml:space="preserve">baſis
              <lb/>
            triangulum a b e: </s>
            <s xml:id="echoid-s4245" xml:space="preserve">& </s>
            <s xml:id="echoid-s4246" xml:space="preserve">alia pyramis
              <lb/>
            intelligatur eundem uerticem ha-
              <lb/>
            bens, & </s>
            <s xml:id="echoid-s4247" xml:space="preserve">baſim b c d e quadrilaterũ: </s>
            <s xml:id="echoid-s4248" xml:space="preserve">
              <lb/>
            ſit autem pyramidis a b e faxis f
              <emph style="sc">K</emph>
            ,
              <lb/>
            & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">grauitatis centrum l: </s>
            <s xml:id="echoid-s4250" xml:space="preserve">& </s>
            <s xml:id="echoid-s4251" xml:space="preserve">pyrami
              <lb/>
            dis b c d e faxis f m, & </s>
            <s xml:id="echoid-s4252" xml:space="preserve">centrum gra
              <lb/>
            uitatis n: </s>
            <s xml:id="echoid-s4253" xml:space="preserve">iunganturq; </s>
            <s xml:id="echoid-s4254" xml:space="preserve">
              <emph style="sc">K</emph>
            m, l n; </s>
            <s xml:id="echoid-s4255" xml:space="preserve">
              <lb/>
            quæ per puncta g h tranſibunt. </s>
            <s xml:id="echoid-s4256" xml:space="preserve">
              <lb/>
            Rurſus eodem modo, quo ſup ra,
              <lb/>
            demonſtrabimus lineas K g m, l h n ſibiipſis æ </s>
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