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

Table of Notes

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          <pb o="274" file="0294" n="294" rhead="GEOMETRIÆ"/>
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        <div xml:id="echoid-div660" type="section" level="1" n="387">
          <head xml:id="echoid-head404" xml:space="preserve">COROLLARIVM XIX.</head>
          <p>
            <s xml:id="echoid-s6769" xml:space="preserve">IN Propof. </s>
            <s xml:id="echoid-s6770" xml:space="preserve">22. </s>
            <s xml:id="echoid-s6771" xml:space="preserve">expoſita figura, & </s>
            <s xml:id="echoid-s6772" xml:space="preserve">exemplo conſtituto, colligi-
              <lb/>
            mus ſolidum ſimilare genicum ex, AG, ad ſolidum ſimilare ge-
              <lb/>
            nitum ex figura, LCFEG, deinptis ſolidis ſimilaribus genitis ex tri-
              <lb/>
            lineis, CLT, YGE, eſſe (ſi, CFEH, ſit circulus) vt parallelepi-
              <lb/>
            pedum ſub baſi parallelogrammo, AG, altitudine, FI, ad cylindri-
              <lb/>
              <figure xlink:label="fig-0294-01" xlink:href="fig-0294-01a" number="187">
                <image file="0294-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0294-01"/>
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            cum ſub baſi maiori portione, TC
              <lb/>
            FEY, altitudine, IM, vna cum,
              <lb/>
            {3/6}, cubi, TY. </s>
            <s xml:id="echoid-s6773" xml:space="preserve">In ellipſi verò, vt
              <lb/>
            parallelepipedum ſub baſiparalle-
              <lb/>
            logrammo, AG, altitudine, FI,
              <lb/>
            ad cylindricum ſub baſi portione,
              <lb/>
            TCFEY, altitudine, MI, vna
              <lb/>
            cum ea parte cubi, TY, vel (rhom
              <lb/>
            bo ab eadem, TY, deſoripto, vt in
              <lb/>
            Theor. </s>
            <s xml:id="echoid-s6774" xml:space="preserve">21.) </s>
            <s xml:id="echoid-s6775" xml:space="preserve">parallelepipedi ſub, T
              <lb/>
            Y, & </s>
            <s xml:id="echoid-s6776" xml:space="preserve">dicto rhombo, ad quam eiu-
              <lb/>
            ſdem cubi, vel parallelepipedi ſex-
              <lb/>
            ta pars ſit, vt quadratum, CE, primæ axis, ad quadratum ſecundæ
              <lb/>
            .</s>
            <s xml:id="echoid-s6777" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6778" xml:space="preserve">ad quadratum, FH. </s>
            <s xml:id="echoid-s6779" xml:space="preserve">Sit ergo conſtitutum exemplum per reuolu-
              <lb/>
            tionem, AG, circa manentem axim, LG, ſiue ergo, CFEH, ſit
              <lb/>
            circulus, ſiue ellipſis, habebit genitus cylindrus ab, AG, ad genitum
              <lb/>
            ſolidum a portione, TCFEY, ſupradictam rationem. </s>
            <s xml:id="echoid-s6780" xml:space="preserve">Vocetur au-
              <lb/>
            tem ſolidum deſcriptum à portione, TCFEY, (ſi ſit portio circu-
              <lb/>
            li) malum roſeum; </s>
            <s xml:id="echoid-s6781" xml:space="preserve">ſi verò ſit portio ellipſis: </s>
            <s xml:id="echoid-s6782" xml:space="preserve">Malum cotoneum.</s>
            <s xml:id="echoid-s6783" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div662" type="section" level="1" n="388">
          <head xml:id="echoid-head405" xml:space="preserve">COROLLARIVM XX.</head>
          <p>
            <s xml:id="echoid-s6784" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s6785" xml:space="preserve">23. </s>
            <s xml:id="echoid-s6786" xml:space="preserve">ium-
              <lb/>
              <figure xlink:label="fig-0294-02" xlink:href="fig-0294-02a" number="188">
                <image file="0294-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0294-02"/>
              </figure>
            pta ex fig. </s>
            <s xml:id="echoid-s6787" xml:space="preserve">Theor.
              <lb/>
            </s>
            <s xml:id="echoid-s6788" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6789" xml:space="preserve">portione minori
              <lb/>
            vtcunque, RFV,
              <lb/>
            quæ ſit portio circu-
              <lb/>
            li, cum illi circum-
              <lb/>
            ſcripto rectangulo, Δ
              <lb/>
            V, aſſumpto etiam
              <lb/>
            integro axi, FH, & </s>
            <s xml:id="echoid-s6790" xml:space="preserve">
              <lb/>
            puncto, @, in ea, vt
              <lb/>
            ibi ſumptum eſt, pa-
              <lb/>
            tet ſolidum ſimilare
              <lb/>
            genitum ex, Δ V, ad
              <lb/>
            ſolidum ſibi </s>
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