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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DE IIS QVAE VEH. IN AQVA.
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              <pb o="34" file="0079" n="79" rhead="DE IIS QVAE VEH. IN AQVA."/>
            ſectione e f c diuiditur: </s>
            <s xml:space="preserve">pars uero lineæ c a, quæ eſt in-
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            ter duas ſectiones proportione reſpondebit parti lineæ
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            ductæ, quæ itidem inter eaſdem ſectiones interiicitur; </s>
            <s xml:space="preserve">hoc
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            est ut in propoſita figura, ſi producatur d b uſque ad c h
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            in l, ut ſectioni e f c in puncto m occurrat; </s>
            <s xml:space="preserve">lineam l
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            b ad b m eãdem proportionem habere, quàm c e ad e a.</s>
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          </p>
          <p style="it">
            <s xml:space="preserve">Produc. </s>
            <s xml:space="preserve">itur enim
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              <anchor type="figure" xlink:label="fig-0079-01a" xlink:href="fig-0079-01"/>
            q f ad eandem lineá
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            c h in n, ſecás a b c
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            ſectionem in o: </s>
            <s xml:space="preserve">& </s>
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              <lb/>
            iuncta b c, quæ tran
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            ſibit per f, ut oſten-
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            ſum eſt, erunt trian-
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            gula c g f, c d b ſi-
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            milia: </s>
            <s xml:space="preserve">itémq; </s>
            <s xml:space="preserve">ſimi-
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            lia íter ſe, c f n, c b l.
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            </s>
            <s xml:space="preserve">quare ut g f ad d b,
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              <anchor type="note" xlink:label="note-0079-01a" xlink:href="note-0079-01"/>
            ita erit c f ad c b:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut c f ad c b, ita
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            f n ad b l. </s>
            <s xml:space="preserve">ergo g f
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              <anchor type="note" xlink:label="note-0079-02a" xlink:href="note-0079-02"/>
            ad d b, ut f n ad b l:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando g f
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            ad f n, ut d b ad b l. </s>
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              <lb/>
            eſt autem d b æqua
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            lis ipſi b l ex trigeſi
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            maquinta primi li-
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              <anchor type="note" xlink:label="note-0079-03a" xlink:href="note-0079-03"/>
            bri conicorum. </s>
            <s xml:space="preserve">ergo
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            & </s>
            <s xml:space="preserve">g f ipſi p i æqua
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            lis erit: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex trige
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            ſimatertia eiuſdem
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            linea c h ſectionem
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            e f c in eodem pun-</s>
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