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 GRA VIT. SOLID.
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              <pb o="11" file="0133" n="133" rhead="DE CENTRO GRA VIT. SOLID."/>
            & </s>
            <s xml:space="preserve">per o ducatur o p ad k m ipſi h g æquidiſtans. </s>
            <s xml:space="preserve">Itaque li
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            nea h m bifariã uſque eò diuidatur, quoad reliqua ſit pars
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            quædam q m, minor o p. </s>
            <s xml:space="preserve">deinde h m, m g diuidantur in
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            partes æ quales ipſi m q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per diuiſiones lineæ ipſi m K
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            æ quidiſtantes ducantur. </s>
            <s xml:space="preserve">puncta uero, in quibus hæ trian-
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            gulorum latera ſecant, coniungantur ductis lineis r s, t u,
              <lb/>
              <anchor type="figure" xlink:label="fig-0133-01a" xlink:href="fig-0133-01"/>
            x y; </s>
            <s xml:space="preserve">quæ baſi g h æquidiſtabunt. </s>
            <s xml:space="preserve">Quoniam enim lineæ g z,
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            h α ſunt æ quales: </s>
            <s xml:space="preserve">itemq; </s>
            <s xml:space="preserve">æquales g m, m h: </s>
            <s xml:space="preserve">ut m g ad g z,
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            ita erit m h, ad h α: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo, ut m z ad z g, ita m α ad
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            α h. </s>
            <s xml:space="preserve">Sed ut m z ad z g, ita k r ad r g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut m α ad α h, ita k s
              <lb/>
              <anchor type="note" xlink:label="note-0133-01a" xlink:href="note-0133-01"/>
            ad s h. </s>
            <s xml:space="preserve">quare ut κ r ad r g, ita k s ad s h. </s>
            <s xml:space="preserve">æ quidiſtant igitur
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              <anchor type="note" xlink:label="note-0133-02a" xlink:href="note-0133-02"/>
            inter ſe ſe r s, g h. </s>
            <s xml:space="preserve">eadem quoque ratione demonſtrabimus
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              <anchor type="note" xlink:label="note-0133-03a" xlink:href="note-0133-03"/>
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