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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DE CENTRO GRAVIT. SOLID.
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              <pb o="28" file="0167" n="167" rhead="DE CENTRO GRAVIT. SOLID."/>
            uel coni portionis axis à centro grauitatis ita diui
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            ditur, ut pars, quæ terminatur ad uerticem reli-
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            quæ partis, quæ ad baſim, ſit tripla.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sit pyramis, cuius baſis triangulum a b c; </s>
            <s xml:space="preserve">axis d e; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">gra
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            uitatis centrum _K_. </s>
            <s xml:space="preserve">Dico lineam d k ipſius _K_ e triplam eſſe.
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            </s>
            <s xml:space="preserve">trianguli enim b d c centrum grauitatis ſit punctum f; </s>
            <s xml:space="preserve">triã
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            guli a d c centrũ g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">trianguli a d b ſit h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur a f,
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            b g, c h. </s>
            <s xml:space="preserve">Quoniam igitur centrũ grauitatis pyramidis in axe
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            cõſiſtit: </s>
            <s xml:space="preserve">ſuntq; </s>
            <s xml:space="preserve">d e, a f, b g, c h eiuſdẽ pyramidis axes: </s>
            <s xml:space="preserve">conue
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              <anchor type="note" xlink:label="note-0167-01a" xlink:href="note-0167-01"/>
            nient omnes in idẽ punctũ _k_, quod eſt grauitatis centrum.
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            </s>
            <s xml:space="preserve">Itaque animo concipiamus hanc pyramidem diuiſam in
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            quatuor pyramides, quarum baſes ſint ipſa pyramidis
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            triangula; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis pun-
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              <anchor type="handwritten" xlink:label="hd-0167-01a" xlink:href="hd-0167-01"/>
              <anchor type="figure" xlink:label="fig-0167-01a" xlink:href="fig-0167-01"/>
            ctum k quæ quidem py-
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            ramides inter ſe æquales
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            ſunt, ut demõſtrabitur.
              <lb/>
            </s>
            <s xml:space="preserve">Ducatur enĩ per lineas
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            d c, d e planum ſecãs, ut
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            ſit ipſius, & </s>
            <s xml:space="preserve">baſis a b c cõ
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            munis ſectio recta linea
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            c e l: </s>
            <s xml:space="preserve">eiuſdẽ uero & </s>
            <s xml:space="preserve">triã-
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            guli a d b ſitlinea d h l. </s>
            <s xml:space="preserve">
              <lb/>
            erit linea a l æqualis ipſi
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            l b: </s>
            <s xml:space="preserve">nam centrum graui-
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            tatis trianguli conſiſtit
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            in linea, quæ ab angulo
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            ad dimidiam baſim per-
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            ducitur, ex tertia deci-
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            ma Archimedis. </s>
            <s xml:space="preserve">quare
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              <anchor type="note" xlink:label="note-0167-02a" xlink:href="note-0167-02"/>
            triangulum a c l æquale
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            eſt triangulo b c l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea pyramis, cuius baſis trian-
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            gulum a c l, uertex d, eſt æqualis pyramidi, cuius baſis b c l
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            triangulum, & </s>
            <s xml:space="preserve">idem uertex. </s>
            <s xml:space="preserve">pyramides enim, quæ ab eodẽ
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              <anchor type="note" xlink:label="note-0167-03a" xlink:href="note-0167-03"/>
            </s>
          </p>
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