Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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            <s xml:id="echoid-s2828" xml:space="preserve">
              <pb o="120" file="0140" n="140" rhead="GEOMETRIÆ"/>
            ei, quam habet, CO, ad, RZ, vel, CD, ad, RX, cum ſunt æqui-
              <lb/>
            angula, ergo æqualia parallelogramma baſes habent altitudinibus,
              <lb/>
            vel lateribus æqualiter baſibus inclinatis reciprocas, quod oſtendere
              <lb/>
            opus erat.</s>
            <s xml:id="echoid-s2829" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div294" type="section" level="1" n="184">
          <head xml:id="echoid-head199" xml:space="preserve">THEOREMA VIII. PROPOS. VIII.</head>
          <p>
            <s xml:id="echoid-s2830" xml:space="preserve">SImilia parallelogramma ſunt in dupla ratione laterum
              <lb/>
            homologorum.</s>
            <s xml:id="echoid-s2831" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2832" xml:space="preserve">Sint ſimilia parallelogramma, AC, EG. </s>
            <s xml:id="echoid-s2833" xml:space="preserve">Dico eadem eſſe in du-
              <lb/>
              <note position="left" xlink:label="note-0140-01" xlink:href="note-0140-01a" xml:space="preserve">lux diff.
                <lb/>
              Sex. El.</note>
            plarat one laterum homologorum: </s>
            <s xml:id="echoid-s2834" xml:space="preserve">Quoniam enim ſunt ſimilia illa
              <lb/>
            ſunt æquiangula, ſint anguli, BCD, FGH, æquales, & </s>
            <s xml:id="echoid-s2835" xml:space="preserve">latera ho-
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              <figure xlink:label="fig-0140-01" xlink:href="fig-0140-01a" number="80">
                <image file="0140-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0140-01"/>
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            mologa, BC, FG; </s>
            <s xml:id="echoid-s2836" xml:space="preserve">CD, GH, ſi ergo pro
              <lb/>
            baſibus ſumpierimus ipſas, BC, FG, erit,
              <lb/>
              <note position="left" xlink:label="note-0140-02" xlink:href="note-0140-02a" xml:space="preserve">6. huius.</note>
            AC, ad, EG, in ratione compoſita ex ea,
              <lb/>
            quam habet, BC, ad, FG, & </s>
            <s xml:id="echoid-s2837" xml:space="preserve">ex ea, quam
              <lb/>
            habet, DC, ad, HG, quæ eſt eadem ei,
              <lb/>
            quam habet, BC, ad, FG, vel, FG, ad
              <lb/>
            tertiam proportionalem duaru, primę nem-
              <lb/>
            pè, BC, & </s>
            <s xml:id="echoid-s2838" xml:space="preserve">ſecundæ, FG, ergo, AC, ad, EG, erit vt, BC, ad ter-
              <lb/>
            tiam proportionalem duarum primę, nempè, BC, & </s>
            <s xml:id="echoid-s2839" xml:space="preserve">@ecundę, FG,
              <lb/>
            .</s>
            <s xml:id="echoid-s2840" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2841" xml:space="preserve">erit in dupla ratione eius, quam habet, BC, ad, FG, vel, CD,
              <lb/>
              <note position="left" xlink:label="note-0140-03" xlink:href="note-0140-03a" xml:space="preserve">Defin. 10.
                <lb/>
              5. Elem.</note>
            ad, GH, quod oſtendere opus erat.</s>
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          </p>
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        <div xml:id="echoid-div296" type="section" level="1" n="185">
          <head xml:id="echoid-head200" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2843" xml:space="preserve">_H_Inc patet, quæ de parallelogrammis in ſuperioribus Propoſitioni-
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            bus oſtenſa ſunt, eadem de eorundem omnibus lineis cum quibuſ.
              <lb/>
            </s>
            <s xml:id="echoid-s2844" xml:space="preserve">uis regulis aſſumptis pariter verificari, nam illa ſunt, vt ipſa paralle-
              <lb/>
              <note position="left" xlink:label="note-0140-04" xlink:href="note-0140-04a" xml:space="preserve">_3. huius._</note>
            logramma.</s>
            <s xml:id="echoid-s2845" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div298" type="section" level="1" n="186">
          <head xml:id="echoid-head201" xml:space="preserve">THEOREMA IX. PROPOS. IX.</head>
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            <s xml:id="echoid-s2846" xml:space="preserve">PArallelogrammorum in eadem altitudine exiſtentium
              <lb/>
            omnia quadrata, regula baſi, iuxta quam altitudo ſum-
              <lb/>
              <note position="left" xlink:label="note-0140-05" xlink:href="note-0140-05a" xml:space="preserve">A. Def. 8.
                <lb/>
              huius.</note>
            pta eſt, ſunt inter ſe, vt quadrata baſium.</s>
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