Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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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:id="echoid-s4096" xml:space="preserve">ſi enim intelligantur duæ pyramides a b c d e, g h k l m, ha-
              <lb/>
            bebunt hæ inter ſe proportionem eandem, quam ipſarum
              <lb/>
            baſes ex ſexta duodecimi elementorum. </s>
            <s xml:id="echoid-s4097" xml:space="preserve">Sed ut baſis a b c d
              <lb/>
            ad g h K l baſim, ita linea o ad lineam p; </s>
            <s xml:id="echoid-s4098" xml:space="preserve">hoc eſt ad lineam q
              <lb/>
            ei æqualem. </s>
            <s xml:id="echoid-s4099" xml:space="preserve">ergo priſma a e ad priſma g m eſt, ut linea o
              <lb/>
            ad lineam q. </s>
            <s xml:id="echoid-s4100" xml:space="preserve">proportio autem o ad q cõpoſita eſt ex pro-
              <lb/>
            portione o ad p, & </s>
            <s xml:id="echoid-s4101" xml:space="preserve">ex proportione p ad q. </s>
            <s xml:id="echoid-s4102" xml:space="preserve">quare priſma
              <lb/>
            a e ad priſma g m, & </s>
            <s xml:id="echoid-s4103" xml:space="preserve">idcirco pyramis a b c d e, ad pyrami-
              <lb/>
            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:id="echoid-s4104" xml:space="preserve">ex proportione altitudinis e f ad m n al
              <lb/>
            titudinem. </s>
            <s xml:id="echoid-s4105" xml:space="preserve">Quòd ſi lineæ e f, m n inæquales ponantur, ſit
              <lb/>
            e f minor: </s>
            <s xml:id="echoid-s4106" xml:space="preserve">& </s>
            <s xml:id="echoid-s4107" xml:space="preserve">ut e f ad m n, ita fiat linea p ad lineam u: </s>
            <s xml:id="echoid-s4108" xml:space="preserve">de
              <lb/>
              <figure xlink:label="fig-0165-01" xlink:href="fig-0165-01a" number="121">
                <image file="0165-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0165-01"/>
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            inde ab ipſa m n abſcindatur r n æqualis e f: </s>
            <s xml:id="echoid-s4109" xml:space="preserve">& </s>
            <s xml:id="echoid-s4110" xml:space="preserve">per r duca-
              <lb/>
            tur planum, quod oppoſitis planis æquidiſtans faciat ſe-
              <lb/>
            ctionem s t. </s>
            <s xml:id="echoid-s4111" xml:space="preserve">erit priſma a e, ad priſma g t, ut baſis a b c d
              <lb/>
            ad baſim g h k l; </s>
            <s xml:id="echoid-s4112" xml:space="preserve">hoc eſt ut o ad p: </s>
            <s xml:id="echoid-s4113" xml:space="preserve">ut autem priſma g t ad
              <lb/>
            priſma g m, ita altitudo r n; </s>
            <s xml:id="echoid-s4114" xml:space="preserve">hoc eſt e f ad altitudinẽ m n;
              <lb/>
            </s>
            <s xml:id="echoid-s4115" xml:space="preserve">
              <note position="right" xlink:label="note-0165-01" xlink:href="note-0165-01a" xml:space="preserve">20. huius</note>
            uidelicet linea p ad lineam u. </s>
            <s xml:id="echoid-s4116" xml:space="preserve">ergo ex æquali priſma a e ad
              <lb/>
            priſma g m eſt, ut linea o ad ipſam u. </s>
            <s xml:id="echoid-s4117" xml:space="preserve">Sed proportio o ad
              <lb/>
            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:id="echoid-s4118" xml:space="preserve">& </s>
            <s xml:id="echoid-s4119" xml:space="preserve">ex proportione p ad u, quæ eſt altitudi-
              <lb/>
            nis e f ad altitudinem m n. </s>
            <s xml:id="echoid-s4120" xml:space="preserve">priſma igitur a e ad priſma g </s>
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