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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        <div type="section" level="1" n="34">
          <p>
            <s xml:space="preserve">
              <pb file="0054" n="54" rhead="ARCHIMEDIS"/>
            modo hum idi ſuperficiem continget.</s>
            <s xml:space="preserve">] _In translatione le-_
              <lb/>
            _gebatur ut baſis ipſius non tangat ſuperficiem humidi ſecundum_
              <lb/>
            _unum ſignum. </s>
            <s xml:space="preserve">nos autem ita uertere maluimus, & </s>
            <s xml:space="preserve">hic & </s>
            <s xml:space="preserve">in ijs,_
              <lb/>
            _quæ ſequuntur, quoniam græci οὐδὲ \~εις, οὐδὲ ἓν, pro οὐ δεὶς, &_</s>
            <s xml:space="preserve">
              <lb/>
            _οὐδε ν frequenter utútur. </s>
            <s xml:space="preserve">ut οὐδ ε ςιν οὐ δεὶς, nullus eſt: </s>
            <s xml:space="preserve">οὐ \’δ ὑφ
              <unsure/>
            ἑ νὸς,_
              <lb/>
            _ànullo & </s>
            <s xml:space="preserve">alia eiuſmodi._</s>
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            <note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve">E</note>
          </div>
        </div>
        <div type="section" level="1" n="35">
          <head xml:space="preserve">PROPOSITIO VII.</head>
          <p>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
              <lb/>
            leuior humido axem habuerit maiorem quidem
              <lb/>
            quàm ſeſquialtérum eius, quæ uſque ad axem;
              <lb/>
            </s>
            <s xml:space="preserve">minorem uero, quàm ut ad eam, quæ uſque ad
              <lb/>
            axem proportionem habeat, quam quindecim
              <lb/>
            ad quatuor: </s>
            <s xml:space="preserve">in humidum demiſſa, adeo ut baſis
              <lb/>
            ipſius tota ſitin humido; </s>
            <s xml:space="preserve">nunquam conſiſtet ita,
              <lb/>
            ut baſis contingat humidi ſuperficiem: </s>
            <s xml:space="preserve">ſed ut to-
              <lb/>
            ta in humido ſit, & </s>
            <s xml:space="preserve">nullo modo eius ſuperficiem
              <lb/>
            contingat.</s>
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            <s xml:space="preserve">SIT portio qualis dicta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">demittatur in humidũ,
              <lb/>
            ut diximus, adeo ut baſis ipſius in uno puncto contingat
              <lb/>
            humidi ſuperficiem. </s>
            <s xml:space="preserve">Demonſtrandum eſt non manere ip-
              <lb/>
            ſam: </s>
            <s xml:space="preserve">ſed reuolui ita ut baſis fuperficiem humidi nullo mo-
              <lb/>
            do contingat. </s>
            <s xml:space="preserve">Secta enim ipſa plano per axem, recto ad ſu
              <lb/>
            perficiem humidi, ſectio ſit a p o l rectanguli coni ſectio:
              <lb/>
            </s>
            <s xml:space="preserve">ſuperficiei humidi ſectio ſit s 1: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectio-
              <lb/>
            nis diameter p f: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">p f in r quidem ita ut r p ſit
              <lb/>
            dupla ipſius r f; </s>
            <s xml:space="preserve">in ω autem ut p f ad r ω proportionem
              <lb/>
            habeat, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ω k ipſi p f ad re-
              <lb/>
            ctos angulos ducatur erit r ω minor, quàm quæ uſque ad
              <lb/>
            axem. </s>
            <s xml:space="preserve">Itaque accipiatur ei, quæ uſque ad axem æqualis rh:</s>
            <s xml:space="preserve"/>
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