Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[91. THEOREMA XXI. PROPOSITIO XXVI.]
[92. THEOREMA XXII. PROPOSITIO XXVII.]
[93. PROBLEMA VI. PROPOSITIO XX VIII.]
[94. THE OREMA XXIII. PROPOSITIO XXIX.]
[95. THEOREMA XXIIII. PROPOSITIO XXX.]
[96. THEOREMA XXV. PROPOSITIO XXXI.]
[97. FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.]
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DE CENTRO GRAVIT. SOLID.
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              <pb o="34" file="0179" n="179" rhead="DE CENTRO GRAVIT. SOLID."/>
            culi, uel ellipſes c d, e ſ a b ad circulum, uel ellipſim a b. </s>
            <s xml:space="preserve">In-
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            telligatur pyramis q baſim habens æqualem tribus rectan
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            gulis a b, e f, c d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">altitudinem eãdem, quam fruſtum a d.
              <lb/>
            </s>
            <s xml:space="preserve">intelligatur etiam conus, uel coni portio q, eadem altitudi
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            ne, cuius baſis ſit tribus circulis, uel tribus ellipſibus a b,
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            e f, c d æqualis. </s>
            <s xml:space="preserve">poſtremo intelligatur pyramis a l b, cuius
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            baſis ſit rectangulum m n o p, & </s>
            <s xml:space="preserve">altitudo eadem, quæ fru-
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            ſti: </s>
            <s xml:space="preserve">itemq, intelligatur conus, uel coni portio a l b, cuius
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            baſis circulus, uel ellipſis circa diametrum a b, & </s>
            <s xml:space="preserve">eadem al
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            titudo. </s>
            <s xml:space="preserve">ut igitur rectangula a b, e f, c d ad rectangulum a b,
              <lb/>
              <anchor type="note" xlink:label="note-0179-01a" xlink:href="note-0179-01"/>
            ita pyramis q ad pyramidem a l b; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut circuli, uel ellip-
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            ſes a b, e f, c d ad a b circulum, uel ellipſim, ita conus, uel co
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            ni portio q ad conum, uel coni portionem a l b. </s>
            <s xml:space="preserve">conus
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            igitur, uel coni portio q ad conum, uel coni portionem
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            a l b eſt, ut pyramis q ad pyramidem a l b. </s>
            <s xml:space="preserve">ſed pyramis
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            a l b ad pyramidem a g b eſt, ut altitudo ad altitudinem, ex
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            20. </s>
            <s xml:space="preserve">huius: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita eſt conus, uel coni portio al b ad conum,
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            uel coni portionem a g b ex 14. </s>
            <s xml:space="preserve">duodecimi elementorum,
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            & </s>
            <s xml:space="preserve">ex iis, quæ nos demonſtrauimus in commentariis in un-
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            decimam de conoidibus, & </s>
            <s xml:space="preserve">ſphæroidibus, propoſitione
              <lb/>
            quarta. </s>
            <s xml:space="preserve">pyramis autem a g b ad pyramidem c g d propor-
              <lb/>
            tionem habet compoſitam ex proportione baſium & </s>
            <s xml:space="preserve">pro
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            portione altitudinum, ex uigeſima prima huius: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſimili-
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            ter conus, uel coni portio a g b a d conum, uel coni portio-
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            nem c g d proportionem habet compoſitã ex eiſdem pro-
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            portionibus, per ea, quæ in dictis commentariis demon-
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            ſtrauimus, propoſitione quinta, & </s>
            <s xml:space="preserve">ſexta: </s>
            <s xml:space="preserve">altitudo enim in
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            utriſque eadem eſt, & </s>
            <s xml:space="preserve">baſes inter ſe ſe eandem habent pro-
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            portionem. </s>
            <s xml:space="preserve">ergo ut pyramis a g b ad pyramidem c g d, ita
              <lb/>
            eſt conus, uel coni portio a g b ad a g d conum, uel coni
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            portionem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per conuerſionẽ rationis, ut pyramis a g b
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            ad fruſtū à pyramide abſciſſum, ita conus uel coni portio
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            a g b ad fruſtum a d. </s>
            <s xml:space="preserve">ex æquali igitur, ut pyramis q ad fru-
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            ſtum à pyramide abſciſſum, ita conus uel coni portio q ad</s>
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