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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FED. COMMANDINI
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            qr, eodem, quo ſupra, modo oſtendemns f g ad p q, ut f h
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            ad p r. </s>
            <s xml:space="preserve">ſed priſma a e ad ipſum k o eſt, ut f h ad p r. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">ut f g axis ad axem p q. </s>
            <s xml:space="preserve">ex quibus fit, ut pyramis a b c d f
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            ad pyrami-
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              <anchor type="figure" xlink:label="fig-0164-01a" xlink:href="fig-0164-01"/>
            dẽ k l m n p
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            eandem-ha
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            beat pro-
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            portionẽ,
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            quãaxis ad
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            axẽ. </s>
            <s xml:space="preserve">quod
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            demonſtrã
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            dũ fuerat.</s>
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            <s xml:space="preserve">Simili ra
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            tione in a-
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            liis priſma-
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            tibus & </s>
            <s xml:space="preserve">py
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            ramidibus eadem demonſtrabuntur.</s>
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          <head xml:space="preserve">THEOREMA XVII. PROPOSITIO XXI.</head>
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            <s xml:space="preserve">Priſmata omnia, & </s>
            <s xml:space="preserve">pyramides inter ſe propor
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            tionem habent compoſitam ex proportione ba-
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            ſium, & </s>
            <s xml:space="preserve">proportione altitudinum.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sint duo priſmata a e, g m: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">priſmatis a e baſis qua
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            drilaterum a b c d, & </s>
            <s xml:space="preserve">altitudo e f: </s>
            <s xml:space="preserve">priſmatis uero g m ba-
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            fis quadrilaterum g h K l, & </s>
            <s xml:space="preserve">altitudo m n. </s>
            <s xml:space="preserve">Dico priſma a e
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            ad priſma g m proportionem habere compoſitam ex pro
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            portione baſis a b c d ad baſim g h k l, & </s>
            <s xml:space="preserve">ex proportione
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            altitudinis e f, ad altitudinem m n.</s>
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          <p>
            <s xml:space="preserve">Sint enim primum e f, m n æquales: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut baſis a b c d
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            ad baſim g h k l, ita fiat linea, in qua o ad lineam, in qua p:
              <lb/>
            </s>
            <s xml:space="preserve">ut autem e f ad m n, ita linea p ad lineam q. </s>
            <s xml:space="preserve">erunt lineæ
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            p q inter ſe æquales. </s>
            <s xml:space="preserve">Itaque priſma a e ad priſma g m eã</s>
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