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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          <p style="it">
            <s xml:id="echoid-s1916" xml:space="preserve">Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
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            ipſis ſectionibus in eandem proportionem ſecari. </s>
            <s xml:id="echoid-s1917" xml:space="preserve">eſt enim
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            diuidendo, conuertendoque cm ad mb, & </s>
            <s xml:id="echoid-s1918" xml:space="preserve">cf ad fb, ut
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            ce ad ea.</s>
            <s xml:id="echoid-s1919" xml:space="preserve"/>
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        <div xml:id="echoid-div139" type="section" level="1" n="44">
          <head xml:id="echoid-head49" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s1920" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1921" xml:space="preserve">illud constare potest; </s>
            <s xml:id="echoid-s1922" xml:space="preserve">lineas, quæ in portioni-
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            bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
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            les angulos contineant, ab ipſis ſimiles quoque portiones
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            abſcindere: </s>
            <s xml:id="echoid-s1923" xml:space="preserve">hoc eſt, ut in propoſita figura, portiones h b c,
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            m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
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            ſimiles eſſe.</s>
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          </p>
          <p style="it">
            <s xml:id="echoid-s1925" xml:space="preserve">
              <emph style="sc">D_ividantvr_</emph>
            enim ch, cm bifariam in punctis p q: </s>
            <s xml:id="echoid-s1926" xml:space="preserve">& </s>
            <s xml:id="echoid-s1927" xml:space="preserve">per
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            ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">erit portio-
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            nis b s c diameter p s, & </s>
            <s xml:id="echoid-s1929" xml:space="preserve">portionis m u c diameter q u. </s>
            <s xml:id="echoid-s1930" xml:space="preserve">Itaque fiat
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            ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
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            quæ ſit s x: </s>
            <s xml:id="echoid-s1931" xml:space="preserve">& </s>
            <s xml:id="echoid-s1932" xml:space="preserve">ut quadratum c t ad quadratum c q, ita fiat f o ad
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            u y. </s>
            <s xml:id="echoid-s1933" xml:space="preserve">iam exijs
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            quæ demóſtra
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            uimus in com-
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            mentarijs in
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            quartam pro-
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            poſitioné. </s>
            <s xml:id="echoid-s1934" xml:space="preserve">Ar-
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            chrmedis de co
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            noidibus, & </s>
            <s xml:id="echoid-s1935" xml:space="preserve">
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            ſphæroidibus,
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            patet quadra-
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            tum c p æqua-
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            le eſſe rectan-
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            gulo p s x:</s>
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