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

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        <div xml:id="echoid-div541" type="section" level="1" n="324">
          <p>
            <s xml:id="echoid-s5324" xml:space="preserve">
              <pb o="219" file="0239" n="239" rhead="LIBER III."/>
            ſemiportio verò. </s>
            <s xml:id="echoid-s5325" xml:space="preserve">OCD, quæ eſt pioximè 16. </s>
            <s xml:id="echoid-s5326" xml:space="preserve">{1/2}, excedit, {2/3}, paral-
              <lb/>
            lelogrammi, OV, ſcilicet 14. </s>
            <s xml:id="echoid-s5327" xml:space="preserve">per 2 {1/2}, ſi ergo ſemiportioni, OCD,
              <lb/>
            quæ eſt proximè 16 {1/2}, iunxerimus exceſſum eiuſdem ſemiportionis
              <lb/>
            ſuper, {2/3}, parallelogrammi, OV, .</s>
            <s xml:id="echoid-s5328" xml:space="preserve">i.</s>
            <s xml:id="echoid-s5329" xml:space="preserve">2 {1/2}, fiet totum conſequens pro-
              <lb/>
            ximè 19. </s>
            <s xml:id="echoid-s5330" xml:space="preserve">hoc ſi detrahatur a toto parallelogrammo, OV, quod eſt
              <lb/>
            21. </s>
            <s xml:id="echoid-s5331" xml:space="preserve">relinquentur 2. </s>
            <s xml:id="echoid-s5332" xml:space="preserve">erit ergo parallelogrammum, OV, ad hoc reſi-
              <lb/>
            duum proximè, vt 21. </s>
            <s xml:id="echoid-s5333" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s5334" xml:space="preserve">vnde & </s>
            <s xml:id="echoid-s5335" xml:space="preserve">omnia quadrata parallelogram-
              <lb/>
            mi, OV, ad omnia quadrata trilinei, DCV, erunt proximè vt 21.
              <lb/>
            </s>
            <s xml:id="echoid-s5336" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s5337" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s5338" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div544" type="section" level="1" n="325">
          <head xml:id="echoid-head342" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5339" xml:space="preserve">_H_INC patet, ſi nos præcisè ſciamus, quam rationem habeant om-
              <lb/>
            nia quadrata parallelogrammi, OV, ad omnia quadrata trilinei,
              <lb/>
            DCV, quia etiam ſcimus, quam rationem habeant omnia quadrata, C
              <lb/>
            D, ad omnia quadrata ſemiportionis, OCD, ſciemus etiam, quam ra-
              <lb/>
            tionem habeant eadem ad rectangula ſub ſemiportione, OCD, & </s>
            <s xml:id="echoid-s5340" xml:space="preserve">trili-
              <lb/>
            neo, DCV, bis ſumpta, & </s>
            <s xml:id="echoid-s5341" xml:space="preserve">item nota erit ratio ad eadem ſemel ſum-
              <lb/>
            pta, quæ ſi iungantur omnibus quadratis ſemiportionis, OCD, compo-
              <lb/>
              <note position="right" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">_PerC.23._
                <lb/>
              _lib.2._</note>
            nentur rectangula ſub para lelogrammo, OV, & </s>
            <s xml:id="echoid-s5342" xml:space="preserve">ſemiportione,
              <lb/>
            OCD, & </s>
            <s xml:id="echoid-s5343" xml:space="preserve">fiet nota ratio omnium quadratorum, OV, ad rectangula
              <lb/>
            ſub parallelogrammo, OV, & </s>
            <s xml:id="echoid-s5344" xml:space="preserve">ſemiportione, OCD, quæ eſt eadem
              <lb/>
              <note position="right" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">_Coroll.1._
                <lb/>
              _26.lib.2._</note>
            ei, quam habet parallelogrammum OV, ad ſemiportionem, OCD,
              <lb/>
            & </s>
            <s xml:id="echoid-s5345" xml:space="preserve">ideò hęc erit nota, ſicut etiam erit nota ratio parallelogrammi cir-
              <lb/>
            culo, vel ellipſi, ABCD, circumſcripti, habentis latera parallela
              <lb/>
            ipſis, AC, BD, ad eundem circulum, vel ellipſim, ABCD, & </s>
            <s xml:id="echoid-s5346" xml:space="preserve">hinc habere-
              <lb/>
            tur circuli quadratura; </s>
            <s xml:id="echoid-s5347" xml:space="preserve">ideò quærendum eſt, quam rationem habeant præ-
              <lb/>
            cise omnia quadrata, OV, ad omnia quadrata trilinei, CDV; </s>
            <s xml:id="echoid-s5348" xml:space="preserve">quod hucuſ-
              <lb/>
            que nec alijs, nec mibi compertum eſſe potuit.</s>
            <s xml:id="echoid-s5349" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div546" type="section" level="1" n="326">
          <head xml:id="echoid-head343" xml:space="preserve">THEOREMA XIII. PROPOS. XIV.</head>
          <p>
            <s xml:id="echoid-s5350" xml:space="preserve">SI circa parallelogrammi rectanguli quodlibet laterum,
              <lb/>
            tamquam circa diametrum integrorum, ſemicirculus,
              <lb/>
            vel ſemiellipſis, etiam ipſo non exiſtente rectangulo, deſ-
              <lb/>
            cripti fuerint, circumferentia autem circuli, vel curua elli-
              <lb/>
            pſis non pertingant, neque ſecet oppoſitum prædicto latus,
              <lb/>
            ſit autem regula parallelogrammi baſis: </s>
            <s xml:id="echoid-s5351" xml:space="preserve">Omnia quadrata
              <lb/>
            dicti parallelogrammi ad omnia quadrata figuræ, quæ reli-
              <lb/>
            quis tribus parallelogrammi lateribus (dempto eo, </s>
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