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>
            <s xml:space="preserve">
              <pb file="0132" n="132" rhead="FED. COMMANDINI"/>
            centrum z: </s>
            <s xml:space="preserve">parallelogram mi a d, θ: </s>
            <s xml:space="preserve">parallelogrammi f g, φ:
              <lb/>
            </s>
            <s xml:space="preserve">parallelogrammi d h, χ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
              <anchor type="figure" xlink:label="fig-0132-01a" xlink:href="fig-0132-01"/>
            parallelogrammi c g centrũ
              <lb/>
            ψ: </s>
            <s xml:space="preserve">atque erit ω punctum me
              <lb/>
            dium uniuſcuiuſque axis, ui
              <lb/>
            delicet eius lineæ, quæ oppo
              <lb/>
            ſitorum planorũ centra con
              <lb/>
            iungit. </s>
            <s xml:space="preserve">Dico ω centrum effe
              <lb/>
            grauitatis ipſius ſolidi. </s>
            <s xml:space="preserve">eſt
              <lb/>
            enim, ut demonſtrauimus,
              <lb/>
              <anchor type="note" xlink:label="note-0132-01a" xlink:href="note-0132-01"/>
            ſolidi a f centrum grauitatis
              <lb/>
            in plano K n; </s>
            <s xml:space="preserve">quod oppoſi-
              <lb/>
            tis planis a d, g f æ quidiſtans
              <lb/>
            reliquorum planorum late-
              <lb/>
            ra biſariam diuidit: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fimili
              <lb/>
            rationeidem centrum eſt in plano o r, æ quidiſtante planis
              <lb/>
            a e, b f oppo ſitis. </s>
            <s xml:space="preserve">ergo in communi ipſorum fectione: </s>
            <s xml:space="preserve">ui-
              <lb/>
            delicet in linea y z. </s>
            <s xml:space="preserve">Sed eſt etiam in plano t u, quod quidẽ
              <lb/>
            y z ſecat in ω. </s>
            <s xml:space="preserve">Conſtat igitur centrum grauitatis ſolidi eſſe
              <lb/>
            punctum ω, medium ſcilicet axium, hoc eſt linearum, quæ
              <lb/>
            planorum oppoſitorum centra coniungunt.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a">
              <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0132-01"/>
            </figure>
            <note position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">6. huius</note>
          </div>
          <p>
            <s xml:space="preserve">Sit aliud prima a f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in eo plana, quæ opponuntur, tri-
              <lb/>
            angula a b c, d e f: </s>
            <s xml:space="preserve">diuiſisq; </s>
            <s xml:space="preserve">bifariam parallelogrammorum
              <lb/>
            lateribus a d, b e, c f in punctis g h κ, per diuiſiones planũ
              <lb/>
            ducatur, quod oppoſitis planis æ quidiſtans faciet ſe ctionẽ
              <lb/>
            triangulum g h k æ quale, & </s>
            <s xml:space="preserve">ſimile ipſis a b c, d e f. </s>
            <s xml:space="preserve">Rurſus
              <lb/>
            diuidatur a b bifariam in l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta c l per ipſam, & </s>
            <s xml:space="preserve">per
              <lb/>
            c _K_ f planum ducatur priſma ſecans, cuius, & </s>
            <s xml:space="preserve">parallelogrã
              <lb/>
            mi a e communis ſcctio ſit l m n. </s>
            <s xml:space="preserve">diuidet pun ctum m li-
              <lb/>
            neam g h bifariam; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ita n diuidet lineam d e: </s>
            <s xml:space="preserve">quoniam
              <lb/>
            triangula a c l, g k m, d f n æ qualia ſunt, & </s>
            <s xml:space="preserve">ſimilia, ut ſu pra
              <lb/>
              <anchor type="note" xlink:label="note-0132-02a" xlink:href="note-0132-02"/>
            demonſtrauimus. </s>
            <s xml:space="preserve">Iam ex iis, quæ tradita ſunt, conſtat cen
              <lb/>
            trum greuitatis priſmatis in plano g h k contineri. </s>
            <s xml:space="preserve">Dico
              <lb/>
            ipſum eſſe in linea k m. </s>
            <s xml:space="preserve">Si enim fieri poteſt, ſit o centrum;</s>
            <s xml:space="preserve"/>
          </p>
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