Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
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            pyramidem, uel conum, uel coni portionem candem pro-
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            portionem habet, quam baſes ab, cd unà cum e ſ ad ba-
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            ſim a b. </s>
            <s xml:space="preserve">quod demonſtrare uolebamus.</s>
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          </p>
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            <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a">
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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>
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            <s xml:space="preserve">Fruſtum uero a d æquale eſſe pyramidi, uel co
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            no, uel coni portioni, cuius baſis conſtat ex baſi-
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            bus a b, c d, e f, & </s>
            <s xml:space="preserve">altitudo fruſti altitudini eſt æ-
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            qualis, hoc modo oſten demus.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Sit fruſtum pyramidis a b c d e f, cuius maior baſis trian-
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            gulum a b c; </s>
            <s xml:space="preserve">minor d e f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano baſibus æquidi-
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            ſtante, quod ſectionem faciat triangulum g h k inter trian-
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            gula a b c, d e f proportionale. </s>
            <s xml:space="preserve">Iam ex iis, quæ demonſtrata
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            ſuntin 23. </s>
            <s xml:space="preserve">huius, patet ſruſtum a b c d e f diuidi in tres pyra
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            mides proportionales; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">earum maiorem eſſe pyramidẽ
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            a b c d minorẽ uero d e f b. </s>
            <s xml:space="preserve">ergo pyramis à triangulo g h k
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            conſtituta, quæ altitudinem habeat ſruſti altitudini æqua-
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            lem, proportionalis eſtinter pyramides a b c d, d e f b: </s>
            <s xml:space="preserve">& </s>
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            idcirco fruſtum a b c d e f tribus dictis pyramidibus æqua
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            le erit. </s>
            <s xml:space="preserve">Itaque ſi intelligatur alia pyra-
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              <anchor type="figure" xlink:label="fig-0176-01a" xlink:href="fig-0176-01"/>
            mis æque alta, quæ baſim habeat ex tri
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            bus baſibus a b c, d e f, g h k conſtan-
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            tem; </s>
            <s xml:space="preserve">perſpicuum eſtipſam eiſdem py-
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            ramidibus, & </s>
            <s xml:space="preserve">propterea ipſi fruſto æ-
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            qualem eſſe.</s>
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            <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a">
              <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0176-01"/>
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          <p>
            <s xml:space="preserve">Rurſus ſit ſruſtum pyramidis a g, cu
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            ius maior baſis quadrilaterum a b c d,
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            minor e f g h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano baſi-
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            bus æquidiſtante, ita ut fiat ſectio qua-
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            drilaterum K lm n, quod ſit proportio
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            nale inter quadrilatera a b c d, e f g h. </s>
            <s xml:space="preserve">Dico pyramidem,
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            cuius baſis ſit æqualis tribus quadrilateris a b c d, _k_ l m n,
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            e f g h, & </s>
            <s xml:space="preserve">altitudo æqualis altitudini fruſti, ipſi fruſto a g
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            æqualem eſſe. </s>
            <s xml:space="preserve">Ducatur enim planum per lineas f b, h d,</s>
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