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

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        <div xml:id="echoid-div489" type="section" level="1" n="295">
          <p>
            <s xml:id="echoid-s4799" xml:space="preserve">
              <pb o="194" file="0214" n="214" rhead="GEOMETRIÆ"/>
            .</s>
            <s xml:id="echoid-s4800" xml:space="preserve">n. </s>
            <s xml:id="echoid-s4801" xml:space="preserve">nabemus parallelepipedum ſub, AB, & </s>
            <s xml:id="echoid-s4802" xml:space="preserve">rectangulo, ADC, & </s>
            <s xml:id="echoid-s4803" xml:space="preserve">
              <lb/>
            ſub, AB, & </s>
            <s xml:id="echoid-s4804" xml:space="preserve">rectingulo, BCD,.</s>
            <s xml:id="echoid-s4805" xml:space="preserve">. ſub, BC, & </s>
            <s xml:id="echoid-s4806" xml:space="preserve">rectangulo ſub, A
              <lb/>
            B, CD, cui ſi iunxeris parallelepipedum ſub, BC, & </s>
            <s xml:id="echoid-s4807" xml:space="preserve">rectangulo ſub,
              <lb/>
            BD, DC, componeour parallelepipedum ſub, BC, & </s>
            <s xml:id="echoid-s4808" xml:space="preserve">rectangulo,
              <lb/>
              <figure xlink:label="fig-0214-01" xlink:href="fig-0214-01a" number="129">
                <image file="0214-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0214-01"/>
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            ADC, quod additum parallele-
              <lb/>
            pipedo ſub, AB, & </s>
            <s xml:id="echoid-s4809" xml:space="preserve">eodem re-
              <lb/>
            ctangulo, ADC, componet pa-
              <lb/>
              <note position="left" xlink:label="note-0214-01" xlink:href="note-0214-01a" xml:space="preserve">35. huius.</note>
            rallelepipedum ſub, AC, & </s>
            <s xml:id="echoid-s4810" xml:space="preserve">re-
              <lb/>
            ctangulo, ADC, quod quidem
              <lb/>
            æquale erit alteri ſummæ prædi-
              <lb/>
            ctæ, nempè parallelepipedo ſub,
              <lb/>
            BC, & </s>
            <s xml:id="echoid-s4811" xml:space="preserve">rectangulo ſub, BD, D
              <lb/>
            C, vna cum, {1/3}, cubi, BC, ergo & </s>
            <s xml:id="echoid-s4812" xml:space="preserve">eorum tripla æqualia erunt ſci-
              <lb/>
            licet parallelepipedum ter ſub, AC, & </s>
            <s xml:id="echoid-s4813" xml:space="preserve">rectangulo, ADC, ſeu ter
              <lb/>
              <note position="left" xlink:label="note-0214-02" xlink:href="note-0214-02a" xml:space="preserve">Schol. 35.
                <lb/>
              huius.</note>
            ſub, AD, & </s>
            <s xml:id="echoid-s4814" xml:space="preserve">rectangulo, ACD, æquabitur parallelepipedo ter ſub,
              <lb/>
            BC, & </s>
            <s xml:id="echoid-s4815" xml:space="preserve">rectangulo, BDC, ſeu ter ſub, BD, & </s>
            <s xml:id="echoid-s4816" xml:space="preserve">rectangulo, BCD,
              <lb/>
            cum cubo, BC, additis verò communibus cubis, AC, CD, fiet pa-
              <lb/>
              <note position="left" xlink:label="note-0214-03" xlink:href="note-0214-03a" xml:space="preserve">38. huius.</note>
            rallelepipedum ter ſub, AD, & </s>
            <s xml:id="echoid-s4817" xml:space="preserve">rectangulo, ACD, cum cubis, A
              <lb/>
            C, CD, ideſt totus cubus, AD, æqualis parallelepipedo ter ſub, B
              <lb/>
              <note position="left" xlink:label="note-0214-04" xlink:href="note-0214-04a" xml:space="preserve">38. huius.</note>
            D, & </s>
            <s xml:id="echoid-s4818" xml:space="preserve">rectangulo, BCD, cum cubis, BC, CD, (quæ integrant
              <lb/>
            cubum, BD,) & </s>
            <s xml:id="echoid-s4819" xml:space="preserve">cum cubo, AC, eſt igitur cubus, AD, æqualis
              <lb/>
            duobus cubis, AC, BD. </s>
            <s xml:id="echoid-s4820" xml:space="preserve">Poſſibile eſt ergo facere, quod propoſi-
              <lb/>
            tum fuit.</s>
            <s xml:id="echoid-s4821" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div491" type="section" level="1" n="296">
          <head xml:id="echoid-head312" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s4822" xml:space="preserve">EX hoc manifeſtum eſt, ſi, AC, ſit latus dati cubi, & </s>
            <s xml:id="echoid-s4823" xml:space="preserve">ſit etiam da-
              <lb/>
            tarecta linea, vt, AB, minor, AC, poſſibile eſſe inuenire duos
              <lb/>
            eubos, vt, AD, DB, ita vt eorum differentia ſit æqualis cubo dato,
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s4824" xml:space="preserve">laterun cubicorum, AD, DB, ſcilicet, AB, pariter diffe-
              <lb/>
            rentia ſit data, eſt. </s>
            <s xml:id="echoid-s4825" xml:space="preserve">n. </s>
            <s xml:id="echoid-s4826" xml:space="preserve">cubus, AC, æqualis dictæ cuborum, AD, DB,
              <lb/>
            differentiæ, vt eſtenſum eſt. </s>
            <s xml:id="echoid-s4827" xml:space="preserve">Cum verò ſimilia ſolida quæunq; </s>
            <s xml:id="echoid-s4828" xml:space="preserve">ſint in
              <lb/>
            tripla ratione linearum, ſeu later um bomologorum eorumdem, ideò
              <lb/>
            erunt, vt cubi ipſarum linearum, ſeu laterum bomologoroum, & </s>
            <s xml:id="echoid-s4829" xml:space="preserve">ideò
              <lb/>
            eandem rationem, quam babet cubus, AD, ad cubum, DB, babebit
              <lb/>
            ex. </s>
            <s xml:id="echoid-s4830" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s4831" xml:space="preserve">Icoſaedrum deſcriptum latere, AD, ad Icoſaedrum deſoriptum
              <lb/>
            latere, BD, prædicto bomologo, & </s>
            <s xml:id="echoid-s4832" xml:space="preserve">vt cubus, AD, ad cubum, AC,
              <lb/>
            ita erit Icoſaedrum, AD, ad Icoſaedrum, AC, nec non colligendo, vt
              <lb/>
            cubus, AD, ad cubos, AC, BD, ita erit Icoſaedrum, AD, ad Ico-
              <lb/>
            ſaedra, AC, BD, ergo Icoſaedrum, AD, æquabitur Icoſaedris, AC,
              <lb/>
            BD, & </s>
            <s xml:id="echoid-s4833" xml:space="preserve">ſuperabit Icoſaedrum, BD, Icoſaedro, AC, ergo ſi datum </s>
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