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 CENTRO GRAVIT. SOLID.
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          <p>
            <s xml:space="preserve">Ex demonſtratis perſpicue apparet, portioni
              <lb/>
            ſphæræ uel ſphæroidis, quæ dimidia maior eſt, cẽ
              <lb/>
            trum grauitatis in axe conſiſtere.</s>
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          </p>
          <p>
            <s xml:space="preserve">Data enim
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              <anchor type="figure" xlink:label="fig-0155-01a" xlink:href="fig-0155-01"/>
            qualibet maio
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            ri portiõe, quo
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            niã totius ſphæ
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            ræ, uel ſphæroi
              <lb/>
            dis grauitatis
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            centrum eſt in
              <lb/>
            axe; </s>
            <s xml:space="preserve">eſt autem
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            & </s>
            <s xml:space="preserve">in axe cen-
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            trum portio-
              <lb/>
            nis minoris:
              <lb/>
            </s>
            <s xml:space="preserve">reliquæ portionis uidelicet maioris centrum in axe neceſ-
              <lb/>
            ſario conſiſtet.</s>
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            <figure xlink:label="fig-0155-01" xlink:href="fig-0155-01a">
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        <div type="section" level="1" n="82">
          <head xml:space="preserve">THE OREMA XIII. PROPOSITIO XVII.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet pyramidis triã
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              <anchor type="figure" xlink:label="fig-0155-02a" xlink:href="fig-0155-02"/>
            gularem baſim habẽtis gra
              <lb/>
            uitatis centrum eſt in pun-
              <lb/>
            cto, in quo ipſius axes con-
              <lb/>
            ueniunt.</s>
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          </p>
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            <figure xlink:label="fig-0155-02" xlink:href="fig-0155-02a">
              <image file="0155-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0155-02"/>
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          <p>
            <s xml:space="preserve">Sit pyramis, cuius baſis trian
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            gulum a b c, axis d e: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">trian
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            guli b d c grauitatis centrum f:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur a f. </s>
            <s xml:space="preserve">erit & </s>
            <s xml:space="preserve">a faxis eiuſ
              <lb/>
            dem pyramidis ex tertia diffini-
              <lb/>
            tione huius. </s>
            <s xml:space="preserve">Itaque quoniam centrum grauitatis eſt in
              <lb/>
            axe d e; </s>
            <s xml:space="preserve">eſt autem & </s>
            <s xml:space="preserve">in axe a f; </s>
            <s xml:space="preserve">quod proxime demonſtraui</s>
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