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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DE IIS QVAE VEH. IN AQVA.
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              <pb o="16" file="0043" n="43" rhead="DE IIS QVAE VEH. IN AQVA."/>
            dratum n o ad quadratum p f. </s>
            <s xml:space="preserve">quadratum igitur n o ad
              <lb/>
            quadratum p f non maiorem proportionem habet, quàm
              <lb/>
            ad quadratum m o. </s>
            <s xml:space="preserve">ex quo eſſicitur, ut p f non ſit minor
              <lb/>
              <anchor type="note" xlink:label="note-0043-01a" xlink:href="note-0043-01"/>
            ipſa o m; </s>
            <s xml:space="preserve">neque p b ipſa o h. </s>
            <s xml:space="preserve">quæ ergo ab h ducitur ad
              <lb/>
              <anchor type="note" xlink:label="note-0043-02a" xlink:href="note-0043-02"/>
            rectos angulos ipſi n o, coibit cum b p inter p & </s>
            <s xml:space="preserve">b. </s>
            <s xml:space="preserve">co-
              <lb/>
            eatin t. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam in rectanguli coniſectione p f eſt æqui
              <lb/>
            diſtans diametro n o; </s>
            <s xml:space="preserve">h t autem ad diametrum perpẽ-
              <lb/>
            dicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">r h æqualis ei, quæ uſque ad axem: </s>
            <s xml:space="preserve">conſtat r t
              <lb/>
            productam ſacere angulos rectos cum ipſa k p ω. </s>
            <s xml:space="preserve">quare
              <lb/>
            & </s>
            <s xml:space="preserve">cum is. </s>
            <s xml:space="preserve">ergo rt perpendicularis eſt ad ſuperſiciem hu
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            midi. </s>
            <s xml:space="preserve">et ſi per b g puncta ducantur æquidiſtantes ipſirt,
              <lb/>
            ad ſuperſiciem humidi perpendicular es erunt. </s>
            <s xml:space="preserve">portio igi
              <lb/>
            tur, qnæ eſt extra humidum, deorſum in humidum feretur
              <lb/>
            ſecundum perpendicularem per b ductam; </s>
            <s xml:space="preserve">quæ uero in-
              <lb/>
            tra humidum ſecundum perpendicularem per g ſurſum
              <lb/>
            feretur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">non manebit ſolida portio a p o l, ſedintra hu
              <lb/>
            midum mouebitur, donecutique ipſa n o ſecundum per-
              <lb/>
            pendicularem ſiat.</s>
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            <figure xlink:label="fig-0042-01" xlink:href="fig-0042-01a">
              <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0042-01"/>
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            <note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">11. quin-
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            ti.</note>
            <note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">A</note>
            <note position="left" xlink:label="note-0042-03" xlink:href="note-0042-03a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">D</note>
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        <div type="section" level="1" n="28">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:space="preserve">_Quare non maiorem proportionem habet tota portio_
              <lb/>
              <anchor type="note" xlink:label="note-0043-03a" xlink:href="note-0043-03"/>
            _ad eam, quæ eſt extra humidum, quam quadratum n o ad_
              <lb/>
            _quadratum m o]_ cum enim magnitudo portionis in bumidum
              <lb/>
            demerſa ad totam portionem non maiorem proportionem babeat,
              <lb/>
            quàm exceſſus, quo quadratum n o excedit quadratum m o, ad ip-
              <lb/>
            ſum no quadratum: </s>
            <s xml:space="preserve">conuertendo per uigeſimáſextam quinti ele-
              <lb/>
            mentorum ex traditione Campani, tota portio ad magnitudinem de
              <lb/>
            merſam non minorem proportionem babebit, quàm quadratum n o
              <lb/>
            ad exceſſum, quo ipſum quadratum no excedit quadratum m o. </s>
            <s xml:space="preserve">In
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            telligatur portio, quæ extra bumidum, magnitudo prima: </s>
            <s xml:space="preserve">quæ in bu
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            mido demerſa est, ſecunda: </s>
            <s xml:space="preserve">tertia autem magnitudo ſit quadratum
              <lb/>
            mo: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">exceſſus, quo quadratum n o excedit quadratum m o ſit
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            quarta. </s>
            <s xml:space="preserve">ex his igitur magnitudinibus, primæ & </s>
            <s xml:space="preserve">ſecundæ ad ſecun-</s>
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