Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb o="32" file="0175" n="175" rhead="DE CENTRO GRAVIT. SOLID."/>
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            <s xml:id="echoid-s4367" xml:space="preserve">SIT fruſtũ pyramidis, uel coni, uel coni portionis a d,
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            cuius maior baſis a b, minor c d. </s>
            <s xml:id="echoid-s4368" xml:space="preserve">& </s>
            <s xml:id="echoid-s4369" xml:space="preserve">ſecetur altero plano
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            baſi æquidiſtante, ita utſectio e f ſit proportionalis inter
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            baſes a b, c d. </s>
            <s xml:id="echoid-s4370" xml:space="preserve">conſtituatur autẽ pyramis, uel conus, uel co-
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            ni portio a g b, cuius baſis ſit eadem, quæ baſis maior fru-
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            ſti, & </s>
            <s xml:id="echoid-s4371" xml:space="preserve">altitudo æqualis. </s>
            <s xml:id="echoid-s4372" xml:space="preserve">Di-
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              <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a" number="129">
                <image file="0175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-01"/>
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            co fruſtum a d ad pyrami-
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            dem, uel conum, uel coni
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            portionem a g b eandem
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            proportionẽ habere, quã
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            utræque baſes, a b, c d unà
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            cum e f ad baſim a b. </s>
            <s xml:id="echoid-s4373" xml:space="preserve">eſt
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            enim fruſtum a d æquale
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            pyramidi, uel cono, uel co-
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            ni portioni, cuius baſis ex
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            tribus baſibus a b, e f, c d
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            conſtat; </s>
            <s xml:id="echoid-s4374" xml:space="preserve">& </s>
            <s xml:id="echoid-s4375" xml:space="preserve">altitudo ipſius
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            altitudini eſt æqualis: </s>
            <s xml:id="echoid-s4376" xml:space="preserve">quod mox oſtendemus. </s>
            <s xml:id="echoid-s4377" xml:space="preserve">Sed pyrami
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            des, coni, uel coni portiões,
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              <figure xlink:label="fig-0175-02" xlink:href="fig-0175-02a" number="130">
                <image file="0175-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-02"/>
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            quæ ſunt æquali altitudine,
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            eãdem inter ſe, quam baſes,
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            proportionem habent, ſicu-
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            ti demonſtratum eſt, partim
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            ab Euclide in duodecimo li-
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              <note position="right" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">6. 11. duo
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              decimi</note>
            bro elementorum, partim à
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            nobis in cõmentariis in un-
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            decimam propoſitionẽ Ar-
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            chimedis de conoidibus, & </s>
            <s xml:id="echoid-s4378" xml:space="preserve">
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            ſphæroidibus. </s>
            <s xml:id="echoid-s4379" xml:space="preserve">quare pyra-
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            mis, uel conus, uel coni por-
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            tio, cuius baſis eſt tribus illis
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            baſibus æqualis ad a g b eam
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            habet proportionem, quam
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            baſes a b, e f, c d ad ab bafim. </s>
            <s xml:id="echoid-s4380" xml:space="preserve">Fruſtum igitur a d ad a g </s>
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Impressum