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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            teſt in portione, quæ recta linea & </s>
            <s xml:space="preserve">obtuſianguli coni ſe-
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            ctione, ſeu hyperbola continetur.</s>
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          <head xml:space="preserve">THE OREMA IIII. PROPOSITIO IIII.</head>
          <p>
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              <emph style="sc">In</emph>
            circulo & </s>
            <s xml:space="preserve">ellipſiidem eſt figuræ & </s>
            <s xml:space="preserve">graui-
              <lb/>
            tatis centrum.</s>
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          </p>
          <p>
            <s xml:space="preserve">SIT circulus, uel ellipſis, cuius centrum a. </s>
            <s xml:space="preserve">Dico a gra-
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            uitatis quoque centrum eſſe. </s>
            <s xml:space="preserve">Si enim fieri poteſt, ſit b cen-
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            trum grauitatis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a b extra figuram in c produca
              <lb/>
            tur: </s>
            <s xml:space="preserve">quam uero proportionem habetlinea c a ad a b, ha-
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            beat circulus a ad alium circulum, in quo d; </s>
            <s xml:space="preserve">uel ellipſis ad
              <lb/>
            aliam ellipſim: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in circulo, uel ellipſi ſigura rectilinea pla-
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            ne deſcribatur adeo, ut tandem relinquantur portiones
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            quædam minores circulo, uel ellipſid; </s>
            <s xml:space="preserve">quæ figura ſit e f g
              <lb/>
            h _k_ l m n. </s>
            <s xml:space="preserve">Illud uero in circulo fieri poſſe ex duodecimo
              <lb/>
            elementorum libro, propoſitione ſecunda manifeſte con-
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            ſtat; </s>
            <s xml:space="preserve">at in ellipſi nos demonſtra-
              <lb/>
              <anchor type="figure" xlink:label="fig-0122-01a" xlink:href="fig-0122-01"/>
            uinius in commentariis in quin-
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            tam propoſitionem Archimedis
              <lb/>
            de conoidibus, & </s>
            <s xml:space="preserve">ſphæroidibus.
              <lb/>
            </s>
            <s xml:space="preserve">erit igitur a centrum grauitatis
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            ipſius figuræ, quod proxime oſtē
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            dimus. </s>
            <s xml:space="preserve">Itaque quoniam circulus
              <lb/>
            a ad circulum d; </s>
            <s xml:space="preserve">uel ellipſis a ad
              <lb/>
            ellipſim d eandem proportionē
              <lb/>
            habet, quam linea c a ad a b: </s>
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              <lb/>
            portiones uero ſunt minores cir
              <lb/>
              <anchor type="note" xlink:label="note-0122-01a" xlink:href="note-0122-01"/>
            culo uel ellipſi d: </s>
            <s xml:space="preserve">habebit circu-
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            lus, uel ellipſis ad portiones ma-
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            iorem proportionem, quàm c a
              <lb/>
              <anchor type="note" xlink:label="note-0122-02a" xlink:href="note-0122-02"/>
            ad a b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuidendo figura recti-
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            linea e f g h _k_ l m n ad portiones</s>
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