Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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              <pb file="0172" n="172" rhead="FED. COMMANDINI"/>
            Dico eas proportion ales eſſe in proportione, quæ eſt la-
              <lb/>
            teris a b adlatus d e, itaut earum maior ſit a b c e, me-
              <lb/>
            dia a d c e, & </s>
            <s xml:id="echoid-s4304" xml:space="preserve">minor d e f c. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">Quoniam enim lineæ d e,
              <lb/>
            a b æquidiſtant; </s>
            <s xml:id="echoid-s4306" xml:space="preserve">& </s>
            <s xml:id="echoid-s4307" xml:space="preserve">interipſas ſunt triangula a b e, a d e;
              <lb/>
            </s>
            <s xml:id="echoid-s4308" xml:space="preserve">erit triangulum a b e
              <lb/>
              <figure xlink:label="fig-0172-01" xlink:href="fig-0172-01a" number="126">
                <image file="0172-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0172-01"/>
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              <note position="left" xlink:label="note-0172-01" xlink:href="note-0172-01a" xml:space="preserve">1. ſextí.</note>
            ad triangulum a d e,
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            ut linea a b ad lineam
              <lb/>
            d e. </s>
            <s xml:id="echoid-s4309" xml:space="preserve">ut autem triangu
              <lb/>
            lum a b e ad triangu-
              <lb/>
            lum a d e, ita pyramis
              <lb/>
              <note position="left" xlink:label="note-0172-02" xlink:href="note-0172-02a" xml:space="preserve">5. duodeci
                <lb/>
              mi.</note>
            a b e c ad pyramidem
              <lb/>
            a d e c: </s>
            <s xml:id="echoid-s4310" xml:space="preserve">habent enim
              <lb/>
            altitudinem eandem,
              <lb/>
            quæ eſt à puncto c ad
              <lb/>
            planum, in quo qua-
              <lb/>
            drilaterum a b e d. </s>
            <s xml:id="echoid-s4311" xml:space="preserve">er-
              <lb/>
              <note position="left" xlink:label="note-0172-03" xlink:href="note-0172-03a" xml:space="preserve">11. quinti.</note>
            go ut a b ad d e, ita pyramis a b e c ad pyramidem a d e c.
              <lb/>
            </s>
            <s xml:id="echoid-s4312" xml:space="preserve">Rurſus quoniam æquidiſtantes ſunt a c, d f; </s>
            <s xml:id="echoid-s4313" xml:space="preserve">erit eadem
              <lb/>
            ratione pyramis a d c e ad pyramidem c d f e, ut a c ad
              <lb/>
              <note position="left" xlink:label="note-0172-04" xlink:href="note-0172-04a" xml:space="preserve">4 ſexti.</note>
            d f. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">Sed ut a c a l d f, ita a b ad d e, quoniam triangula
              <lb/>
            a b c, d e f ſimilia ſunt, ex nona huius. </s>
            <s xml:id="echoid-s4315" xml:space="preserve">quare ut pyramis
              <lb/>
            a b c e ad pyramidem a d c e, ita pyramis a d c e ad ipſam
              <lb/>
            d e f c. </s>
            <s xml:id="echoid-s4316" xml:space="preserve">fruſtum igitur a b c d e f diuiditur in tres pyramides
              <lb/>
            proportionales in ea proportione, quæ eſt lateris a b ad d e
              <lb/>
            latus, & </s>
            <s xml:id="echoid-s4317" xml:space="preserve">earum maior eſt c a b e, media a d c e, & </s>
            <s xml:id="echoid-s4318" xml:space="preserve">minor
              <lb/>
            d e f c. </s>
            <s xml:id="echoid-s4319" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s4320" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div260" type="section" level="1" n="89">
          <head xml:id="echoid-head96" xml:space="preserve">PROBLEMA V. PROPOSITIO XXIIII.</head>
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            <s xml:id="echoid-s4321" xml:space="preserve">
              <emph style="sc">Qvodlibet</emph>
            fruſtum pyramidis, uel coni,
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            uel coni portionis, plano baſi æquidiſtanti ita ſe-
              <lb/>
            care, ut ſectio ſit proportionalis inter maiorem,
              <lb/>
            & </s>
            <s xml:id="echoid-s4322" xml:space="preserve">minorem baſim.</s>
            <s xml:id="echoid-s4323" xml:space="preserve"/>
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