Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s3078" xml:space="preserve">
              <pb o="5" file="0121" n="121" rhead="DE CENTRO GRAVIT. SOLID."/>
            quo ſcilicet ln, om conueniunt. </s>
            <s xml:id="echoid-s3079" xml:space="preserve">Poſtremo in figura
              <lb/>
            a p l q b r m s c t n u d x o y centrum grauitatis trian
              <lb/>
            guli pay, & </s>
            <s xml:id="echoid-s3080" xml:space="preserve">trapezii ploy eſtin linea a z: </s>
            <s xml:id="echoid-s3081" xml:space="preserve">trapeziorum
              <lb/>
            uero lqxo, q b d x centrum eſtin linea z k: </s>
            <s xml:id="echoid-s3082" xml:space="preserve">& </s>
            <s xml:id="echoid-s3083" xml:space="preserve">trapeziorũ
              <lb/>
            b r u d, r m n u in k φ: </s>
            <s xml:id="echoid-s3084" xml:space="preserve">& </s>
            <s xml:id="echoid-s3085" xml:space="preserve">denique trapezii m s t n; </s>
            <s xml:id="echoid-s3086" xml:space="preserve">& </s>
            <s xml:id="echoid-s3087" xml:space="preserve">triangu
              <lb/>
            li s c t in φ c. </s>
            <s xml:id="echoid-s3088" xml:space="preserve">quare magnitudinis ex his compoſitæ centrū
              <lb/>
            in linea a c conſiſtit. </s>
            <s xml:id="echoid-s3089" xml:space="preserve">Rurſus trianguli q b r, & </s>
            <s xml:id="echoid-s3090" xml:space="preserve">trapezii q l
              <lb/>
            m r centrum eſt in linea b χ: </s>
            <s xml:id="echoid-s3091" xml:space="preserve">trapeziorum l p s m, p a c s,
              <lb/>
            a y t c, y o n t in linea χ φ: </s>
            <s xml:id="echoid-s3092" xml:space="preserve">trapeziiq; </s>
            <s xml:id="echoid-s3093" xml:space="preserve">o x u n, & </s>
            <s xml:id="echoid-s3094" xml:space="preserve">trianguli
              <lb/>
            x d u centrum in ψ d. </s>
            <s xml:id="echoid-s3095" xml:space="preserve">totius ergo magnitudinis centrum
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            eſtin linea b d. </s>
            <s xml:id="echoid-s3096" xml:space="preserve">ex quo ſequitur, centrum grauitatis figuræ
              <lb/>
            a p l q b r m s c t n u d x o y eſſe punctū _K_, lineis ſcilicet a c,
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            b d commune, quæ omnia demonſtrare oportebat.</s>
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        <div xml:id="echoid-div201" type="section" level="1" n="66">
          <head xml:id="echoid-head73" xml:space="preserve">THE OREMA III. PROPOSITIO III.</head>
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            <s xml:id="echoid-s3098" xml:space="preserve">Cuiuslibet portio-
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              <figure xlink:label="fig-0121-01" xlink:href="fig-0121-01a" number="77">
                <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0121-01"/>
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            nis circuli, & </s>
            <s xml:id="echoid-s3099" xml:space="preserve">ellipſis,
              <lb/>
            quæ dimidia non ſit
              <lb/>
            maior, centrum graui
              <lb/>
            tatis in portionis dia-
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            metro conſiſtit.</s>
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          <p>
            <s xml:id="echoid-s3101" xml:space="preserve">HOC eodem prorſus
              <lb/>
            modo demonſtrabitur,
              <lb/>
            quo in libro de centro gra
              <lb/>
            uitatis planorum ab Ar-
              <lb/>
            chimede demonſtratũ eſt,
              <lb/>
            in portione cõtenta recta
              <lb/>
            linea, & </s>
            <s xml:id="echoid-s3102" xml:space="preserve">rectanguli coni ſe
              <lb/>
            ctione grauitatis cẽtrum
              <lb/>
            eſſe in diametro portio-
              <lb/>
            nis. </s>
            <s xml:id="echoid-s3103" xml:space="preserve">Etita demonſtrari po
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