Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11.] PROPOSITIO IIII.
[12.] PROPOSITIO V.
[13.] PROPOSITIO VI.
[14.] PROPOSITIO VII.
[15.] POSITIO II.
[16.] COMMENTARIVS.
[17.] PROPOSITIO VIII.
[18.] COMMENTARIVS.
[19.] PROPOSITIO IX.
[20.] COMMENTARIVS.
[21.] ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.
[22.] PROPOSITIO II.
[23.] COMMENTARIVS.
[24.] PROPOSITIO III.
[25.] PROPOSITIO IIII.
[26.] COMMENTARIVS.
[27.] PROPOSITIO V.
[28.] COMMENTARIVS.
[29.] PROPOSITIO VI.
[30.] COMMENTARIVS.
[31.] LEMMAI.
[32.] LEMMA II.
[33.] LEMMA III.
[34.] LEMMA IIII.
[35.] PROPOSITIO VII.
[36.] PROPOSITIO VIII.
[37.] COMMENTARIVS.
[38.] PROPOSITIO IX.
[39.] COMMENTARIVS.
[40.] PROPOSITIO X.
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            in linea e b punctũ g, it aut ſit g e æqualis e f. </s>
            <s xml:id="echoid-s3150" xml:space="preserve">erit g por-
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            tionis a b c centrum. </s>
            <s xml:id="echoid-s3151" xml:space="preserve">nam ſi hæ portiones, quæ æquales
              <lb/>
            & </s>
            <s xml:id="echoid-s3152" xml:space="preserve">ſimiles ſunt, inter ſe ſe aptentur, ita ut b e cadat in d e,
              <lb/>
            & </s>
            <s xml:id="echoid-s3153" xml:space="preserve">punctum b in d cadet, & </s>
            <s xml:id="echoid-s3154" xml:space="preserve">g in f: </s>
            <s xml:id="echoid-s3155" xml:space="preserve">figuris autem æquali-
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            bus, & </s>
            <s xml:id="echoid-s3156" xml:space="preserve">ſimilibus inter ſe aptatis, centra quoque grauitatis
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            ipſarum inter ſe aptata erunt, ex quinta petitione Archi-
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            medis in libro de centro grauitatis planorum. </s>
            <s xml:id="echoid-s3157" xml:space="preserve">Quare cum
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            portionis a d c centrum grauitatis ſit ſ: </s>
            <s xml:id="echoid-s3158" xml:space="preserve">& </s>
            <s xml:id="echoid-s3159" xml:space="preserve">portionis
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            a b c centrum g: </s>
            <s xml:id="echoid-s3160" xml:space="preserve">magnitudinis; </s>
            <s xml:id="echoid-s3161" xml:space="preserve">quæ ex utriſque efficitur:
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            </s>
            <s xml:id="echoid-s3162" xml:space="preserve">hoc eſt circuli uel ellipſis grauitatis centrum in medio li-
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            neæ f g, quod eſt e, conſiſtet, ex quarta propoſitione eiuſ-
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            dem libri Archimedis. </s>
            <s xml:id="echoid-s3163" xml:space="preserve">ergo circuli, uel ellipſis centrum
              <lb/>
            grauitatis eſt idem, quod figuræ centrum. </s>
            <s xml:id="echoid-s3164" xml:space="preserve">atque illud eſt,
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            quod demonſtrare oportebat.</s>
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            <s xml:id="echoid-s3166" xml:space="preserve">Ex quibus ſequitur portionis circuli, uel ellip-
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            ſis, quæ dimidia maior ſit, centrum grauitatis in
              <lb/>
            diametro quoque ipſius conſiſtere.</s>
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          <figure number="81">
            <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0124-01"/>
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            <s xml:id="echoid-s3168" xml:space="preserve">Sit enim maior portio a b c, cu_i_us diameter b d, & </s>
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            pleatur circulus, uel ellipſis, ut portio reliqua ſit a e c, </s>
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