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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            & </s>
            <s xml:space="preserve">denique punctum h pyramidis a b c d e f grauitatis eſſe
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            centrum, & </s>
            <s xml:space="preserve">ita in aliis.</s>
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            <note position="right" xlink:label="note-0168-01" xlink:href="note-0168-01a" xml:space="preserve">2. ſexti.</note>
            <figure xlink:label="fig-0169-01" xlink:href="fig-0169-01a">
              <image file="0169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0169-01"/>
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            <s xml:space="preserve">Sit conus, uel coni portio axem habens b d: </s>
            <s xml:space="preserve">ſecetur que
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            plano per axem, quod ſectionem faciat triangulum a b c:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b d axis diuidatur in e, ita ut b e ipſius e d ſit tripla. </s>
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            Dico punctum e coni, uel coni portionis, grauitatis
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            eſſe centrum. </s>
            <s xml:space="preserve">Sienim fieri poteſt, ſit centrum f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pro-
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            ducatur e f extra figuram in g. </s>
            <s xml:space="preserve">quam uero proportionem
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            habet g e ad e f, habeat baſis coni, uel coni portionis, hoc
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            eſt circulus, uel ellipſis circa diametrum a c ad aliud ſpa-
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            cium, in quo h. </s>
            <s xml:space="preserve">Itaque in circulo, uel ellipſi plane deſcri-
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            batur rectilinea figura a k l m c n o p, ita ut quæ relinquũ-
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            tur portiones ſint minores ſpacio h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">intelligatur pyra-
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            mis baſim habens rectilineam figuram a K l m c n o p, & </s>
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            axem b d; </s>
            <s xml:space="preserve">cuius quidem grauitatis centrum erit punctum
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            e, ut iam demonſtrauimus. </s>
            <s xml:space="preserve">Et quoniam portiones ſunt
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            minores ſpacio h, circulus, uel ellipſis ad portiones ma-
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              <anchor type="figure" xlink:label="fig-0170-01a" xlink:href="fig-0170-01"/>
            iorem proportionem habet, quam g e a d e f. </s>
            <s xml:space="preserve">ſed ut circu-
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            lus, uel ellipſis ad figuram rectilineam ſibi inſcriptam, ita
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            conus, uel coni portio ad pyramidem, quæ figuram rectili-
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            neam pro baſi habet; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">altitudinem æqualem: </s>
            <s xml:space="preserve">etenim ſu-</s>
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