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="0142" n="142" rhead="FED. COMMANDINI"/>
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            linea x cum ſit minor circulo, uel ellipſi, eſt etiam minor fi-
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            gura rectilinea y. </s>
            <s xml:space="preserve">ergo pyramis x pyramide y minor erit.
              <lb/>
            </s>
            <s xml:space="preserve">Sed & </s>
            <s xml:space="preserve">maior; </s>
            <s xml:space="preserve">quod fieri nõ poteſt. </s>
            <s xml:space="preserve">At ſi conus, uel coni por
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            tio x ponatur minor pyramide y: </s>
            <s xml:space="preserve">ſit alter conus æque al-
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            tus, uel altera coni portio χ ipſi pyramidi y æqualis. </s>
            <s xml:space="preserve">erit
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            eius baſis circulus, uel ellipſis maior circulo, uel ellipſi x,
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            quorum exceſſus ſit ſpacium ω. </s>
            <s xml:space="preserve">Siigitur in circulo, uel elli-
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            pſi χ figura rectilinea deſcribatur, ita ut portiones relictæ
              <lb/>
            ſint ω ſpacio minores, eiuſinodi figura adhuc maior erit cir
              <lb/>
            culo, uel ellipſi x, hoc eſt figura rectilinea _y_. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p_y_ramis in
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            ea conſtituta minor cono, uel coni portione χ, hoc eſt mi-
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            nor p_y_ramide_y_. </s>
            <s xml:space="preserve">eſt ergo ut χ figura rectilinea ad figuram
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            rectilineam _y_, ita pyramis χ ad pyramidem _y_. </s>
            <s xml:space="preserve">quare cum
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            figura rectilinea χ ſit maior figura_y_: </s>
            <s xml:space="preserve">erit & </s>
            <s xml:space="preserve">p_y_ramis χ p_y_-
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            ramide_y_ maior. </s>
            <s xml:space="preserve">ſed erat minor; </s>
            <s xml:space="preserve">quod rurſus fieri non po-
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            teſt. </s>
            <s xml:space="preserve">non eſt igitur conus, uel coni portio x neque maior,
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            neque minor p_y_ramide_y_. </s>
            <s xml:space="preserve">ergo ipſi neceſſario eſt æqualis. </s>
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            Itaque quoniam ut conus ad conum, uel coni portio ad co</s>
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