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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FED. COMMANDINI
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          <p>
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              <pb file="0182" n="182" rhead="FED. COMMANDINI"/>
            nis, quouſque in unum punctum r conueniant; </s>
            <s xml:space="preserve">erit pyra-
              <lb/>
            midis a b c r, & </s>
            <s xml:space="preserve">pyramidis d e f r grauitatis centrum in li-
              <lb/>
            nea r h. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">reliquæ magnitudinis, uidelicet fruſti cen-
              <lb/>
            trum in eadem linea neceſſario comperietur. </s>
            <s xml:space="preserve">Iungantur
              <lb/>
            d b, d c, d h, d m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per lineas d b, d c ducto altero plano
              <lb/>
            intelligatur fruſtum in duas pyramides diuiſum: </s>
            <s xml:space="preserve">in pyra-
              <lb/>
            midem quidem, cuius baſis eſt triangulum a b c, uertex d:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in eam, cuius idem uertex, & </s>
            <s xml:space="preserve">baſis trapezium b c f e. </s>
            <s xml:space="preserve">erit
              <lb/>
            igitur pyramidis a b c d axis d h, & </s>
            <s xml:space="preserve">pyramidis b c f e d axis
              <lb/>
            d m: </s>
            <s xml:space="preserve">atque erunt tres axes g h, d h, d m in eodem plano
              <lb/>
            d a K l. </s>
            <s xml:space="preserve">ducatur præterea per o linea ſt ip ſi a K æquidiſtãs,
              <lb/>
            quæ lineam d h in u ſecet: </s>
            <s xml:space="preserve">per p uero ducatur x y æquidi-
              <lb/>
            ſtans eidem, ſecansque d m in
              <lb/>
              <anchor type="figure" xlink:label="fig-0182-01a" xlink:href="fig-0182-01"/>
            z: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur z u, quæ ſecet
              <lb/>
            g h in φ. </s>
            <s xml:space="preserve">tranſibit ea per q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            erunt φ q unum, atque idem
              <lb/>
            pun ctum; </s>
            <s xml:space="preserve">ut inferius appare-
              <lb/>
            bit. </s>
            <s xml:space="preserve">Quoniam igitur linea u o
              <lb/>
            æ quidiſtat ipſi d g, erit d u ad
              <lb/>
              <anchor type="note" xlink:label="note-0182-01a" xlink:href="note-0182-01"/>
            u h, ut g o ad o h. </s>
            <s xml:space="preserve">Sed g o tri-
              <lb/>
            pla eſt o h. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">d u ipſius
              <lb/>
            u h eſt tripla: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ideo pyrami-
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            dis a b c d centrum grauitatis
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            erit punctum 11. </s>
            <s xml:space="preserve">Rurſus quo-
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            niam z y ipſi d l æquidiſtat, d z
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            a d z m eſt, utly ad y m: </s>
            <s xml:space="preserve">eſtque
              <lb/>
            ly ad y m, ut g p ad p n. </s>
            <s xml:space="preserve">ergo
              <lb/>
            d z ad z m eſt, ut g p ad p n.
              <lb/>
            </s>
            <s xml:space="preserve">Quòd cum g p ſit tripla p n; </s>
            <s xml:space="preserve">
              <lb/>
            erit etiam d z ipſius z m tri-
              <lb/>
            pla. </s>
            <s xml:space="preserve">atque ob eandem cauſ-
              <lb/>
            ſam punctum z eſt centrũ gra-
              <lb/>
            uitatis pyramidis b c f e d. </s>
            <s xml:space="preserve">iun
              <lb/>
            ctaigitur z u, in ea erit cẽtrum</s>
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