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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DE IIS QVAE VEH. IN AQVA.
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              <pb o="44" file="0099" n="99" rhead="DE IIS QVAE VEH. IN AQVA."/>
            gura: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia eadem diſponantur demonſtrabimus rurſum
              <lb/>
            n t æqualem eſſe ipſi u i: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portiones a u q, a n z inter
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            ſe ſe æquales.
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            Itaque quoniã
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            ĩ portionibus
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            æqualibus, & </s>
            <s xml:space="preserve">ſi
              <lb/>
            milibus a u q l,
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            a n z g ductæ
              <lb/>
            sũt a q, a z, por
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            tiones æqua-
              <lb/>
            les auferentes;
              <lb/>
            </s>
            <s xml:space="preserve">cum diametris
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            portionum æ-
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            quales angu-
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            los cõtinebũt. </s>
            <s xml:space="preserve">
              <lb/>
            ergo triangulo
              <lb/>
            rum n l s, u ω c
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            anguli, qui cõ-
              <lb/>
            ſiſtũt ad l ω pũ-
              <lb/>
            cta, æquales ſunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b s recta linea æqualis ipſi b c: </s>
            <s xml:space="preserve">ſ r ipſi cr,
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            n χ ipſi u h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">χ tipſi h i. </s>
            <s xml:space="preserve">quòd cum u y dupla ſit ipſius y i,
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            erit n χ maior, quàm dupla χ t. </s>
            <s xml:space="preserve">Sit igitur n m ipſius m t du
              <lb/>
            pla. </s>
            <s xml:space="preserve">Rurſus ex his manifeſtum eſt, non manere ipſam por-
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            tionem; </s>
            <s xml:space="preserve">ſed inclinari ex parte a: </s>
            <s xml:space="preserve">ponebatur autem portio
              <lb/>
            humidi ſuperficiem in uno puncto contingere. </s>
            <s xml:space="preserve">ergo ne-
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            ceſſe eſt, ut eius baſis in humidum magis demergatur.</s>
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            <figure xlink:label="fig-0097-01" xlink:href="fig-0097-01a">
              <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0097-01"/>
            </figure>
            <figure xlink:label="fig-0098-01" xlink:href="fig-0098-01a">
              <image file="0098-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0098-01"/>
            </figure>
            <figure xlink:label="fig-0099-01" xlink:href="fig-0099-01a">
              <image file="0099-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0099-01"/>
            </figure>
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        <div type="section" level="1" n="57">
          <head xml:space="preserve">DEMONSTRATIO QVINT AE PARTIS.</head>
          <p>
            <s xml:space="preserve">HABEAT denique portio ad humidum in grauitate
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            minorem proportionem, quàm quadratum f p ad quadra-
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            tum b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet portio ad humidũ
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            in grauitate, eandem quadratum, quod fit à linea ψ habeat
              <lb/>
            ad quadratum b d. </s>
            <s xml:space="preserve">erit χ minor ipſa p f. </s>
            <s xml:space="preserve">Rurſus aptetur</s>
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