Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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              <pb o="27" file="0165" n="165" rhead="DE CENTRO GRAVIT. SOLID."/>
            proportionem habet, quam baſis a b c d ad baſim g h k l:
              <lb/>
            </s>
            <s xml:space="preserve">ſi enim intelligantur duæ pyramides a b c d e, g h k l m, ha-
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            bebunt hæ inter ſe proportionem eandem, quam ipſarum
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            baſes ex ſexta duodecimi elementorum. </s>
            <s xml:space="preserve">Sed ut baſis a b c d
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            ad g h K l baſim, ita linea o ad lineam p; </s>
            <s xml:space="preserve">hoc eſt ad lineam q
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            ei æqualem. </s>
            <s xml:space="preserve">ergo priſma a e ad priſma g m eſt, ut linea o
              <lb/>
            ad lineam q. </s>
            <s xml:space="preserve">proportio autem o ad q cõpoſita eſt ex pro-
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            portione o ad p, & </s>
            <s xml:space="preserve">ex proportione p ad q. </s>
            <s xml:space="preserve">quare priſma
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            a e ad priſma g m, & </s>
            <s xml:space="preserve">idcirco pyramis a b c d e, ad pyrami-
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            dem g h K l m proportionem habet ex eiſdem proportio-
              <lb/>
            nibus compoſitam, uidelicet ex proportione baſis a b c d
              <lb/>
            ad baſim g h _K_ l, & </s>
            <s xml:space="preserve">ex proportione altitudinis e f ad m n al
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            titudinem. </s>
            <s xml:space="preserve">Quòd ſi lineæ e f, m n inæquales ponantur, ſit
              <lb/>
            e f minor: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut e f ad m n, ita fiat linea p ad lineam u: </s>
            <s xml:space="preserve">de
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              <anchor type="figure" xlink:label="fig-0165-01a" xlink:href="fig-0165-01"/>
            inde ab ipſa m n abſcindatur r n æqualis e f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per r duca-
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            tur planum, quod oppoſitis planis æquidiſtans faciat ſe-
              <lb/>
            ctionem s t. </s>
            <s xml:space="preserve">erit priſma a e, ad priſma g t, ut baſis a b c d
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            ad baſim g h k l; </s>
            <s xml:space="preserve">hoc eſt ut o ad p: </s>
            <s xml:space="preserve">ut autem priſma g t ad
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            priſma g m, ita altitudo r n; </s>
            <s xml:space="preserve">hoc eſt e f ad altitudinẽ m n;
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            </s>
            <s xml:space="preserve">
              <anchor type="note" xlink:label="note-0165-01a" xlink:href="note-0165-01"/>
            uidelicet linea p ad lineam u. </s>
            <s xml:space="preserve">ergo ex æquali priſma a e ad
              <lb/>
            priſma g m eſt, ut linea o ad ipſam u. </s>
            <s xml:space="preserve">Sed proportio o ad
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            u cõpoſita eſt ex proportione o ad p, quæ eſt baſis a b c d
              <lb/>
            ad baſim g h k l; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex proportione p ad u, quæ eſt altitudi-
              <lb/>
            nis e f ad altitudinem m n. </s>
            <s xml:space="preserve">priſma igitur a e ad priſma g m</s>
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