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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              <pb file="0186" n="186" rhead="FED. COMMANDINI"/>
            fruſtum pyramidis ſit abſciſſum. </s>
            <s xml:space="preserve">erit ex iis quæ proxime
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            tradidimus, fruſti pyramidis a d centrum grauitatis l. </s>
            <s xml:space="preserve">Quo
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            niam igitur portiones ſpacio o minores ſunt; </s>
            <s xml:space="preserve">habebit cir
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            culus, uel ellipſis a b ad
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              <anchor type="figure" xlink:label="fig-0186-01a" xlink:href="fig-0186-01"/>
            portiones dictas maiorẽ
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            proportionem, quàm n l
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            ad lm. </s>
            <s xml:space="preserve">ſed ut circulus, uel
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            ellipſis a b ad portiones,
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            ita a p b conus, uel coni
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            portio ad ſolidas portio-
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            nes, id quod ſupra demon
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            ſtratum eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut circulus
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            uel ellipſis c d ad portio-
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              <anchor type="note" xlink:label="note-0186-01a" xlink:href="note-0186-01"/>
            nes, quæ ipſi inſunt, ita co
              <lb/>
            nus, uel coni portio c p d
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            ad ſolidas ipſius portio-
              <lb/>
            nes. </s>
            <s xml:space="preserve">Quòd cum figuræ in
              <lb/>
            circulis, uel ellipſibus a b
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            c d deſcriptæ ſimiles ſint,
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            erit proportio circuli, uel
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            ellipſis a b ad ſuas portio
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            nes, eadẽ, quæ circuli uel
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            ellipſis c d ad ſuas. </s>
            <s xml:space="preserve">ergo
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            conus, uel coni portio a p
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            b ad portiones ſolidas eã-
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            dem habet proportionẽ,
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            quam conus, uel coni por
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            tio c p d ad ſolidas ipſius
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            portiones. </s>
            <s xml:space="preserve">reliquum igi-
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              <anchor type="note" xlink:label="note-0186-02a" xlink:href="note-0186-02"/>
            tur coni, uel coni portionis fruſtũ, ſcilicet a d ad reliquas
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            portiones ſolidas in ipſo contentas eandem proportionẽ
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            habet, quam conus, uel coni portio a p b ad ſolidas portio
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            nes: </s>
            <s xml:space="preserve">hoc eſt eandem, quam circulus, uel ellipſis a b ad por
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            tiones planas. </s>
            <s xml:space="preserve">quare fruſtum coni, uel coni portionis a d</s>
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