Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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              <pb o="39" file="0189" n="189" rhead="DE CENTRO GRAVIT. SOLID."/>
            dem, cuius baſis eſt quadratum a b c d, & </s>
            <s xml:id="echoid-s4728" xml:space="preserve">altitudo e g: </s>
            <s xml:id="echoid-s4729" xml:space="preserve">& </s>
            <s xml:id="echoid-s4730" xml:space="preserve">
              <lb/>
            in pyramidem, cuius eadé baſis, altitudoq; </s>
            <s xml:id="echoid-s4731" xml:space="preserve">f g; </s>
            <s xml:id="echoid-s4732" xml:space="preserve">ut ſint e g,
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            g f ſemidiametri ſphæræ, & </s>
            <s xml:id="echoid-s4733" xml:space="preserve">linea una. </s>
            <s xml:id="echoid-s4734" xml:space="preserve">Cũigitur g ſit ſphæ-
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            ræ centrum, erit etiam centrum circuli, qui circa quadratũ
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            a b c d deſcribitur: </s>
            <s xml:id="echoid-s4735" xml:space="preserve">& </s>
            <s xml:id="echoid-s4736" xml:space="preserve">propterea eiuſdem quadrati grauita
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            tis centrum: </s>
            <s xml:id="echoid-s4737" xml:space="preserve">quod in prima propoſitione huius demon-
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            ſtratum eſt. </s>
            <s xml:id="echoid-s4738" xml:space="preserve">quare pyramidis a b c d e axis erit e g: </s>
            <s xml:id="echoid-s4739" xml:space="preserve">& </s>
            <s xml:id="echoid-s4740" xml:space="preserve">pyra
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            midis a b c d f axis f g. </s>
            <s xml:id="echoid-s4741" xml:space="preserve">Itaque ſit h centrum grauitatis py-
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            ramidis a b c d e, & </s>
            <s xml:id="echoid-s4742" xml:space="preserve">pyramidis a b c d f centrum ſit _K_: </s>
            <s xml:id="echoid-s4743" xml:space="preserve">per-
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            ſpicuum eſt ex uigeſima ſecunda propoſitione huius, lineã
              <lb/>
            e h triplam eſſe h g: </s>
            <s xml:id="echoid-s4744" xml:space="preserve">cõ
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              <figure xlink:label="fig-0189-01" xlink:href="fig-0189-01a" number="140">
                <image file="0189-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0189-01"/>
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            ponendoq; </s>
            <s xml:id="echoid-s4745" xml:space="preserve">e g ipſius g
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            h quadruplam. </s>
            <s xml:id="echoid-s4746" xml:space="preserve">& </s>
            <s xml:id="echoid-s4747" xml:space="preserve">eadẽ
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            ratione f g quadruplã
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            ipſius g k. </s>
            <s xml:id="echoid-s4748" xml:space="preserve">quod cum e
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            g, g f ſintæquales, & </s>
            <s xml:id="echoid-s4749" xml:space="preserve">h
              <lb/>
            g, g _k_ neceſſario æqua-
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            les erunt. </s>
            <s xml:id="echoid-s4750" xml:space="preserve">ergo ex quar
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            ta propoſitione primi
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            libri Archimedis de cẽ-
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            tro grauitatis planorũ,
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            totius octahedri, quod
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            ex dictis pyramidibus
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            conſtat, centrum graui
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            tatis erit punctum g idem, quodipſius ſphæræ centrum.</s>
            <s xml:id="echoid-s4751" xml:space="preserve"/>
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            <s xml:id="echoid-s4752" xml:space="preserve">Sit icoſahedrum a d deſcriptum in ſphæra, cuius centrū
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            ſit g. </s>
            <s xml:id="echoid-s4753" xml:space="preserve">Dico g ipſius icoſahedri grauitatis eſſe centrum. </s>
            <s xml:id="echoid-s4754" xml:space="preserve">Si
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            enim ab angnlo a per g ducatur rectalinea uſque ad ſphæ
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            ræ ſuperficiem; </s>
            <s xml:id="echoid-s4755" xml:space="preserve">conſtat ex ſexta decima propoſitione libri
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            tertii decimi elementorum, cadere eam in angulum ipſi a
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            oppoſitum. </s>
            <s xml:id="echoid-s4756" xml:space="preserve">cadat in d: </s>
            <s xml:id="echoid-s4757" xml:space="preserve">ſitq; </s>
            <s xml:id="echoid-s4758" xml:space="preserve">una aliqua baſis icoſahedri tri-
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            angulum a b c: </s>
            <s xml:id="echoid-s4759" xml:space="preserve">& </s>
            <s xml:id="echoid-s4760" xml:space="preserve">iunctæ b g, c g producantur, & </s>
            <s xml:id="echoid-s4761" xml:space="preserve">cadant in
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            angulos e f, ipſis b c oppoſitos. </s>
            <s xml:id="echoid-s4762" xml:space="preserve">Itaque per triangula
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            a b c, d e f ducantur plana ſphæram ſecantia. </s>
            <s xml:id="echoid-s4763" xml:space="preserve">erunt hæ </s>
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