Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <p>
            <s xml:id="echoid-s4380" xml:space="preserve">
              <pb file="0176" n="176" rhead="FED. COMMANDINI"/>
            pyramidem, uel conum, uel coni portionem candem pro-
              <lb/>
            portionem habet, quam baſes ab, cd unà cum e ſ ad ba-
              <lb/>
            ſim a b. </s>
            <s xml:id="echoid-s4381" xml:space="preserve">quod demonſtrare uolebamus.</s>
            <s xml:id="echoid-s4382" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4383" xml:space="preserve">Fruſtum uero a d æquale eſſe pyramidi, uel co
              <lb/>
            no, uel coni portioni, cuius baſis conſtat ex baſi-
              <lb/>
            bus a b, c d, e f, & </s>
            <s xml:id="echoid-s4384" xml:space="preserve">altitudo fruſti altitudini eſt æ-
              <lb/>
            qualis, hoc modo oſten demus.</s>
            <s xml:id="echoid-s4385" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4386" xml:space="preserve">Sit fruſtum pyramidis a b c d e f, cuius maior baſis trian-
              <lb/>
            gulum a b c; </s>
            <s xml:id="echoid-s4387" xml:space="preserve">minor d e f: </s>
            <s xml:id="echoid-s4388" xml:space="preserve">& </s>
            <s xml:id="echoid-s4389" xml:space="preserve">ſecetur plano baſibus æquidi-
              <lb/>
            ſtante, quod ſectionem faciat triangulum g h k inter trian-
              <lb/>
            gula a b c, d e f proportionale. </s>
            <s xml:id="echoid-s4390" xml:space="preserve">Iam ex iis, quæ demonſtrata
              <lb/>
            ſuntin 23. </s>
            <s xml:id="echoid-s4391" xml:space="preserve">huius, patet ſruſtum a b c d e f diuidi in tres pyra
              <lb/>
            mides proportionales; </s>
            <s xml:id="echoid-s4392" xml:space="preserve">& </s>
            <s xml:id="echoid-s4393" xml:space="preserve">earum maiorem eſſe pyramidẽ
              <lb/>
            a b c d minorẽ uero d e f b. </s>
            <s xml:id="echoid-s4394" xml:space="preserve">ergo pyramis à triangulo g h k
              <lb/>
            conſtituta, quæ altitudinem habeat ſruſti altitudini æqua-
              <lb/>
            lem, proportionalis eſtinter pyramides a b c d, d e f b: </s>
            <s xml:id="echoid-s4395" xml:space="preserve">& </s>
            <s xml:id="echoid-s4396" xml:space="preserve">
              <lb/>
            idcirco fruſtum a b c d e f tribus dictis pyramidibus æqua
              <lb/>
            le erit. </s>
            <s xml:id="echoid-s4397" xml:space="preserve">Itaque ſi intelligatur alia pyra-
              <lb/>
              <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a" number="131">
                <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0176-01"/>
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            mis æque alta, quæ baſim habeat ex tri
              <lb/>
            bus baſibus a b c, d e f, g h k conſtan-
              <lb/>
            tem; </s>
            <s xml:id="echoid-s4398" xml:space="preserve">perſpicuum eſtipſam eiſdem py-
              <lb/>
            ramidibus, & </s>
            <s xml:id="echoid-s4399" xml:space="preserve">propterea ipſi fruſto æ-
              <lb/>
            qualem eſſe.</s>
            <s xml:id="echoid-s4400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4401" xml:space="preserve">Rurſus ſit ſruſtum pyramidis a g, cu
              <lb/>
            ius maior baſis quadrilaterum a b c d,
              <lb/>
            minor e f g h: </s>
            <s xml:id="echoid-s4402" xml:space="preserve">& </s>
            <s xml:id="echoid-s4403" xml:space="preserve">ſecetur plano baſi-
              <lb/>
            bus æquidiſtante, ita ut fiat ſectio qua-
              <lb/>
            drilaterum K lm n, quod ſit proportio
              <lb/>
            nale inter quadrilatera a b c d, e f g h. </s>
            <s xml:id="echoid-s4404" xml:space="preserve">Dico pyramidem,
              <lb/>
            cuius baſis ſit æqualis tribus quadrilateris a b c d, _k_ l m n,
              <lb/>
            e f g h, & </s>
            <s xml:id="echoid-s4405" xml:space="preserve">altitudo æqualis altitudini fruſti, ipſi fruſto a g
              <lb/>
            æqualem eſſe. </s>
            <s xml:id="echoid-s4406" xml:space="preserve">Ducatur enim planum per lineas f b, h </s>
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