Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[41.] COMMENTARIVS.
[42.] LEMMA I.
[43.] LEMMA II.
[44.] LEMMA III.
[45.] LEMMA IIII.
[46.] LEMMA V.
[47.] LEMMA VI.
[48.] II.
[49.] III.
[50.] IIII.
[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.
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            <s xml:id="echoid-s2409" xml:space="preserve">
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            quia o g ipſius g x eſt dupla. </s>
            <s xml:id="echoid-s2410" xml:space="preserve">Sit p h dupla h t: </s>
            <s xml:id="echoid-s2411" xml:space="preserve">& </s>
            <s xml:id="echoid-s2412" xml:space="preserve">iun-
              <lb/>
            cta h κ ad ω producatur. </s>
            <s xml:id="echoid-s2413" xml:space="preserve">erit totius quidem portionis cen
              <lb/>
            trum grauitatis k; </s>
            <s xml:id="echoid-s2414" xml:space="preserve">partis eius, quæ intra humidum h; </s>
            <s xml:id="echoid-s2415" xml:space="preserve">eius
              <lb/>
            uero, quæ extra humidum in linea κ ω, quod ſit ω. </s>
            <s xml:id="echoid-s2416" xml:space="preserve">Itaque
              <lb/>
            demonſtrabitur
              <lb/>
              <figure xlink:label="fig-0092-01" xlink:href="fig-0092-01a" number="58">
                <image file="0092-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0092-01"/>
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            ſimiliter & </s>
            <s xml:id="echoid-s2417" xml:space="preserve">k z ad
              <lb/>
            humidi ſuperſi-
              <lb/>
            ciem perpẽdicu-
              <lb/>
            laris, & </s>
            <s xml:id="echoid-s2418" xml:space="preserve">quæ per
              <lb/>
            puncta h ω æqui-
              <lb/>
            diſtantes ipſi κ z
              <lb/>
            ducuntur. </s>
            <s xml:id="echoid-s2419" xml:space="preserve">quare
              <lb/>
            nõ manebit por
              <lb/>
            tio, ſed inclinabi
              <lb/>
            tur, donec baſis
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            ipſius in uno pũ
              <lb/>
            cto contingat ſu
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            perficiem humi-
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            di: </s>
            <s xml:id="echoid-s2420" xml:space="preserve">atque ita con
              <lb/>
            ſiſtet. </s>
            <s xml:id="echoid-s2421" xml:space="preserve">nam in por
              <lb/>
            tionibus æquali-
              <lb/>
            bus a o q l, a p m l, ductæ erunt ab extremitatibus baſium
              <lb/>
            a q, a m, quæ æquales portiones abſcindunt: </s>
            <s xml:id="echoid-s2422" xml:space="preserve">etenim a o q
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            ipſi a p m, utin ſuperioribus æqualis demonſtrabitur. </s>
            <s xml:id="echoid-s2423" xml:space="preserve">ergo
              <lb/>
              <note position="left" xlink:label="note-0092-01" xlink:href="note-0092-01a" xml:space="preserve">E</note>
            æquales faciunt acutos angulos a q, a m cum diametris ba
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            ſium: </s>
            <s xml:id="echoid-s2424" xml:space="preserve">quòd anguli ad χ & </s>
            <s xml:id="echoid-s2425" xml:space="preserve">n æquales ſint. </s>
            <s xml:id="echoid-s2426" xml:space="preserve">quare ſi ducta
              <lb/>
            h k ad ω producatur, erit totius portionis grauitatis cen-
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            trum k; </s>
            <s xml:id="echoid-s2427" xml:space="preserve">partis eius, quæ in humido h; </s>
            <s xml:id="echoid-s2428" xml:space="preserve">at eius, quæ extra
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            humidum in linea h κ; </s>
            <s xml:id="echoid-s2429" xml:space="preserve">quod ſit ω: </s>
            <s xml:id="echoid-s2430" xml:space="preserve">& </s>
            <s xml:id="echoid-s2431" xml:space="preserve">h k ad humidi ſuper-
              <lb/>
            ficiem perpendicularis. </s>
            <s xml:id="echoid-s2432" xml:space="preserve">per eaſdem igitur rectas lineas,
              <lb/>
            quod quidem in humido eſt, ſurſum, & </s>
            <s xml:id="echoid-s2433" xml:space="preserve">quod extra humi-
              <lb/>
            dum deorſum feretur. </s>
            <s xml:id="echoid-s2434" xml:space="preserve">quare manebit portio, cuius baſis
              <lb/>
            humidi ſuperficiem in uno puncto continget: </s>
            <s xml:id="echoid-s2435" xml:space="preserve">& </s>
            <s xml:id="echoid-s2436" xml:space="preserve">axis cum
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            ipſa angulum faciet æqualem angulo χ. </s>
            <s xml:id="echoid-s2437" xml:space="preserve">Similiter demon-
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              <note position="left" xlink:label="note-0092-02" xlink:href="note-0092-02a" xml:space="preserve">F</note>
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