Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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          <pb o="31" file="0173" n="173" rhead="DE CENTRO GRAVIT. SOLID."/>
          <p>
            <s xml:id="echoid-s4324" xml:space="preserve">SIT fruſtum pyramidis a e, cuius maior baſis triangu-
              <lb/>
            lum a b c, minor d e f: </s>
            <s xml:id="echoid-s4325" xml:space="preserve">& </s>
            <s xml:id="echoid-s4326" xml:space="preserve">oporteat ipſum plano, quod baſi
              <lb/>
            æquidiſtet, ita ſecare, ut ſectio ſit proportionalis inter triã
              <lb/>
            gula a b c, d e f. </s>
            <s xml:id="echoid-s4327" xml:space="preserve">Inueniatur inter lineas a b, d e media pro-
              <lb/>
            portionalis, quæ ſit b g: </s>
            <s xml:id="echoid-s4328" xml:space="preserve">& </s>
            <s xml:id="echoid-s4329" xml:space="preserve">à puncto g erigatur g h æquidi-
              <lb/>
            ſtans b e, ſecansq; </s>
            <s xml:id="echoid-s4330" xml:space="preserve">a d in h: </s>
            <s xml:id="echoid-s4331" xml:space="preserve">deinde per h ducatur planum
              <lb/>
            baſibus æ quidiſtans, cuius ſectio ſit triangulum h _k_ 1. </s>
            <s xml:id="echoid-s4332" xml:space="preserve">Dico
              <lb/>
            triangulum h K l proportionale eſſe inter triangula a b c,
              <lb/>
            d e f, hoc eſt triangulum a b c ad
              <lb/>
              <figure xlink:label="fig-0173-01" xlink:href="fig-0173-01a" number="127">
                <image file="0173-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0173-01"/>
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            triangulum h K l eandem habere
              <lb/>
            proportionem, quam triãgulum
              <lb/>
            h K l ad ipſum d e f. </s>
            <s xml:id="echoid-s4333" xml:space="preserve">Quoniã enim
              <lb/>
            lineæ a b, h K æquidiſtantium pla
              <lb/>
              <note position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">16. unde
                <lb/>
              cimi</note>
            norum ſectiones inter ſe æquidi-
              <lb/>
            ſtant: </s>
            <s xml:id="echoid-s4334" xml:space="preserve">atque æquidiſtant b _k_, g h:
              <lb/>
            </s>
            <s xml:id="echoid-s4335" xml:space="preserve">linea h _k_ ipſi g b eſt æqualis: </s>
            <s xml:id="echoid-s4336" xml:space="preserve">& </s>
            <s xml:id="echoid-s4337" xml:space="preserve">pro
              <lb/>
              <note position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">34. primi</note>
            pterea proportionalis inter a b,
              <lb/>
            d e. </s>
            <s xml:id="echoid-s4338" xml:space="preserve">quare ut a b ad h K, ita eſt h
              <emph style="sc">K</emph>
              <lb/>
            ad d e. </s>
            <s xml:id="echoid-s4339" xml:space="preserve">fiat ut h k ad d e, ita d e
              <lb/>
            ad aliam lineam, in qua ſit m. </s>
            <s xml:id="echoid-s4340" xml:space="preserve">erit
              <lb/>
            ex æquali ut a b ad d e, ita h k ad
              <lb/>
            m. </s>
            <s xml:id="echoid-s4341" xml:space="preserve">Et quoniam triangula a b c,
              <lb/>
              <note position="right" xlink:label="note-0173-03" xlink:href="note-0173-03a" xml:space="preserve">9. huius
                <lb/>
              corol.</note>
            h K l, d e f ſimilia ſunt; </s>
            <s xml:id="echoid-s4342" xml:space="preserve">triangulū
              <lb/>
            a b c ad triangulum h k l eſt, ut li-
              <lb/>
              <note position="right" xlink:label="note-0173-04" xlink:href="note-0173-04a" xml:space="preserve">20. ſexti</note>
            nea a b ad lineam d e: </s>
            <s xml:id="echoid-s4343" xml:space="preserve">triangulũ
              <lb/>
            autem h k l ad ipſum d e f eſt, ut h _k_ ad m. </s>
            <s xml:id="echoid-s4344" xml:space="preserve">ergo tríangulum
              <lb/>
              <note position="right" xlink:label="note-0173-05" xlink:href="note-0173-05a" xml:space="preserve">11. quinti</note>
            a b c ad triangulum h k l eandem proportionem habet,
              <lb/>
            quam triangulum h K l ad ipſum d e f. </s>
            <s xml:id="echoid-s4345" xml:space="preserve">Eodem modo in a-
              <lb/>
            liis fruſtis pyramidis idem demonſtrabitur.</s>
            <s xml:id="echoid-s4346" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4347" xml:space="preserve">Sit fruſtum coni, uel coni portionis a d: </s>
            <s xml:id="echoid-s4348" xml:space="preserve">& </s>
            <s xml:id="echoid-s4349" xml:space="preserve">ſecetur plano
              <lb/>
            per axem, cuius ſectio ſit a b c d, ita ut maior ipſius baſis ſit
              <lb/>
            circulus, uel ellipſis circa diametrum a b; </s>
            <s xml:id="echoid-s4350" xml:space="preserve">minor circa c d.
              <lb/>
            </s>
            <s xml:id="echoid-s4351" xml:space="preserve">Rurſus inter lineas a b, c d inueniatur proportionalis b e: </s>
            <s xml:id="echoid-s4352" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s4353" xml:space="preserve">ab e ducta e ſ æquid_i_ſtante b d, quæ lineam c a in f </s>
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