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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              <pb file="0134" n="134" rhead="FED. COMMANDINI"/>
            t u, x y ipſi g h æquidiſtare. </s>
            <s xml:space="preserve">Et quoniam triangula, quæ
              <lb/>
            fiunt à lineis K y, y u, u s, s h æqualia ſuntinter ſe, & </s>
            <s xml:space="preserve">ſimilia
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            triangulo K m h: </s>
            <s xml:space="preserve">habebit triangulum K m h ad triangulũ
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              <anchor type="note" xlink:label="note-0134-01a" xlink:href="note-0134-01"/>
            K δ y duplam proportionem eius, quæ eſt lineæ k h ad K y.
              <lb/>
            </s>
            <s xml:space="preserve">ſed _K_ h poſita eſt quadrupla ipſius k y. </s>
            <s xml:space="preserve">ergo triangulum
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            κ m h ad triangulum _K_ δ y eãdem proportionem habebit,
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            quam ſexdecim ad unũ & </s>
            <s xml:space="preserve">ad quatuor triangula k δ y, y u,
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            u s, s α h habebit eandem, quam fexdecim ad quatuor, hoc
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            eſt quam h K ad κ y: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſimiliter eandem habere demonſtra
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            bitur trian-
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              <anchor type="figure" xlink:label="fig-0134-01a" xlink:href="fig-0134-01"/>
            gulum κ m g
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            ad quatuor
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            triãgula K δ
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            x, x γ t, t β r,
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            r z g. </s>
            <s xml:space="preserve">quare
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              <anchor type="note" xlink:label="note-0134-02a" xlink:href="note-0134-02"/>
            totum trian
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            gulum K g h
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            ad omnia tri
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            angula g z r,
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            r β t, t γ x, x δ
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            _K_, K δ y, y u,
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            u s, s α h ita
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            erit, ut h κ a d
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            k y, hoc eſt
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            ut h m ad m
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            q. </s>
            <s xml:space="preserve">Si igitur in
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            triangulis a b c, d e f deſcribantur figuræ ſimiles ei, quæ de-
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            ſcripta eſt in g h K triangulo: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per lineas ſibi reſp onden-
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            tes plana ducantur: </s>
            <s xml:space="preserve">totum priſma a f diuiſum eritin tria
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            ſolida parallelepipeda y γ, u β, s z, quorum baſes ſunt æ qua
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            les & </s>
            <s xml:space="preserve">ſimiles ipſis parallelogrammis y γ, u β, s z: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in octo
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            priſmata g z r, r β t, t γ x, x δ K, κ δ y, y u, u s, s α h: </s>
            <s xml:space="preserve">quorum
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            item baſes æquales, & </s>
            <s xml:space="preserve">ſimiles ſunt dictis triangulis; </s>
            <s xml:space="preserve">altitu-
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            do autem in omnibus, totius priſmatis altitudini æ qualis.</s>
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