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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ARCHIMEDIS
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            cto continget. </s>
            <s xml:space="preserve">Itaque iuncta cm producatur ad ſectionem a b c in p:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à p ad a c ducatur p q, quæ ipſi b d æquidiſtet. </s>
            <s xml:space="preserve">quoniam igi-
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            tur linea c h contingit ſectionem e f c in c puncto; </s>
            <s xml:space="preserve">habebit l m
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            ad m d proportionem eandem, quam c d ad d e, ex quinta propoſi-
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            tione Archimedis in libro de quadratura parabolæ. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propter triá
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            gulorum c m d, c p q
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              <anchor type="figure" xlink:label="fig-0080-01a" xlink:href="fig-0080-01"/>
            ſimilitudinem, ut c m
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            ad c d, ita erit c p ad
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            c q: </s>
            <s xml:space="preserve">permutandôq;
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            </s>
            <s xml:space="preserve">ut c m ad c p, ita c d
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            ad c q. </s>
            <s xml:space="preserve">ut autem c m
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            ad c p, ſic c e ad c a: </s>
            <s xml:space="preserve">
              <lb/>
            quod proxime demó-
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            ſtrauimus. </s>
            <s xml:space="preserve">quare ut
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            c e ad c a, ſit c d ad
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            c q: </s>
            <s xml:space="preserve">hoc eſt ut totum
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            ad totum, ſic pars ad
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            partem, reliquum igi
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            tur d e ad reliquum
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            q a eſt ut c e ad c a; </s>
            <s xml:space="preserve">
              <lb/>
            uidelicet ut c d ad
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            c q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando
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            c d ad d e, ut c q ad
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            q a. </s>
            <s xml:space="preserve">êſtq; </s>
            <s xml:space="preserve">l m ad m
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            d, ut c d ad d e. </s>
            <s xml:space="preserve">ergo
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            l m ad m d, ut c q ad
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            q a. </s>
            <s xml:space="preserve">ſed l b ad b d
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            ex quinta Archime-
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            dis, quam diximus; </s>
            <s xml:space="preserve">
              <lb/>
            eſt ut c d ad d a. </s>
            <s xml:space="preserve">con
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            ſtat igitur ex antece-
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            denti lemmate c d ad d q ita eſſe, ut l b ad b m. </s>
            <s xml:space="preserve">ut autem c d ad d q,
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              <anchor type="note" xlink:label="note-0080-01a" xlink:href="note-0080-01"/>
            ita c m ad m p. </s>
            <s xml:space="preserve">ergo l b ad b m, ut c m ad m p. </s>
            <s xml:space="preserve">Quòd cum demon
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            ſtratum fuerit, c m ad m p, ut c e ad e a: </s>
            <s xml:space="preserve">habebit l b ad b m eandé</s>
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