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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            itemq; </s>
            <s xml:space="preserve">ſimilia triangula a b c, e f g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a c d, e g h. </s>
            <s xml:space="preserve">idcir-
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            coq; </s>
            <s xml:space="preserve">latera ſibi ipſis reſpondentia eandem inter ſe ſe pro-
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            portionem ſeruant. </s>
            <s xml:space="preserve">Vt igitur duplum lateris a b unà
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            cum latere e f ad duplum lateris e f unà cum a b, ita eſt
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            duplum a d late-
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              <anchor type="figure" xlink:label="fig-0184-01a" xlink:href="fig-0184-01"/>
            ris unà cum late-
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            re e h ad duplum
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            e h unà cum a d:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita in aliis. </s>
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            Rurſus fruſtum
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            a g ad pyramidẽ,
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            cuius eadem eſt
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            bafis, & </s>
            <s xml:space="preserve">æqualis
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            altitudo eandem
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            proportionẽ ha
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            bet, quam fruſtũ
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            l f ad pyramidẽ,
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            quæ eſt eadẽ ba-
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            ſi, & </s>
            <s xml:space="preserve">æquali alti-
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            tudine: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſimili-
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            ter quam l h fru-
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            ſtum ad pyrami-
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            dem, quæ ex ea-
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            dẽ baſi, & </s>
            <s xml:space="preserve">æquali
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            altitudine con-
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            ſtat. </s>
            <s xml:space="preserve">nam ſi inter
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            ipſas baſes me-
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            diæ proportio-
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            nales conſtituan
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            tur, tres baſes ſimul ſumptæ ad maiorem baſim in om-
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            nibus eodem modo ſe habebunt. </s>
            <s xml:space="preserve">Vnde fit, ut axes K l,
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            q r, t u à punctis p s x in eandem proportionem ſecen-
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            tur. </s>
            <s xml:space="preserve">ergo linea x s per p tranſibit: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">lineæ r u, s x, q t in-
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              <anchor type="note" xlink:label="note-0184-01a" xlink:href="note-0184-01"/>
            ter ſe æquidiſtantes erunt. </s>
            <s xml:space="preserve">Itaque cum fruſti a g latera pro-</s>
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