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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              <pb file="0050" n="50" rhead="ARCHIMEDIS"/>
            nea h m ad li-
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              <anchor type="figure" xlink:label="fig-0050-01a" xlink:href="fig-0050-01"/>
            neam fc. </s>
            <s xml:space="preserve">at uero
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            ut h m ad f c, ita
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            o h ad a f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut
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            quadratum h m
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            ad quadratú g l,
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            ita linea h b ad
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            b g; </s>
            <s xml:space="preserve">hoc est b g
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            ad b f. </s>
            <s xml:space="preserve">ex quibus
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            ſequitur o h ad
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            a f ita eſſe, ut b g
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            ad b f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permu
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            tando oh ad b g,
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            ut a f ad f b. </s>
            <s xml:space="preserve">ſed
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            eſt a f dupla ip-
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            ſius fb: </s>
            <s xml:space="preserve">ſunt eni
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            a b, b f æquales
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            ex 35 primi libri
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            conicorum. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">h o ipſius g b
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            eſt dupla. </s>
            <s xml:space="preserve">quod demonſtrare oportebat.</s>
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            <note position="right" xlink:label="note-0049-02" xlink:href="note-0049-02a" xml:space="preserve">4. ſexti.</note>
            <note position="right" xlink:label="note-0049-03" xlink:href="note-0049-03a" xml:space="preserve">22. ſexti.
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            cor. 20. ſe
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            xti.</note>
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          <head xml:space="preserve">LEMMA IIII.</head>
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            <s xml:space="preserve">Iiſdem manentibus, & </s>
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            ad diametrum, quæ ſectionem in puncto m conting at;
              <lb/>
            </s>
            <s xml:space="preserve">Dico h q ad q o eandem proportionem habere, quam
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            habet g h ad c n.</s>
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            <s xml:space="preserve">F_IAT_ enim h r æqualis g f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cumtriangula a f c, o p n ſimi
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            lia ſint, & </s>
            <s xml:space="preserve">p n ſit æqualis f c; </s>
            <s xml:space="preserve">eodem modo demonſtrabimus p o, f a
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            inter ſe æquales eſſe. </s>
            <s xml:space="preserve">quare p o ipſius f b dupla erit. </s>
            <s xml:space="preserve">Sed eſt h o du
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            pla g b. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliqua p h reliquæ f g; </s>
            <s xml:space="preserve">uidelicet ipſius r h eſt du-</s>
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