Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[21. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.]
[22. PROPOSITIO II.]
[23. COMMENTARIVS.]
[24. PROPOSITIO III.]
[25. PROPOSITIO IIII.]
[26. COMMENTARIVS.]
[27. PROPOSITIO V.]
[28. COMMENTARIVS.]
[29. PROPOSITIO VI.]
[30. COMMENTARIVS.]
[31. LEMMAI.]
[32. LEMMA II.]
[33. LEMMA III.]
[34. LEMMA IIII.]
[35. PROPOSITIO VII.]
[36. PROPOSITIO VIII.]
[37. COMMENTARIVS.]
[38. PROPOSITIO IX.]
[39. COMMENTARIVS.]
[40. PROPOSITIO X.]
[41. COMMENTARIVS.]
[42. LEMMA I.]
[43. LEMMA II.]
[44. LEMMA III.]
[45. LEMMA IIII.]
[46. LEMMA V.]
[47. LEMMA VI.]
[48. II.]
[49. III.]
[50. IIII.]
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DE CENTRO GRAVIT. SOLID.
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              <pb o="7" file="0125" n="125" rhead="DE CENTRO GRAVIT. SOLID."/>
            metrum habens e d. </s>
            <s xml:space="preserve">Quoniam igitur circuli uel ellipſis
              <lb/>
            a e c b grauitatis centrum eſt in diametro b e, & </s>
            <s xml:space="preserve">portio-
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            nis a e c centrum in linea e d: </s>
            <s xml:space="preserve">reliquæ portionis, uidelicet
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            a b c centrum grauitatis in ipſa b d conſiſtat neceſſe eſt, ex
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            octaua propoſitione eiuſdem.</s>
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          </p>
        </div>
        <div type="section" level="1" n="69">
          <head xml:space="preserve">THEOREMA V. PROPOSITIO V.</head>
          <p>
            <s xml:space="preserve">SI priſma ſecetur plano oppoſitis planis æqui
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            diſtante, ſectio erit figura æqualis & </s>
            <s xml:space="preserve">ſimilis ei,
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            quæ eſt oppoſitorum planorum, centrum graui
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            tatis in axe habens.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sit priſma, in quo plana oppoſita ſint triangula a b c,
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            d e f; </s>
            <s xml:space="preserve">axis g h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano iam dictis planis æquidiſtã
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            te; </s>
            <s xml:space="preserve">quod faciat ſectionem
              <emph style="sc">K</emph>
            l m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axi in pũcto n occurrat.
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            </s>
            <s xml:space="preserve">Dico _k_ l m triangulum æquale eſſe, & </s>
            <s xml:space="preserve">ſimile triangulis a b c
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            d e f; </s>
            <s xml:space="preserve">atque eius grauitatis centrum eſſe punctum n. </s>
            <s xml:space="preserve">Quo-
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            niam enim plana a b c
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              <anchor type="figure" xlink:label="fig-0125-01a" xlink:href="fig-0125-01"/>
            K l m æquidiſtantia ſecã
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              <anchor type="note" xlink:label="note-0125-01a" xlink:href="note-0125-01"/>
            tur a plano a e; </s>
            <s xml:space="preserve">rectæ li-
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            neæ a b, K l, quæ ſunt ip
              <lb/>
            ſorum cõmunes ſectio-
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            nes inter ſe ſe æquidi-
              <lb/>
            ſtant. </s>
            <s xml:space="preserve">Sed æquidiſtant
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            a d, b e; </s>
            <s xml:space="preserve">cum a e ſit para
              <lb/>
            lelogrammum, ex priſ-
              <lb/>
            matis diffinitione. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">al parallelogrammũ
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            erit; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea linea
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              <anchor type="note" xlink:label="note-0125-02a" xlink:href="note-0125-02"/>
            _k_l, ipſi a b æqualis. </s>
            <s xml:space="preserve">Si-
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            militer demonſtrabitur
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            l m æquidiſtans, & </s>
            <s xml:space="preserve">æqua
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            lis b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">m
              <emph style="sc">K</emph>
            ipſi c a.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0125-01" xlink:href="fig-0125-01a">
              <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0125-01"/>
            </figure>
            <note position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">16. unde-
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            cimi.</note>
            <note position="right" xlink:label="note-0125-02" xlink:href="note-0125-02a" xml:space="preserve">34. prim@</note>
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