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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ARCHIME DIS
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            dam non minor est proportio, quàm tertiæ & </s>
            <s xml:space="preserve">quartæ ad quartam;
              <lb/>
            </s>
            <s xml:space="preserve">est enim quadratum m o unà cum exceſſu, quo quadratum n o exce
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            dit quadratum m o æquale ipſi n o quadrato. </s>
            <s xml:space="preserve">quare per conuerſio
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            nem rationis ex 30 eiuſdem, primæ & </s>
            <s xml:space="preserve">ſecundæ ad primam non ma-
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            ior proportio erit, quàm tertiæ & </s>
            <s xml:space="preserve">quartæ ad tertiam: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco to-
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            ta portio ad portionem eam, quæ est extra bumidum non maiorem
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            proportionem babebit, quàm quadratum n o ad quadratum mo. </s>
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              <lb/>
            quod demonstrandum proponebatur.</s>
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            <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">A</note>
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            <s xml:space="preserve">Habet autem tota portio ad eam, quæ extra humidum
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            proportionem eandem, quam quadratum n o ad quadra
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            tum p f.</s>
            <s xml:space="preserve">] _Ex uigeſimaſexta libri de conoidibus, & </s>
            <s xml:space="preserve">ſpbæroi-_
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            _dibus._</s>
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            <s xml:space="preserve">Ex quo eſſicitur, ut p ſ non ſit minor ipſa o m; </s>
            <s xml:space="preserve">neque
              <lb/>
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            pb ipſa o h.</s>
            <s xml:space="preserve">] _Sequitur illud ex decima & </s>
            <s xml:space="preserve">decimaquarta quinti,_
              <lb/>
            _& </s>
            <s xml:space="preserve">ex uigeſimaſecunda ſexti elementorum, ut ſuperius dictum eſt._</s>
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            <s xml:space="preserve">Quæ ergo ab h ducitur ad rectos angulos ipſi n o coi-
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            bit cum p b inter p & </s>
            <s xml:space="preserve">b.</s>
            <s xml:space="preserve">] _Cur boc ita contingat, nos proxi-_
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            _me explicauimus._</s>
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            <note position="left" xlink:label="note-0044-03" xlink:href="note-0044-03a" xml:space="preserve">D</note>
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          <head xml:space="preserve">PROPOSITIO VI.</head>
          <p>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
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            leuior humido axem habuerit maiorem quidem
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            quàm ſeſquialterum eius, quæ uſque ad axem,
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            minorem nero, quàm ut ad eam, quæ uſque ad
              <lb/>
            axem proportionem habeat, quam quindecim
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            ad quatuor; </s>
            <s xml:space="preserve">in humidum demiſſa adeo, ut baſis
              <lb/>
            ipſius contingat humidum, nunquam conſiſtet
              <lb/>
            inclinata ita, ut baſis in uno puncto humidum
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            contingat.</s>
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