Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[1. None]
[2. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBRI DVO. A FEDERICO COMMANDINO VRBINATE IN PRISTINVM NITOREM RESTITVTI, ET COMMENTARIIS ILLVSTRATI.]
[3. CVM PRIVILEGIO IN ANNOS X. BONONIAE,]
[4. M D LXV.]
[5. RANVTIO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[6. Federicus Commandinus.]
[7. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER PRIMVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. POSITIO.]
[8. PROPOSITIO I.]
[9. PROPOSITIO II.]
[10. PROPOSITIO III.]
[11. PROPOSITIO IIII.]
[12. PROPOSITIO V.]
[13. PROPOSITIO VI.]
[14. PROPOSITIO VII.]
[15. POSITIO II.]
[16. COMMENTARIVS.]
[17. PROPOSITIO VIII.]
[18. COMMENTARIVS.]
[19. PROPOSITIO IX.]
[20. COMMENTARIVS.]
[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.]
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ARCHIMEDIS
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        <div type="section" level="1" n="45">
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              <pb file="0078" n="78" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:space="preserve">per conuer-
              <lb/>
              <anchor type="figure" xlink:label="fig-0078-01a" xlink:href="fig-0078-01"/>
            ſionem rationis
              <lb/>
            ut e b ad e g,
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            ita f d ad f h.
              <lb/>
            </s>
            <s xml:space="preserve">eſt autem ut a e
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            ad e b, ita c f
              <lb/>
            ad f d. </s>
            <s xml:space="preserve">ex æqua
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            li igitur ut a e
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            ad e g, ita c f
              <lb/>
            ad f h.</s>
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          </p>
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            <figure xlink:label="fig-0078-01" xlink:href="fig-0078-01a">
              <image file="0078-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0078-01"/>
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              <emph style="sc">A_liter_</emph>
            . </s>
            <s xml:space="preserve">Aptentur lineæ a b, c d inter ſe ſe, ita ut ad partes
              <lb/>
            a c angulum faciant; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſint a c in uno atque eodem puncto: </s>
            <s xml:space="preserve">deinde
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            iungantur d b, h g, fe. </s>
            <s xml:space="preserve">cum igitur ſit ut a e ad e b, ita c f, hoc eſt
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            a f ad f d; </s>
            <s xml:space="preserve">æquidiſtabit fe ipſi d b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſimiliter h g eidem d b
              <lb/>
              <anchor type="note" xlink:label="note-0078-01a" xlink:href="note-0078-01"/>
            æquidiſtabit: </s>
            <s xml:space="preserve">quoniam a h ad h d eſt, ut a g ad g b. </s>
            <s xml:space="preserve">ergo f c, h g
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            inter ſe ſe æquidiſtant: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco ut a e ad e g, ita a f; </s>
            <s xml:space="preserve">hoc eſt c f ad
              <lb/>
            fh. </s>
            <s xml:space="preserve">quod demonſtrare oportebat.</s>
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            <note position="left" xlink:label="note-0078-01" xlink:href="note-0078-01a" xml:space="preserve">2. ſexti:</note>
            <note position="left" xlink:label="note-0078-02" xlink:href="note-0078-02a" xml:space="preserve">30. primi</note>
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        <div type="section" level="1" n="46">
          <head xml:space="preserve">LEMMA V.</head>
          <p style="it">
            <s xml:space="preserve">Sint rurſus duæ portiones ſimiles, contentæ rectis li-
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            neis, & </s>
            <s xml:space="preserve">rectangulorum conorum ſectionibus, ut in ſupe-
              <lb/>
            riori figura a b c, cuius diameter b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">e f c, cuius
              <lb/>
            diameter f g: </s>
            <s xml:space="preserve">ducaturque à puncto e linea e h, diame-
              <lb/>
            tris b d, f g æquidiſtans, quæ ſectionem a b c in _k_ ſe-
              <lb/>
            cet: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à puncto c ducatur c h contingens ſectionem
              <lb/>
            a b c in c conueniensque cumlinea e h in h, quæ ſectio
              <lb/>
            nem quoque e f c in eodem c puncto continget, ut demon
              <lb/>
            strabitur. </s>
            <s xml:space="preserve">Dico lineam ductam ab ipſa c h uſque ad ſe-
              <lb/>
            ctionem e f c, ita ut lineæ e h æquidistet, in eandem pro
              <lb/>
            portionem diuidi à ſectione a b c; </s>
            <s xml:space="preserve">in quam linea c a à</s>
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