Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s2993" xml:space="preserve">
              <pb o="4" file="0119" n="119" rhead="DE CENTRO GRAVIT. SOLID."/>
            o n ipſi a c. </s>
            <s xml:id="echoid-s2994" xml:space="preserve">Quoniam enim triangulorum a b k, a d k, latus
              <lb/>
            b k eſt æquale lateri k d, & </s>
            <s xml:id="echoid-s2995" xml:space="preserve">a k utrique commune; </s>
            <s xml:id="echoid-s2996" xml:space="preserve">anguliq́;
              <lb/>
            </s>
            <s xml:id="echoid-s2997" xml:space="preserve">ad k recti baſis a b baſi a d; </s>
            <s xml:id="echoid-s2998" xml:space="preserve">& </s>
            <s xml:id="echoid-s2999" xml:space="preserve">reliqui anguli reliquis an-
              <lb/>
              <note position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">8. primi</note>
            gulis æquales erunt. </s>
            <s xml:id="echoid-s3000" xml:space="preserve">eadem quoqueratione oſtendetur b c
              <lb/>
            æqualis c d; </s>
            <s xml:id="echoid-s3001" xml:space="preserve">& </s>
            <s xml:id="echoid-s3002" xml:space="preserve">a b ipſi
              <lb/>
              <figure xlink:label="fig-0119-01" xlink:href="fig-0119-01a" number="75">
                <image file="0119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0119-01"/>
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            b c. </s>
            <s xml:id="echoid-s3003" xml:space="preserve">quare omnes a b,
              <lb/>
            b c, c d, d a ſunt æqua-
              <lb/>
            les. </s>
            <s xml:id="echoid-s3004" xml:space="preserve">& </s>
            <s xml:id="echoid-s3005" xml:space="preserve">quoniam anguli
              <lb/>
            ad a æquales ſunt angu
              <lb/>
            lis ad c; </s>
            <s xml:id="echoid-s3006" xml:space="preserve">erunt anguli b
              <lb/>
            a c, a c d coalterni inter
              <lb/>
            ſe æquales; </s>
            <s xml:id="echoid-s3007" xml:space="preserve">itemq́; </s>
            <s xml:id="echoid-s3008" xml:space="preserve">d a c,
              <lb/>
            a c b. </s>
            <s xml:id="echoid-s3009" xml:space="preserve">ergo c d ipſi b a;
              <lb/>
            </s>
            <s xml:id="echoid-s3010" xml:space="preserve">& </s>
            <s xml:id="echoid-s3011" xml:space="preserve">a d ipſi b c æquidi-
              <lb/>
            ſtat. </s>
            <s xml:id="echoid-s3012" xml:space="preserve">Atuero cum lineæ
              <lb/>
            a b, c d inter ſe æquidi-
              <lb/>
            ſtantes bifariam ſecen-
              <lb/>
            tur in punctis e g; </s>
            <s xml:id="echoid-s3013" xml:space="preserve">erit li
              <lb/>
            nea l e k g n diameter ſe
              <lb/>
            ctionis, & </s>
            <s xml:id="echoid-s3014" xml:space="preserve">linea una, ex
              <lb/>
            demonſtratis in uigeſi-
              <lb/>
            ma octaua ſecundi coni
              <lb/>
            corum. </s>
            <s xml:id="echoid-s3015" xml:space="preserve">Et eadem ratione linea una m f k h o. </s>
            <s xml:id="echoid-s3016" xml:space="preserve">Sunt autẽ a d,
              <lb/>
            b c inter ſe ſe æquales, & </s>
            <s xml:id="echoid-s3017" xml:space="preserve">æquidiſtantes. </s>
            <s xml:id="echoid-s3018" xml:space="preserve">quare & </s>
            <s xml:id="echoid-s3019" xml:space="preserve">earum di-
              <lb/>
            midiæ a h, b f; </s>
            <s xml:id="echoid-s3020" xml:space="preserve">itemq́; </s>
            <s xml:id="echoid-s3021" xml:space="preserve">h d, f e; </s>
            <s xml:id="echoid-s3022" xml:space="preserve">& </s>
            <s xml:id="echoid-s3023" xml:space="preserve">quæ ipſas coniunguntrectæ
              <lb/>
              <note position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">33. primit</note>
            lineæ æquales, & </s>
            <s xml:id="echoid-s3024" xml:space="preserve">æquidiſtantes erunt. </s>
            <s xml:id="echoid-s3025" xml:space="preserve">æquidiſtãt igitur b a,
              <lb/>
            c d diametro m o: </s>
            <s xml:id="echoid-s3026" xml:space="preserve">& </s>
            <s xml:id="echoid-s3027" xml:space="preserve">pariter a d, b c ipſi l n æquidiſtare o-
              <lb/>
            ſtendemus. </s>
            <s xml:id="echoid-s3028" xml:space="preserve">Si igitur manẽte diametro a c intelligatur a b c
              <lb/>
            portio ellipſis ad portionem a d c moueri, cum primum b
              <lb/>
            applicuerit ad d, cõgruet tota portio toti portioni, lineaq́;
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            </s>
            <s xml:id="echoid-s3029" xml:space="preserve">b a lineæ a d; </s>
            <s xml:id="echoid-s3030" xml:space="preserve">& </s>
            <s xml:id="echoid-s3031" xml:space="preserve">b c ipſi c d congruet: </s>
            <s xml:id="echoid-s3032" xml:space="preserve">punctum uero e ca-
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            det in h; </s>
            <s xml:id="echoid-s3033" xml:space="preserve">f in g: </s>
            <s xml:id="echoid-s3034" xml:space="preserve">& </s>
            <s xml:id="echoid-s3035" xml:space="preserve">linea k e in lineam k h: </s>
            <s xml:id="echoid-s3036" xml:space="preserve">& </s>
            <s xml:id="echoid-s3037" xml:space="preserve">k f in k g. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">qua
              <lb/>
            re & </s>
            <s xml:id="echoid-s3039" xml:space="preserve">el in h o, et fm in g n. </s>
            <s xml:id="echoid-s3040" xml:space="preserve">Atipſa lz in z o; </s>
            <s xml:id="echoid-s3041" xml:space="preserve">et m φ in φ n
              <lb/>
            cadet. </s>
            <s xml:id="echoid-s3042" xml:space="preserve">congruet igitur triangulum l k z triangulo o k z: </s>
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