Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[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.
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            <s xml:id="echoid-s2617" xml:space="preserve">
              <pb o="44" file="0099" n="99" rhead="DE IIS QVAE VEH. IN AQVA."/>
            gura: </s>
            <s xml:id="echoid-s2618" xml:space="preserve">& </s>
            <s xml:id="echoid-s2619" xml:space="preserve">alia eadem diſponantur demonſtrabimus rurſum
              <lb/>
            n t æqualem eſſe ipſi u i: </s>
            <s xml:id="echoid-s2620" xml:space="preserve">& </s>
            <s xml:id="echoid-s2621" xml:space="preserve">portiones a u q, a n z inter
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            ſe ſe æquales.
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            </s>
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            Itaque quoniã
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            ĩ portionibus
              <lb/>
            æqualibus, & </s>
            <s xml:id="echoid-s2623" xml:space="preserve">ſi
              <lb/>
            milibus a u q l,
              <lb/>
            a n z g ductæ
              <lb/>
            sũt a q, a z, por
              <lb/>
            tiones æqua-
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            les auferentes;
              <lb/>
            </s>
            <s xml:id="echoid-s2624" xml:space="preserve">cum diametris
              <lb/>
            portionum æ-
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            quales angu-
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            los cõtinebũt. </s>
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              <lb/>
            ergo triangulo
              <lb/>
            rum n l s, u ω c
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            anguli, qui cõ-
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            ſiſtũt ad l ω pũ-
              <lb/>
            cta, æquales ſunt: </s>
            <s xml:id="echoid-s2626" xml:space="preserve">& </s>
            <s xml:id="echoid-s2627" xml:space="preserve">b s recta linea æqualis ipſi b c: </s>
            <s xml:id="echoid-s2628" xml:space="preserve">ſ r ipſi cr,
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            n χ ipſi u h: </s>
            <s xml:id="echoid-s2629" xml:space="preserve">& </s>
            <s xml:id="echoid-s2630" xml:space="preserve">χ tipſi h i. </s>
            <s xml:id="echoid-s2631" xml:space="preserve">quòd cum u y dupla ſit ipſius y i,
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            erit n χ maior, quàm dupla χ t. </s>
            <s xml:id="echoid-s2632" xml:space="preserve">Sit igitur n m ipſius m t du
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            pla. </s>
            <s xml:id="echoid-s2633" xml:space="preserve">Rurſus ex his manifeſtum eſt, non manere ipſam por-
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            tionem; </s>
            <s xml:id="echoid-s2634" xml:space="preserve">ſed inclinari ex parte a: </s>
            <s xml:id="echoid-s2635" xml:space="preserve">ponebatur autem portio
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            humidi ſuperficiem in uno puncto contingere. </s>
            <s xml:id="echoid-s2636" xml:space="preserve">ergo ne-
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            ceſſe eſt, ut eius baſis in humidum magis demergatur.</s>
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          <head xml:id="echoid-head62" xml:space="preserve">DEMONSTRATIO QVINT AE PARTIS.</head>
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            <s xml:id="echoid-s2638" xml:space="preserve">HABEAT denique portio ad humidum in grauitate
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            minorem proportionem, quàm quadratum f p ad quadra-
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            tum b d: </s>
            <s xml:id="echoid-s2639" xml:space="preserve">& </s>
            <s xml:id="echoid-s2640" xml:space="preserve">quam proportionem habet portio ad humidũ
              <lb/>
            in grauitate, eandem quadratum, quod fit à linea ψ habeat
              <lb/>
            ad quadratum b d. </s>
            <s xml:id="echoid-s2641" xml:space="preserve">erit χ minor ipſa p f. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">Rurſus </s>
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