Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[81. THE OREMA XII. PROPOSITIO XVI.]
[82. THE OREMA XIII. PROPOSITIO XVII.]
[83. THEOREMA XIIII. PROPOSITIO XVIII.]
[84. THEOREMA XV. PROPOSITIO XIX.]
[85. THE OREMA XVI. PROPOSITIO XX.]
[86. THEOREMA XVII. PROPOSITIO XXI.]
[87. THE OREMA XVIII. PROPOSITIO XXII.]
[88. THEOREMA XIX. PROPOSITIO XXIII.]
[89. PROBLEMA V. PROPOSITIO XXIIII.]
[90. THEOREMA XX. PROPOSITIO XXV.]
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DE CENTRO GRAVIT. SOLID.
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              <pb o="39" file="0189" n="189" rhead="DE CENTRO GRAVIT. SOLID."/>
            dem, cuius baſis eſt quadratum a b c d, & </s>
            <s xml:space="preserve">altitudo e g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            in pyramidem, cuius eadé baſis, altitudoq; </s>
            <s xml:space="preserve">f g; </s>
            <s xml:space="preserve">ut ſint e g,
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            g f ſemidiametri ſphæræ, & </s>
            <s xml:space="preserve">linea una. </s>
            <s xml:space="preserve">Cũigitur g ſit ſphæ-
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            ræ centrum, erit etiam centrum circuli, qui circa quadratũ
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            a b c d deſcribitur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea eiuſdem quadrati grauita
              <lb/>
            tis centrum: </s>
            <s xml:space="preserve">quod in prima propoſitione huius demon-
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            ſtratum eſt. </s>
            <s xml:space="preserve">quare pyramidis a b c d e axis erit e g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pyra
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            midis a b c d f axis f g. </s>
            <s xml:space="preserve">Itaque ſit h centrum grauitatis py-
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            ramidis a b c d e, & </s>
            <s xml:space="preserve">pyramidis a b c d f centrum ſit _K_: </s>
            <s xml:space="preserve">per-
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            ſpicuum eſt ex uigeſima ſecunda propoſitione huius, lineã
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            e h triplam eſſe h g: </s>
            <s xml:space="preserve">cõ
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              <anchor type="figure" xlink:label="fig-0189-01a" xlink:href="fig-0189-01"/>
            ponendoq; </s>
            <s xml:space="preserve">e g ipſius g
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            h quadruplam. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eadẽ
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            ratione f g quadruplã
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            ipſius g k. </s>
            <s xml:space="preserve">quod cum e
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            g, g f ſintæquales, & </s>
            <s xml:space="preserve">h
              <lb/>
            g, g _k_ neceſſario æqua-
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            les erunt. </s>
            <s xml:space="preserve">ergo ex quar
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            ta propoſitione primi
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            libri Archimedis de cẽ-
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            tro grauitatis planorũ,
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            totius octahedri, quod
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            ex dictis pyramidibus
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            conſtat, centrum graui
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            tatis erit punctum g idem, quodipſius ſphæræ centrum.</s>
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          </p>
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            <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a">
              <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0189-01"/>
            </figure>
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          <p>
            <s xml:space="preserve">Sit icoſahedrum a d deſcriptum in ſphæra, cuius centrū
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            ſit g. </s>
            <s xml:space="preserve">Dico g ipſius icoſahedri grauitatis eſſe centrum. </s>
            <s xml:space="preserve">Si
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            enim ab angnlo a per g ducatur rectalinea uſque ad ſphæ
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            ræ ſuperficiem; </s>
            <s xml:space="preserve">conſtat ex ſexta decima propoſitione libri
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            tertii decimi elementorum, cadere eam in angulum ipſi a
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            oppoſitum. </s>
            <s xml:space="preserve">cadat in d: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">una aliqua baſis icoſahedri tri-
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            angulum a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iunctæ b g, c g producantur, & </s>
            <s xml:space="preserve">cadant in
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            angulos e f, ipſis b c oppoſitos. </s>
            <s xml:space="preserve">Itaque per triangula
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            a b c, d e f ducantur plana ſphæram ſecantia. </s>
            <s xml:space="preserve">erunt hæ ſe-</s>
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