Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
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          <head xml:space="preserve">THE OREMA XII. PROPOSITIO XVI.</head>
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            <s xml:space="preserve">In ſphæra, & </s>
            <s xml:space="preserve">ſphæroide idem eſt grauitatis, & </s>
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            figuræ centrum.</s>
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            <s xml:space="preserve">Secetur ſphæra, uel ſphæroid
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            no per axem ducto;
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            </s>
            <s xml:space="preserve">quod ſectionem faciat circulum,
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            ellipſim a b c d, cuius
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            diameter, & </s>
            <s xml:space="preserve">ſphæræ, uelſphæroidis axis d b; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">centrume. </s>
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            Dico e grauitatis etiam centrum eſſe. </s>
            <s xml:space="preserve">ſecetur enim altero
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            plano per e, ad planum ſecans recto, cuius fectio ſit circu-
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            lus circa diametrum a c. </s>
            <s xml:space="preserve">erunt a d c, a b c dimidiæ portio-
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            nes ſphæræ, uel fphæroidis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam portionis a d c gra
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            uitatis centrum eſt in linea d, & </s>
            <s xml:space="preserve">centrum portionis a b c in
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            ipſa b e; </s>
            <s xml:space="preserve">totius ſphæræ, uel ſphæroidis grauitatis centrum
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            in axe d b conſiſtet. </s>
            <s xml:space="preserve">Quòd ſi portionis a d c centrum graui
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            tatis ponatur eſſe f. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fiat ipſi f e æqualis e g: </s>
            <s xml:space="preserve">punctũ g por
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            tionis a b c centrum erit. </s>
            <s xml:space="preserve">ſolidis enim figuris ſimilibus & </s>
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            æqualibus inter ſe aptatis, & </s>
            <s xml:space="preserve">centra grauitatis ipſarum in-
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            ter fe aptentur neceſſe eſt. </s>
            <s xml:space="preserve">ex quo fit, ut magnitudinis, quæ
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            ex utriſque cõſtat, hoc eſt ipſius ſphæræ, uel ſphæroidis gra
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            uitatis centrum ſitin medio lineæ f g, uidelicet in e. </s>
            <s xml:space="preserve">Sphæ-
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            ræ igitur, uel ſphæroidis grauitatis centrum eſtidem, quod
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            centrum figuræ.</s>
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            <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>
            <note position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">4 Arch-
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            medis.</note>
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