Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[41. COMMENTARIVS.]
[42. LEMMA I.]
[43. LEMMA II.]
[44. LEMMA III.]
[45. LEMMA IIII.]
[46. LEMMA V.]
[47. LEMMA VI.]
[48. II.]
[49. III.]
[50. IIII.]
[51. V.]
[52. DEMONSTRATIO SECVNDAE PARTIS.]
[53. COMMENTARIVS.]
[54. DEMONSTRATIO TERTIAE PARTIS.]
[55. COMMENTARIVS.]
[56. DEMONSTRATIO QVARTAE PARTIS.]
[57. DEMONSTRATIO QVINT AE PARTIS.]
[58. FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.]
[59. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.]
[60. CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.]
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DE IIS QVAE VEH. IN AQVA.
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              <pb o="39" file="0089" n="89" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _neæ autem a d inter ſe æquales ſunt. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ipſæ a η, a θ. </s>
            <s xml:space="preserve">Sed ſunt_
              <lb/>
            _æquales a o, a q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">earum dimidiæ a t a n. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliquæ t η, n θ_
              <lb/>
            _boc eſt p g, m y. </s>
            <s xml:space="preserve">ut autem p g ad g h, ita m y ad y c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutan_
              <lb/>
              <anchor type="note" xlink:label="note-0089-01a" xlink:href="note-0089-01"/>
            _do, ut p g ad m y, ita g s ad y c. </s>
            <s xml:space="preserve">quare g s, y c æquales ſunt: </s>
            <s xml:space="preserve">&_</s>
            <s xml:space="preserve">
              <lb/>
            _ipſarum dimidiæ b s, b c: </s>
            <s xml:space="preserve">ex quibus ſequitur ut & </s>
            <s xml:space="preserve">reliquæ s r, c r_:
              <lb/>
            </s>
            <s xml:space="preserve">_& </s>
            <s xml:space="preserve">idcirco p z, m u & </s>
            <s xml:space="preserve">u n, z t inter ſe ſunt æquales_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="9">
            <note position="left" xlink:label="note-0088-05" xlink:href="note-0088-05a" xml:space="preserve">K</note>
            <figure xlink:label="fig-0088-01" xlink:href="fig-0088-01a">
              <image file="0088-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0088-01"/>
            </figure>
            <note position="left" xlink:label="note-0088-06" xlink:href="note-0088-06a" xml:space="preserve">4. ſexti.</note>
            <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">34. primi</note>
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          <p>
            <s xml:space="preserve">Quoniam igitur m u minor eſt, quàm dupla u n.</s>
            <s xml:space="preserve">] _Eſt_
              <lb/>
              <anchor type="note" xlink:label="note-0089-02a" xlink:href="note-0089-02"/>
            _enim m h ipſius h n dupla, & </s>
            <s xml:space="preserve">m u minor ipſa m h. </s>
            <s xml:space="preserve">ergo m u minor_
              <lb/>
            _eſt, quàm dupla h n; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">multo minor, quàm dupla ipſius u n_.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="10">
            <note position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">L</note>
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          <p>
            <s xml:space="preserve">Non ergo manebit portio, ſed reuoluetur, ita ut baſis ip
              <lb/>
              <anchor type="note" xlink:label="note-0089-03a" xlink:href="note-0089-03"/>
            ſius humidi ſuperſiciem nullo modo contingat. </s>
            <s xml:space="preserve">quoniam
              <lb/>
            nunc in uno puncto contingens ſurſum fertur ex parte a.</s>
            <s xml:space="preserve">]
              <lb/>
            _Tranſlatio ſic habet. </s>
            <s xml:space="preserve">non ergo manet portio ſed inclinabitur, ut ba_-
              <lb/>
            _ſis ipſius nec ſecundum unum tang at ſuperficiem humidi, quoniam_
              <lb/>
            _nunc ſecundum unum tacta ipſa reclinatur. </s>
            <s xml:space="preserve">Quæ nos ex alijs Ar_-
              <lb/>
            _chimedis locis, & </s>
            <s xml:space="preserve">perſpicuitatis cauſſa in eum modum corrigenda_
              <lb/>
            _duximus. </s>
            <s xml:space="preserve">In ſexta enim propoſitione huius ita ſcribit, ut habetur in_
              <lb/>
            _tranſlatione. </s>
            <s xml:space="preserve">reuoluetur ergo ſolidum a p o l, & </s>
            <s xml:space="preserve">baſis ipſius nó tan_
              <lb/>
            _get ſuperficiem humidi ſecundum unum ſignum. </s>
            <s xml:space="preserve">Rurſus in ſeptima_
              <lb/>
            _propoſitione. </s>
            <s xml:space="preserve">manifeſtum igitur, quòd reuoluetur ſolidum ita ut ba_-
              <lb/>
            _ſis ipſius nec ſecundum unum ſignum contingat ſuperficiem humidi_,
              <lb/>
            _quoniam nunc ſecundum unum tangens deorſum fertur ex parte l_.
              <lb/>
            </s>
            <s xml:space="preserve">_At uero portionem ſurſum ferri ex parte a manifeſte constat. </s>
            <s xml:space="preserve">nam_
              <lb/>
            _cumperpendicularis ad ſuperficiem humidi, quæ tranſit per ω ad_
              <lb/>
            _partes a cadat, & </s>
            <s xml:space="preserve">quæ per e ad partes l, neceſſe eſt ut centrum ω_
              <lb/>
            _ſurſum, e uero deorſum feratur_.</s>
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          <div type="float" level="2" n="11">
            <note position="right" xlink:label="note-0089-03" xlink:href="note-0089-03a" xml:space="preserve">M</note>
          </div>
          <p>
            <s xml:space="preserve">Perſpicuum eſtigitur portionem conſiſtere ita, ut axis
              <lb/>
              <anchor type="note" xlink:label="note-0089-04a" xlink:href="note-0089-04"/>
            cum ſuperficie humidi faciat angulum maiorem angu-
              <lb/>
            10 χ.</s>
            <s xml:space="preserve">] _Iuncta enim a x producatur, ut diametrum b d ſe_-
              <lb/>
            _cet in λ, & </s>
            <s xml:space="preserve">ab o puncto ipſi æquidistans ducatur o χ. </s>
            <s xml:space="preserve">con_-
              <lb/>
            _tinget eaſectionem in o, ut in prima figura: </s>
            <s xml:space="preserve">atque erit angu_-
              <lb/>
              <anchor type="note" xlink:label="note-0089-05a" xlink:href="note-0089-05"/>
            _lus ad χ angulo ad λ æqualis. </s>
            <s xml:space="preserve">Sed angulus ad y æqualis est_
              <lb/>
            _angulo ad θ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">angulus a θ d maior angulo a λ d; </s>
            <s xml:space="preserve">quod ex_-
              <lb/>
              <anchor type="note" xlink:label="note-0089-06a" xlink:href="note-0089-06"/>
            _traipſum cadat. </s>
            <s xml:space="preserve">ergo angulus ad y eo, qui ad χ maior erit_.</s>
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