Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb file="0154" n="154" rhead="FED. COMMANDINI"/>
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        <div xml:id="echoid-div235" type="section" level="1" n="81">
          <head xml:id="echoid-head88" xml:space="preserve">THE OREMA XII. PROPOSITIO XVI.</head>
          <p>
            <s xml:id="echoid-s3850" xml:space="preserve">In ſphæra, & </s>
            <s xml:id="echoid-s3851" xml:space="preserve">ſphæroide idem eſt grauitatis, & </s>
            <s xml:id="echoid-s3852" xml:space="preserve">
              <lb/>
            figuræ centrum.</s>
            <s xml:id="echoid-s3853" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3854" xml:space="preserve">Secetur ſphæra, uel ſphæroid
              <gap/>
            no per axem ducto;
              <lb/>
            </s>
            <s xml:id="echoid-s3855" xml:space="preserve">quod ſectionem faciat circulum,
              <gap/>
            ellipſim a b c d, cuius
              <lb/>
            diameter, & </s>
            <s xml:id="echoid-s3856" xml:space="preserve">ſphæræ, uelſphæroidis axis d b; </s>
            <s xml:id="echoid-s3857" xml:space="preserve">& </s>
            <s xml:id="echoid-s3858" xml:space="preserve">centrume. </s>
            <s xml:id="echoid-s3859" xml:space="preserve">
              <lb/>
            Dico e grauitatis etiam centrum eſſe. </s>
            <s xml:id="echoid-s3860" xml:space="preserve">ſecetur enim altero
              <lb/>
            plano per e, ad planum ſecans recto, cuius fectio ſit circu-
              <lb/>
            lus circa diametrum a c. </s>
            <s xml:id="echoid-s3861" xml:space="preserve">erunt a d c, a b c dimidiæ portio-
              <lb/>
            nes ſphæræ, uel fphæroidis. </s>
            <s xml:id="echoid-s3862" xml:space="preserve">& </s>
            <s xml:id="echoid-s3863" xml:space="preserve">quoniam portionis a d c gra
              <lb/>
            uitatis centrum eſt in linea d, & </s>
            <s xml:id="echoid-s3864" xml:space="preserve">centrum portionis a b c in
              <lb/>
            ipſa b e; </s>
            <s xml:id="echoid-s3865" xml:space="preserve">totius ſphæræ, uel ſphæroidis grauitatis centrum
              <lb/>
            in axe d b conſiſtet. </s>
            <s xml:id="echoid-s3866" xml:space="preserve">Quòd ſi portionis a d c centrum graui
              <lb/>
            tatis ponatur eſſe f. </s>
            <s xml:id="echoid-s3867" xml:space="preserve">& </s>
            <s xml:id="echoid-s3868" xml:space="preserve">fiat ipſi f e æqualis e g: </s>
            <s xml:id="echoid-s3869" xml:space="preserve">punctũ g por
              <lb/>
              <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a" number="107">
                <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0154-01"/>
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            tionis a b c centrum erit. </s>
            <s xml:id="echoid-s3870" xml:space="preserve">ſolidis enim figuris ſimilibus & </s>
            <s xml:id="echoid-s3871" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">per 2. pe-
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              titionem</note>
            æqualibus inter ſe aptatis, & </s>
            <s xml:id="echoid-s3872" xml:space="preserve">centra grauitatis ipſarum in-
              <lb/>
            ter fe aptentur neceſſe eſt. </s>
            <s xml:id="echoid-s3873" xml:space="preserve">ex quo fit, ut magnitudinis, quæ
              <lb/>
              <note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">4 Arch-
                <lb/>
              medis.</note>
            ex utriſque cõſtat, hoc eſt ipſius ſphæræ, uel ſphæroidis gra
              <lb/>
            uitatis centrum ſitin medio lineæ f g, uidelicet in e. </s>
            <s xml:id="echoid-s3874" xml:space="preserve">Sphæ-
              <lb/>
            ræ igitur, uel ſphæroidis grauitatis centrum eſtidem, quod
              <lb/>
            centrum figuræ.</s>
            <s xml:id="echoid-s3875" xml:space="preserve"/>
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