Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[61. ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.]
[62. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.]
[63. PETITIONES.]
[64. THEOREMA I. PROPOSITIO I.]
[65. THEOREMA II. PROPOSITIO II.]
[66. THE OREMA III. PROPOSITIO III.]
[67. THE OREMA IIII. PROPOSITIO IIII.]
[68. ALITER.]
[69. THEOREMA V. PROPOSITIO V.]
[70. COROLLARIVM.]
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DE IIS QVAE VEH. IN AQVA.
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            <s xml:space="preserve">
              <pb o="2" file="0015" n="15" rhead="DE IIS QVAE VEH. IN AQVA."/>
            loq; </s>
            <s xml:space="preserve">lineæ ſumptæ circulus deſcribatur. </s>
            <s xml:space="preserve">cadet ergo ipſius
              <lb/>
            circunferentia partim
              <lb/>
              <anchor type="figure" xlink:label="fig-0015-01a" xlink:href="fig-0015-01"/>
            extra lineam a b c d, par
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            tim intra; </s>
            <s xml:space="preserve">quoniam ea,
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            quæ ex centro quibuſ-
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            dam quidem à puncto
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            k ad ipſam ductis eſtma
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            ior; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quibuſdam mi-
              <lb/>
            nor. </s>
            <s xml:space="preserve">Itaq; </s>
            <s xml:space="preserve">ſit circuli de-
              <lb/>
            ſcripti circunferentia
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            fb h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex b ad k ducta
              <lb/>
            linea, iungãtur fk k h e,
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            quæ angulos æquales faciant. </s>
            <s xml:space="preserve">deſcribatur autem & </s>
            <s xml:space="preserve">ex cen
              <lb/>
            tro k circunferentia quædam x o p in plano, & </s>
            <s xml:space="preserve">in humido.
              <lb/>
            </s>
            <s xml:space="preserve">ergo partes humidi, quæ ſunt ad circunferentiam x o p æ-
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            qualiter iacent, ac continuatæ inter ſe ſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">premũtur qui
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            dem partes, quæ ad x o circunferentiam, humido, quod lo
              <lb/>
            co a b continetur: </s>
            <s xml:space="preserve">quæ uero ad circunferentiam o p pre-
              <lb/>
            muntur humido, quod continetur b e. </s>
            <s xml:space="preserve">inæqualiter igitur
              <lb/>
            premuntur partes humidi ad cir cunferentiã x o, & </s>
            <s xml:space="preserve">ad o p. </s>
            <s xml:space="preserve">
              <lb/>
            quare minus preſſæ à magis presſis expellentur. </s>
            <s xml:space="preserve">non er-
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            go conſiſtet humidum. </s>
            <s xml:space="preserve">Atqui ponebatur conſiſtens, & </s>
            <s xml:space="preserve">ma
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            nens. </s>
            <s xml:space="preserve">neceſſarium eſt igitur lineam a b c d eſſe circuli cir
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            cunferentiam, cuius centrum k. </s>
            <s xml:space="preserve">Similiter autem demon-
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            ſtrabitur, & </s>
            <s xml:space="preserve">ſi quomodocunque aliter ſuperficies humidi
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            plano ſecta fuerit per centrum terræ ſectionem circuli cir
              <lb/>
            cunferentiam eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">centrum ipſius eſſe, quod & </s>
            <s xml:space="preserve">terræ cen
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            trum. </s>
            <s xml:space="preserve">Ex quibus conſtat ſuperficiem humidi conſiſtentis,
              <lb/>
              <anchor type="note" xlink:label="note-0015-01a" xlink:href="note-0015-01"/>
            atque manentis ſphæricam eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eius ſphæræ centrum
              <lb/>
            idem, quod centrum terræ: </s>
            <s xml:space="preserve">quoniam eiuſmodi eſt, ut ſecta
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            per idem ſemper punctum ſectionem faciat circuli circun
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            ferentiam, centrum habentis punctum illud, per quod ipſa
              <lb/>
            plano ſecatur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0015-01" xlink:href="fig-0015-01a">
              <image file="0015-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0015-01"/>
            </figure>
            <note position="right" xlink:label="note-0015-01" xlink:href="note-0015-01a" xml:space="preserve">Prima hu
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            ius.</note>
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