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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            <s xml:space="preserve">
              <pb file="0042" n="42" rhead="ARCHIMEDIS"/>
            & </s>
            <s xml:space="preserve">ſectionis diameter no: </s>
            <s xml:space="preserve">ſuperſiciei autem humidi ſectio
              <lb/>
            ſit is. </s>
            <s xml:space="preserve">Quoniam igitur axis non eſt ſecundum perpendicu
              <lb/>
            larem; </s>
            <s xml:space="preserve">ipſa no cum is non faciet angulos æquales. </s>
            <s xml:space="preserve">Du-
              <lb/>
            catur k ω contingens ſectionem apol in p; </s>
            <s xml:space="preserve">atque ipſi is
              <lb/>
            æquidiſtans: </s>
            <s xml:space="preserve">per p autem ducatur p f æquidiſtās ipſi n o:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſumantur grauitatum centra: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ipſius a p o l ſolidi
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            centrum r; </s>
            <s xml:space="preserve">eius quod extra humidum ſit b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta br
              <lb/>
            producatur adg,
              <lb/>
              <anchor type="figure" xlink:label="fig-0042-01a" xlink:href="fig-0042-01"/>
            quodſit centrum
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            grauitatis ſolidi ĩ
              <lb/>
            humido demerſi:
              <lb/>
            </s>
            <s xml:space="preserve">ſumatur præterea
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            r h æ qualis ei, quæ
              <lb/>
            uſque ad axẽ: </s>
            <s xml:space="preserve">o h
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            autem dupla ipſi-
              <lb/>
            us h m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">alia fiãt,
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            ſicuti ſuperius di-
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            ctum eſt. </s>
            <s xml:space="preserve">Itaque
              <lb/>
            cum portio ad hu
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            midum in grauita
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            te non maiorem
              <lb/>
            proportionem ha
              <lb/>
            bere ponatur, quã
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            exceſſus, quo quadratum n o excedit quadratum m o, ad
              <lb/>
            ipſum n o quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem in grauita
              <lb/>
            te portio habet ad humidum æqualis molis, eandem ha-
              <lb/>
            beat magnitudo portionis demerſa ad totam portio-
              <lb/>
            nem, quod demonſtratum eſt in prima propoſitione: </s>
            <s xml:space="preserve">
              <lb/>
            magnitudo demerſa non maiorem proportionem ha-
              <lb/>
              <anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/>
            bebit ad totam portionem, quàm ſit dicta illa propor-
              <lb/>
            portio. </s>
            <s xml:space="preserve">quare non maiorem proportionem habet tota
              <lb/>
              <anchor type="note" xlink:label="note-0042-02a" xlink:href="note-0042-02"/>
            portio ad eam quæ eſt extra humidum, quàm quadratum
              <lb/>
            no ad quadratum m o. </s>
            <s xml:space="preserve">habet autem tota portio ad eam,
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              <anchor type="note" xlink:label="note-0042-03a" xlink:href="note-0042-03"/>
            quæ extra humidum proportionem eandem, quam qua-</s>
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