Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[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.]
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ARCHIMEDIS
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            & </s>
            <s xml:space="preserve">quam proportionem habet quadratum e ψ ad quadra-
              <lb/>
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            tum ψ b, eandem habet dimidium lineæ _k_ r ad lineã ψ b.
              <lb/>
            </s>
            <s xml:space="preserve">quare maiorem babet proportionem _k_ r ad i y, quàm di-
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              <anchor type="note" xlink:label="note-0058-02a" xlink:href="note-0058-02"/>
            midium k r ad ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco i y minor eſt, quàm dupla
              <lb/>
              <anchor type="note" xlink:label="note-0058-03a" xlink:href="note-0058-03"/>
            ψ b. </s>
            <s xml:space="preserve">eſt autem ipſius o i dupla. </s>
            <s xml:space="preserve">ergo o i minor eſt, quàm
              <lb/>
            ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">i ω maior, quàm ψ r. </s>
            <s xml:space="preserve">ſed ψ r eſt æqualis ipſi f. </s>
            <s xml:space="preserve">maior
              <lb/>
              <anchor type="note" xlink:label="note-0058-04a" xlink:href="note-0058-04"/>
            igitur eſt i ω, quàm f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam portio ad humidum in
              <lb/>
            grauitate eam ponitur habere proportionem, quam qua-
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            dratum f q ad quadratum b d: </s>
            <s xml:space="preserve">quam uero proportionem
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            habet portio ad humidum in grauitate, eam habet pars ip
              <lb/>
            ſius demerſa ad totam portionem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam pars ipſius de-
              <lb/>
            merſa habet ad totam, eandem habet quadratum p m ad
              <lb/>
            quadratnm o n: </s>
            <s xml:space="preserve">ſequitur quadratum p m ad quadratum
              <lb/>
            o n eam proportionem habere, quam quadratum f q ad
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            b d quadratum.
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            </s>
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            atque ideo ſ q æ-
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            qualis eſt ipſi p m.
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            </s>
            <s xml:space="preserve">demõſtrata eſt au
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            tem p h maior,
              <lb/>
            quàm f. </s>
            <s xml:space="preserve">cõſtat igi
              <lb/>
            tur p m minorem
              <lb/>
            eſſe, quàm ſeſqui-
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            alterã ipſius p h:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco p h ma
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            iorem, quàm du-
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            plam h m. </s>
            <s xml:space="preserve">Sit p z
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            ipſius z m dupla. </s>
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              <lb/>
            erit t quidem cẽ-
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            trũ grauitatis to-
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            tius ſolidi: </s>
            <s xml:space="preserve">centrũ
              <lb/>
            eius partis, quæ intra humidum, punctumz: </s>
            <s xml:space="preserve">reliquæ uero
              <lb/>
            partis centrum erit in linea z t producta uſque ad g. </s>
            <s xml:space="preserve">Eodẽ
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              <anchor type="note" xlink:label="note-0058-07a" xlink:href="note-0058-07"/>
            modo demonſtrabitur linea th perpendicularis ad ſuper-
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            ficiem humidi. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portio demerſa in humido ſeretur extra</s>
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