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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            q o; </s>
            <s xml:space="preserve">uidelicet ut h g ad f p: </s>
            <s xml:space="preserve">quod proxime demonſtr atum eſt. </s>
            <s xml:space="preserve">At
              <lb/>
              <anchor type="note" xlink:label="note-0052-01a" xlink:href="note-0052-01"/>
            ueroipſi g q æquales ſunt duæ lineæ ſimul ſumptæ qb, hoc eſt h b,
              <lb/>
              <anchor type="note" xlink:label="note-0052-02a" xlink:href="note-0052-02"/>
            & </s>
            <s xml:space="preserve">b g: </s>
            <s xml:space="preserve">atque ipſi q a æqualis eſt h f. </s>
            <s xml:space="preserve">Sienim ab æqualibus h b,
              <lb/>
            bq, æqualia fb,
              <lb/>
              <anchor type="figure" xlink:label="fig-0052-01a" xlink:href="fig-0052-01"/>
            ba demantur, re
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            manentia æqua-
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            lia erunt. </s>
            <s xml:space="preserve">ergo
              <lb/>
            dempta h g ex
              <lb/>
            duabus lineis h
              <lb/>
            b, h g, relinqui-
              <lb/>
            tur dupla ipſius
              <lb/>
            b g; </s>
            <s xml:space="preserve">hoc eſt o h:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">dempta p f ex
              <lb/>
            f h, reliqua est
              <lb/>
            b p. </s>
            <s xml:space="preserve">quare o h
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              <anchor type="note" xlink:label="note-0052-03a" xlink:href="note-0052-03"/>
            ad h p, eſt ut g q
              <lb/>
            ad q a. </s>
            <s xml:space="preserve">Sed ut
              <lb/>
            g q ad q a, ita
              <lb/>
            h q ad q o; </s>
            <s xml:space="preserve">hoc
              <lb/>
            eſt h g ad n c:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut o h ad h p,
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              <anchor type="note" xlink:label="note-0052-04a" xlink:href="note-0052-04"/>
            ita g b ad c k. </s>
            <s xml:space="preserve">eſt
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            cnim o h dupla
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            g b, & </s>
            <s xml:space="preserve">h p item
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            dupla gf; </s>
            <s xml:space="preserve">hoc eſt
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            c k. </s>
            <s xml:space="preserve">eandem igitur proportionem habet h g ad n c, qnam g b ad
              <lb/>
            c k: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando n c ad c k eandem habet, quam b g ad g b.</s>
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          </p>
          <div type="float" level="2" n="2">
            <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">2. lem:</note>
            <note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">4. lem.</note>
            <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a">
              <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0052-01"/>
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            <note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve">19. quinti</note>
            <note position="left" xlink:label="note-0052-04" xlink:href="note-0052-04a" xml:space="preserve">15. quin-
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            ti.</note>
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          <p style="it">
            <s xml:space="preserve">Sumatur deinde aliud quod uis punctum in ſectum in ſectione,
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            quod ſit s: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per s duæ lineæ ducantur: </s>
            <s xml:space="preserve">st quidem
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            æquidistans ipſi db, diametrumque in puncto t ſecans;
              <lb/>
            </s>
            <s xml:space="preserve">s u uero æquidistans ac, & </s>
            <s xml:space="preserve">ſecans c e in u. </s>
            <s xml:space="preserve">Dico u c
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            ad ck maiorem proportionem habere, quamtg ad gb.</s>
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