Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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            <s xml:space="preserve">
              <pb o="4" file="0119" n="119" rhead="DE CENTRO GRAVIT. SOLID."/>
            o n ipſi a c. </s>
            <s xml:space="preserve">Quoniam enim triangulorum a b k, a d k, latus
              <lb/>
            b k eſt æquale lateri k d, & </s>
            <s xml:space="preserve">a k utrique commune; </s>
            <s xml:space="preserve">anguliq́;
              <lb/>
            </s>
            <s xml:space="preserve">ad k recti baſis a b baſi a d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reliqui anguli reliquis an-
              <lb/>
              <anchor type="note" xlink:label="note-0119-01a" xlink:href="note-0119-01"/>
            gulis æquales erunt. </s>
            <s xml:space="preserve">eadem quoqueratione oſtendetur b c
              <lb/>
            æqualis c d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a b ipſi
              <lb/>
              <anchor type="figure" xlink:label="fig-0119-01a" xlink:href="fig-0119-01"/>
            b c. </s>
            <s xml:space="preserve">quare omnes a b,
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            b c, c d, d a ſunt æqua-
              <lb/>
            les. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam anguli
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            ad a æquales ſunt angu
              <lb/>
            lis ad c; </s>
            <s xml:space="preserve">erunt anguli b
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            a c, a c d coalterni inter
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            ſe æquales; </s>
            <s xml:space="preserve">itemq́; </s>
            <s xml:space="preserve">d a c,
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            a c b. </s>
            <s xml:space="preserve">ergo c d ipſi b a;
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a d ipſi b c æquidi-
              <lb/>
            ſtat. </s>
            <s xml:space="preserve">Atuero cum lineæ
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            a b, c d inter ſe æquidi-
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            ſtantes bifariam ſecen-
              <lb/>
            tur in punctis e g; </s>
            <s xml:space="preserve">erit li
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            nea l e k g n diameter ſe
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            ctionis, & </s>
            <s xml:space="preserve">linea una, ex
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            demonſtratis in uigeſi-
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            ma octaua ſecundi coni
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            corum. </s>
            <s xml:space="preserve">Et eadem ratione linea una m f k h o. </s>
            <s xml:space="preserve">Sunt autẽ a d,
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            b c inter ſe ſe æquales, & </s>
            <s xml:space="preserve">æquidiſtantes. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">earum di-
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            midiæ a h, b f; </s>
            <s xml:space="preserve">itemq́; </s>
            <s xml:space="preserve">h d, f e; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ ipſas coniunguntrectæ
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              <anchor type="note" xlink:label="note-0119-02a" xlink:href="note-0119-02"/>
            lineæ æquales, & </s>
            <s xml:space="preserve">æquidiſtantes erunt. </s>
            <s xml:space="preserve">æquidiſtãt igitur b a,
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            c d diametro m o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pariter a d, b c ipſi l n æquidiſtare o-
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            ſtendemus. </s>
            <s xml:space="preserve">Si igitur manẽte diametro a c intelligatur a b c
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            portio ellipſis ad portionem a d c moueri, cum primum b
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            applicuerit ad d, cõgruet tota portio toti portioni, lineaq́;
              <lb/>
            </s>
            <s xml:space="preserve">b a lineæ a d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b c ipſi c d congruet: </s>
            <s xml:space="preserve">punctum uero e ca-
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            det in h; </s>
            <s xml:space="preserve">f in g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">linea k e in lineam k h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">k f in k g. </s>
            <s xml:space="preserve">qua
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            re & </s>
            <s xml:space="preserve">el in h o, et fm in g n. </s>
            <s xml:space="preserve">Atipſa lz in z o; </s>
            <s xml:space="preserve">et m φ in φ n
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            cadet. </s>
            <s xml:space="preserve">congruet igitur triangulum l k z triangulo o k z: </s>
            <s xml:space="preserve">et</s>
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