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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              <pb file="0050" n="50" rhead="ARCHIMEDIS"/>
            nea h m ad li-
              <lb/>
              <anchor type="figure" xlink:label="fig-0050-01a" xlink:href="fig-0050-01"/>
            neam fc. </s>
            <s xml:space="preserve">at uero
              <lb/>
            ut h m ad f c, ita
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            o h ad a f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut
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            quadratum h m
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            ad quadratú g l,
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            ita linea h b ad
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            b g; </s>
            <s xml:space="preserve">hoc est b g
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            ad b f. </s>
            <s xml:space="preserve">ex quibus
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            ſequitur o h ad
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            a f ita eſſe, ut b g
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            ad b f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permu
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            tando oh ad b g,
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            ut a f ad f b. </s>
            <s xml:space="preserve">ſed
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            eſt a f dupla ip-
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            ſius fb: </s>
            <s xml:space="preserve">ſunt eni
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            a b, b f æquales
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            ex 35 primi libri
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            conicorum. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">h o ipſius g b
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            eſt dupla. </s>
            <s xml:space="preserve">quod demonſtrare oportebat.</s>
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            <note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">4. ſexti.</note>
            <note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve">22. ſexti.
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            cor. 20. ſe
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            xti.</note>
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          <head xml:space="preserve">LEMMA IIII.</head>
          <p style="it">
            <s xml:space="preserve">Iiſdem manentibus, & </s>
            <s xml:space="preserve">à puncto m ducta m q uſque
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            ad diametrum, quæ ſectionem in puncto m conting at;
              <lb/>
            </s>
            <s xml:space="preserve">Dico h q ad q o eandem proportionem habere, quam
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            habet g h ad c n.</s>
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          </p>
          <p style="it">
            <s xml:space="preserve">F_IAT_ enim h r æqualis g f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cumtriangula a f c, o p n ſimi
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            lia ſint, & </s>
            <s xml:space="preserve">p n ſit æqualis f c; </s>
            <s xml:space="preserve">eodem modo demonſtrabimus p o, f a
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            inter ſe æquales eſſe. </s>
            <s xml:space="preserve">quare p o ipſius f b dupla erit. </s>
            <s xml:space="preserve">Sed eſt h o du
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            pla g b. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliqua p h reliquæ f g; </s>
            <s xml:space="preserve">uidelicet ipſius r h eſt du-</s>
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