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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ARCHIMEDIS
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            midum demiſſa adeo, ut baſis ipſius tota ſit in hu
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            mido, & </s>
            <s xml:space="preserve">poſita inclinata, nec conuertetur ita, ut
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            axis ipſius ſecũdum perpendicularem ſit, nec ma
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            nebit inclinata, niſi quãdo axis cum ſuperficie hu
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            midi angulum fecerit æqualem angulo ſimiliter
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            ut prius, aſſumpto.</s>
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            <s xml:space="preserve">SIT portio, qualis dicta eſt: </s>
            <s xml:space="preserve">ponaturq; </s>
            <s xml:space="preserve">d b æ qualis axi
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            portionis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b _k_ quidem ſit dupla ipſius _k_ d; </s>
            <s xml:space="preserve">k r autem
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            æqualis ei, quæ uſque ad axem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">c b ſeſquialtera b r.
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            </s>
            <s xml:space="preserve">Quam uero proportionem habet portio ad humidum in
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            grauitate, eam habeat exceſſus, quo quadratum b d exce-
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            dit quadratum f q, ad ipſum b d quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit f ipſius
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            q dupla. </s>
            <s xml:space="preserve">conſtat igitur exceſſum, quo quadratum b d ex-
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            cedit quadratum
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              <anchor type="figure" xlink:label="fig-0064-01a" xlink:href="fig-0064-01"/>
            b c ad quadratum
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            b d, minorem ha-
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            bere proportio-
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            nem, quàm exceſ-
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            ſus, quo quadratũ
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            b d excedit qua-
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            dratum f q ad b d
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            quadratum. </s>
            <s xml:space="preserve">eſt e-
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            nim b c exceſſus
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            quo axis portiõis
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            maior eſt, quã ſeſ-
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            quialter eius, quæ
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            uſque ad axem.
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            </s>
            <s xml:space="preserve">quare quadr atum
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              <anchor type="note" xlink:label="note-0064-01a" xlink:href="note-0064-01"/>
            b d magis excedit
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            quadratum f q, quàm b c quadratum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">idcirco linea f q
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            minor eſt, quàm b c itemq; </s>
            <s xml:space="preserve">f minor, quàm br. </s>
            <s xml:space="preserve">Sit ipſi ſ</s>
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