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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DE CENTRO GRAVIT. SOLID.
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          <pb o="32" file="0175" n="175" rhead="DE CENTRO GRAVIT. SOLID."/>
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            <s xml:space="preserve">SIT fruſtũ pyramidis, uel coni, uel coni portionis a d,
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            cuius maior baſis a b, minor c d. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur altero plano
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            baſi æquidiſtante, ita utſectio e f ſit proportionalis inter
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            baſes a b, c d. </s>
            <s xml:space="preserve">conſtituatur autẽ pyramis, uel conus, uel co-
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            ni portio a g b, cuius baſis ſit eadem, quæ baſis maior fru-
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            ſti, & </s>
            <s xml:space="preserve">altitudo æqualis. </s>
            <s xml:space="preserve">Di-
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              <anchor type="figure" xlink:label="fig-0175-01a" xlink:href="fig-0175-01"/>
            co fruſtum a d ad pyrami-
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            dem, uel conum, uel coni
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            portionem a g b eandem
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            proportionẽ habere, quã
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            utræque baſes, a b, c d unà
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            cum e f ad baſim a b. </s>
            <s xml:space="preserve">eſt
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            enim fruſtum a d æquale
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            pyramidi, uel cono, uel co-
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            ni portioni, cuius baſis ex
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            tribus baſibus a b, e f, c d
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            conſtat; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">altitudo ipſius
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            altitudini eſt æqualis: </s>
            <s xml:space="preserve">quod mox oſtendemus. </s>
            <s xml:space="preserve">Sed pyrami
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            des, coni, uel coni portiões,
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              <anchor type="figure" xlink:label="fig-0175-02a" xlink:href="fig-0175-02"/>
            quæ ſunt æquali altitudine,
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            eãdem inter ſe, quam baſes,
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            proportionem habent, ſicu-
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            ti demonſtratum eſt, partim
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            ab Euclide in duodecimo li-
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              <anchor type="note" xlink:label="note-0175-01a" xlink:href="note-0175-01"/>
            bro elementorum, partim à
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            nobis in cõmentariis in un-
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            decimam propoſitionẽ Ar-
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            chimedis de conoidibus, & </s>
            <s xml:space="preserve">
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            ſphæroidibus. </s>
            <s xml:space="preserve">quare pyra-
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            mis, uel conus, uel coni por-
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            tio, cuius baſis eſt tribus illis
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            baſibus æqualis ad a g b eam
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            habet proportionem, quam
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            baſes a b, e f, c d ad ab bafim. </s>
            <s xml:space="preserve">Fruſtum igitur a d ad a g b</s>
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