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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          <head xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:space="preserve">Sint duæ portionis ſimiles, contentæ rectis lineis, & </s>
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              <lb/>
            rectangulorum conorum ſectionibus; </s>
            <s xml:space="preserve">a b c quidem ma-
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            ior, cuius diameter b d; </s>
            <s xml:space="preserve">e f c uero minor, cuius diameter
              <lb/>
            fg: </s>
            <s xml:space="preserve">aptenturq; </s>
            <s xml:space="preserve">inter ſeſe, ita ut maior minorem includat
              <lb/>
            & </s>
            <s xml:space="preserve">ſint earum baſes a c, e c in eadem recta linea, ut idẽ
              <lb/>
            punctum c ſit utriuſque terminus: </s>
            <s xml:space="preserve">ſumatur deinde in ſe
              <lb/>
            ctione a b c quodlibet punctum b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur h c. </s>
            <s xml:space="preserve">Di
              <lb/>
            co lineam h c ad partem ſui ipſius, quæ inter c, & </s>
            <s xml:space="preserve">ſe-
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            ctionem e f c interiicitur, eam proportionẽ habere, quam
              <lb/>
            habet a c ad c e.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">_
              <emph style="sc">Dvcatvr</emph>
            _ b c, quæ tranſibit per f. </s>
            <s xml:space="preserve">quoniam enim portiones
              <lb/>
            ſimiles ſunt, diametri cú baſibus æquales continent angulos. </s>
            <s xml:space="preserve">quare
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            æquidiſtant inter ſe ſe b d, f g: </s>
            <s xml:space="preserve">éſtq; </s>
            <s xml:space="preserve">b d ad a c, ut f g ad e c:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permu-
              <lb/>
              <anchor type="figure" xlink:label="fig-0074-01a" xlink:href="fig-0074-01"/>
            tando b d ad
              <lb/>
            f g, ut a c ad
              <lb/>
            c e: </s>
            <s xml:space="preserve">hoc eſt
              <lb/>
              <anchor type="note" xlink:label="note-0074-01a" xlink:href="note-0074-01"/>
            ut earum di-
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            midiæ d c ad
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            c g. </s>
            <s xml:space="preserve">ergo ex
              <lb/>
            antecedēti lé
              <lb/>
            mate ſequi-
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            tur lineá b c
              <lb/>
            per punctum
              <lb/>
            f tranſire.
              <lb/>
            </s>
            <s xml:space="preserve">Ducatur præ
              <lb/>
            terea à puncto h ad diametrum b d linea h K, æquidiſtans baſi
              <lb/>
            a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta k c, quæ diametrum f g ſecet in l; </s>
            <s xml:space="preserve">per l ducatur</s>
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