Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[71. THEOREMA VI. PROPOSITIO VI.]
[72. THE OREMA VII. PROPOSITIO VII.]
[73. THE OREMA VIII. PROPOSITIO VIII.]
[74. THE OREMA IX. PROPOSITIO IX.]
[75. PROBLEMA I. PROPOSITIO X.]
[76. PROBLEMA II. PROPOSITIO XI.]
[77. PROBLEMA III. PROPOSITIO XII.]
[78. PROBLEMA IIII. PROPOSITIO XIII.]
[79. THEOREMA X. PROPOSITIO XIIII.]
[80. THE OREMA XI. PROPOSITIO XV.]
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FED. COMMANDINI
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          <head xml:space="preserve">THE OREMA XII. PROPOSITIO XVI.</head>
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            <s xml:space="preserve">In ſphæra, & </s>
            <s xml:space="preserve">ſphæroide idem eſt grauitatis, & </s>
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            figuræ centrum.</s>
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            <s xml:space="preserve">Secetur ſphæra, uel ſphæroid
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            no per axem ducto;
              <lb/>
            </s>
            <s xml:space="preserve">quod ſectionem faciat circulum,
              <gap/>
            ellipſim a b c d, cuius
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            diameter, & </s>
            <s xml:space="preserve">ſphæræ, uelſphæroidis axis d b; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">centrume. </s>
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            Dico e grauitatis etiam centrum eſſe. </s>
            <s xml:space="preserve">ſecetur enim altero
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            plano per e, ad planum ſecans recto, cuius fectio ſit circu-
              <lb/>
            lus circa diametrum a c. </s>
            <s xml:space="preserve">erunt a d c, a b c dimidiæ portio-
              <lb/>
            nes ſphæræ, uel fphæroidis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam portionis a d c gra
              <lb/>
            uitatis centrum eſt in linea d, & </s>
            <s xml:space="preserve">centrum portionis a b c in
              <lb/>
            ipſa b e; </s>
            <s xml:space="preserve">totius ſphæræ, uel ſphæroidis grauitatis centrum
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            in axe d b conſiſtet. </s>
            <s xml:space="preserve">Quòd ſi portionis a d c centrum graui
              <lb/>
            tatis ponatur eſſe f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fiat ipſi f e æqualis e g: </s>
            <s xml:space="preserve">punctũ g por
              <lb/>
              <anchor type="figure" xlink:label="fig-0154-01a" xlink:href="fig-0154-01"/>
            tionis a b c centrum erit. </s>
            <s xml:space="preserve">ſolidis enim figuris ſimilibus & </s>
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              <anchor type="note" xlink:label="note-0154-01a" xlink:href="note-0154-01"/>
            æqualibus inter ſe aptatis, & </s>
            <s xml:space="preserve">centra grauitatis ipſarum in-
              <lb/>
            ter fe aptentur neceſſe eſt. </s>
            <s xml:space="preserve">ex quo fit, ut magnitudinis, quæ
              <lb/>
              <anchor type="note" xlink:label="note-0154-02a" xlink:href="note-0154-02"/>
            ex utriſque cõſtat, hoc eſt ipſius ſphæræ, uel ſphæroidis gra
              <lb/>
            uitatis centrum ſitin medio lineæ f g, uidelicet in e. </s>
            <s xml:space="preserve">Sphæ-
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            ræ igitur, uel ſphæroidis grauitatis centrum eſtidem, quod
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            centrum figuræ.</s>
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            <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a">
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            <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">per 2. pe-
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            titionem</note>
            <note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">4 Arch-
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            medis.</note>
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