Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[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.
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            <s xml:id="echoid-s2642" xml:space="preserve">
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            quædam recta linea g i, ſectionibus a g q l, a x d interiecta,
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            & </s>
            <s xml:id="echoid-s2643" xml:space="preserve">ipſi b d æquidiſtans; </s>
            <s xml:id="echoid-s2644" xml:space="preserve">quæ mediam coni ſectionem in pun
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            cto h, & </s>
            <s xml:id="echoid-s2645" xml:space="preserve">rectam
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              <figure xlink:label="fig-0100-01" xlink:href="fig-0100-01a" number="66">
                <image file="0100-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0100-01"/>
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            lineam r y in y
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            ſecet. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">demonſtra
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            bitur g h dupla
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            h i, quemadmo-
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            dum demonſtra
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            ta eſt o g ipſius
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            g x dupla. </s>
            <s xml:id="echoid-s2647" xml:space="preserve">duca-
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            tur poſtea g ω cõ
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            tingens a g q l ſe
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            ctioneming: </s>
            <s xml:id="echoid-s2648" xml:space="preserve">& </s>
            <s xml:id="echoid-s2649" xml:space="preserve">
              <lb/>
            g c ad b d perpé
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            dicularis: </s>
            <s xml:id="echoid-s2650" xml:space="preserve">iun-
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            ctaq; </s>
            <s xml:id="echoid-s2651" xml:space="preserve">ai produ-
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            catur ad q. </s>
            <s xml:id="echoid-s2652" xml:space="preserve">erit
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            ergo a i æqualis
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            i q: </s>
            <s xml:id="echoid-s2653" xml:space="preserve">& </s>
            <s xml:id="echoid-s2654" xml:space="preserve">a q ipſi g ω
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            æquidiſtans. </s>
            <s xml:id="echoid-s2655" xml:space="preserve">Demonſtrandũ eſt portionẽ in humidũ demiſ
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            fam, inclinatamq; </s>
            <s xml:id="echoid-s2656" xml:space="preserve">adeo, ut baſis ipſius non cõtingat humi-
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            dũ, conſiſtere inclinatã ita, ut axis cum ſuperficie humidi
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            angulum faciat minorem angulo φ: </s>
            <s xml:id="echoid-s2657" xml:space="preserve">& </s>
            <s xml:id="echoid-s2658" xml:space="preserve">baſis humidi ſuper-
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            ficiem nullo modo contingat. </s>
            <s xml:id="echoid-s2659" xml:space="preserve">Demittatur enim in humi-
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            dum; </s>
            <s xml:id="echoid-s2660" xml:space="preserve">& </s>
            <s xml:id="echoid-s2661" xml:space="preserve">conſiſtat ita, ut baſis ipſius in uno puncto contin-
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            gat ſuperficiem humidi. </s>
            <s xml:id="echoid-s2662" xml:space="preserve">ſecta autem portione per axem,
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            plano ad humidi ſuperficiem recto, ſit portionis ſectio a n
              <lb/>
            z l rectanguli coni ſectio: </s>
            <s xml:id="echoid-s2663" xml:space="preserve">ſuperficiei humidi a z: </s>
            <s xml:id="echoid-s2664" xml:space="preserve">axis autẽ
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            portionis, & </s>
            <s xml:id="echoid-s2665" xml:space="preserve">ſectionis diameter b d: </s>
            <s xml:id="echoid-s2666" xml:space="preserve">ſeceturq; </s>
            <s xml:id="echoid-s2667" xml:space="preserve">b d in pun-
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            ctis _K_ r, ut ſuperius dictum eſt: </s>
            <s xml:id="echoid-s2668" xml:space="preserve">& </s>
            <s xml:id="echoid-s2669" xml:space="preserve">ducatur n f quidem ipſi
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            a z æquidiſtans, & </s>
            <s xml:id="echoid-s2670" xml:space="preserve">contingens coni ſectionem in pũcto n;
              <lb/>
            </s>
            <s xml:id="echoid-s2671" xml:space="preserve">n t uero æquidiſtans ipſi b d: </s>
            <s xml:id="echoid-s2672" xml:space="preserve">& </s>
            <s xml:id="echoid-s2673" xml:space="preserve">n s ad eandem perpendi-
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            cularis. </s>
            <s xml:id="echoid-s2674" xml:space="preserve">Quoniam igitur portio ad humidum in grauitate,
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            cam habet proportionem, quam quadratum, quod fit à </s>
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