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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            quæ quidem in centro conueniunt. </s>
            <s xml:id="echoid-s2876" xml:space="preserve">idem igitur eſt centrum
              <lb/>
            grauitatis quadrati, & </s>
            <s xml:id="echoid-s2877" xml:space="preserve">circuli centrum.</s>
            <s xml:id="echoid-s2878" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2879" xml:space="preserve">Sit pentagonum æquilaterum, & </s>
            <s xml:id="echoid-s2880" xml:space="preserve">æquiangulum in circu-
              <lb/>
            lo deſcriptum a b c d e: </s>
            <s xml:id="echoid-s2881" xml:space="preserve">& </s>
            <s xml:id="echoid-s2882" xml:space="preserve">iun-
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              <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a" number="72">
                <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0116-01"/>
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            cta b d, bifariamq́; </s>
            <s xml:id="echoid-s2883" xml:space="preserve">in ſ diuiſa,
              <lb/>
            ducatur c f, & </s>
            <s xml:id="echoid-s2884" xml:space="preserve">producatur ad
              <lb/>
            circuli circumferentiam in g;
              <lb/>
            </s>
            <s xml:id="echoid-s2885" xml:space="preserve">quæ lineam a e in h ſecet: </s>
            <s xml:id="echoid-s2886" xml:space="preserve">de-
              <lb/>
            inde iungantur a c, c e. </s>
            <s xml:id="echoid-s2887" xml:space="preserve">Eodem
              <lb/>
            modo, quo ſupra demonſtra-
              <lb/>
            bimus angulum b c f æqualem
              <lb/>
            eſſe angulo d c f; </s>
            <s xml:id="echoid-s2888" xml:space="preserve">& </s>
            <s xml:id="echoid-s2889" xml:space="preserve">angulos
              <lb/>
            ad f utroſque rectos: </s>
            <s xml:id="echoid-s2890" xml:space="preserve">& </s>
            <s xml:id="echoid-s2891" xml:space="preserve">idcir-
              <lb/>
            colineam c f g per circuli cen
              <lb/>
            trum tranſire. </s>
            <s xml:id="echoid-s2892" xml:space="preserve">Quoniam igi-
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            tur latera c b, b a, & </s>
            <s xml:id="echoid-s2893" xml:space="preserve">c d, d e æqualia ſunt; </s>
            <s xml:id="echoid-s2894" xml:space="preserve">& </s>
            <s xml:id="echoid-s2895" xml:space="preserve">æquales anguli
              <lb/>
            c b a, c d e: </s>
            <s xml:id="echoid-s2896" xml:space="preserve">erit baſis c a baſi c e, & </s>
            <s xml:id="echoid-s2897" xml:space="preserve">angulus b c a angulo
              <lb/>
              <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">4. Primi.</note>
            d c e æqualis. </s>
            <s xml:id="echoid-s2898" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s2899" xml:space="preserve">reliquus a c h, reliquo e c h. </s>
            <s xml:id="echoid-s2900" xml:space="preserve">eſt au-
              <lb/>
            tem c h utrique triangulo a c h, e c h communis. </s>
            <s xml:id="echoid-s2901" xml:space="preserve">quare
              <lb/>
            baſis a h æqualis eſt baſi h e: </s>
            <s xml:id="echoid-s2902" xml:space="preserve">& </s>
            <s xml:id="echoid-s2903" xml:space="preserve">anguli, quiad h recti: </s>
            <s xml:id="echoid-s2904" xml:space="preserve">ſuntq́;
              <lb/>
            </s>
            <s xml:id="echoid-s2905" xml:space="preserve">recti, qui ad f. </s>
            <s xml:id="echoid-s2906" xml:space="preserve">ergo lineæ a e, b d inter ſe ſe æquidiſtant. </s>
            <s xml:id="echoid-s2907" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0116-02" xlink:href="note-0116-02a" xml:space="preserve">08. primi.</note>
            Itaque cum trapezij a b d e latera b d, a e æquidiſtantia à li
              <lb/>
            nea fh bifariam diuidantur; </s>
            <s xml:id="echoid-s2908" xml:space="preserve">centrum grauitatis ipſius erit
              <lb/>
            in linea f h, ex ultima eiuſdem libri Archimedis. </s>
            <s xml:id="echoid-s2909" xml:space="preserve">Sed trian-
              <lb/>
              <note position="left" xlink:label="note-0116-03" xlink:href="note-0116-03a" xml:space="preserve">13. Archi-
                <lb/>
              medis.</note>
            guli b c d centrum grauitatis eſt in linea c f. </s>
            <s xml:id="echoid-s2910" xml:space="preserve">ergo in eadem
              <lb/>
            linea c h eſt centrum grauitatis trapezij a b d e, & </s>
            <s xml:id="echoid-s2911" xml:space="preserve">trian-
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            guli b c d: </s>
            <s xml:id="echoid-s2912" xml:space="preserve">hoc eſt pentagoni ipſius centrum & </s>
            <s xml:id="echoid-s2913" xml:space="preserve">centrum
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            circuli. </s>
            <s xml:id="echoid-s2914" xml:space="preserve">Rurſus ſi iuncta a d, bifariamq́; </s>
            <s xml:id="echoid-s2915" xml:space="preserve">ſecta in k, duca-
              <lb/>
            tur e k l: </s>
            <s xml:id="echoid-s2916" xml:space="preserve">demonſtrabimus in ipſa utrumque centrum in
              <lb/>
            eſſe. </s>
            <s xml:id="echoid-s2917" xml:space="preserve">Sequitur ergo, ut punctum, in quo lineæ c g, e l con-
              <lb/>
            ueniunt, idem ſit centrum circuli, & </s>
            <s xml:id="echoid-s2918" xml:space="preserve">centrum grauitatis
              <lb/>
            pentagoni.</s>
            <s xml:id="echoid-s2919" xml:space="preserve"/>
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            <s xml:id="echoid-s2920" xml:space="preserve">Sit hexagonum a b c d e f æquilaterum, & </s>
            <s xml:id="echoid-s2921" xml:space="preserve">æquiangulum
              <lb/>
            in circulo deſignatum: </s>
            <s xml:id="echoid-s2922" xml:space="preserve">iunganturq́; </s>
            <s xml:id="echoid-s2923" xml:space="preserve">b d, a c: </s>
            <s xml:id="echoid-s2924" xml:space="preserve">& </s>
            <s xml:id="echoid-s2925" xml:space="preserve">bifariam </s>
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