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

Table of contents

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[501.] B. SECTIO II.
Page: 372 (352)
[502.] C. SECTIO III.
Page: 372 (352)
[503.] D. SECTIO IV.
Page: 373 (353)
[504.] + COROLL. VIII. SECTIO I.
Page: 373 (353)
[505.] A. SECTIO II.
Page: 373 (353)
[506.] B. SECTIO III.
Page: 373 (353)
[507.] C. SECTIO IV.
Page: 374 (354)
[508.] D. SECTIO V.
Page: 374 (354)
[509.] COROLLARIVM IX.
Page: 374 (354)
[510.] COROLL X. SECTIO PRIOR.
Page: 374 (354)
[511.] SECTIO POSTERIOR.
Page: 375 (355)
[512.] COROLLARIVM XI.
Page: 375 (355)
[513.] COROLL. XII. SECTIO PRIOR.
Page: 375 (355)
[514.] SECTIO POSTERIOR,
Page: 376 (356)
[515.] COROLL. XIII. SECTIO PRIOR.
Page: 376 (356)
[516.] SECTIO POSTERIOR.
Page: 377 (357)
[517.] COROLLARIVM XIV.
Page: 377 (357)
[518.] COROLLARIVM XV.
Page: 377 (357)
[519.] COROLLARIVM XVI.
Page: 378 (358)
[520.] COROLLARIVM XVII.
Page: 378 (358)
[521.] COROLL XVIII. SECTIO PRIOR.
Page: 378 (358)
[522.] SECTIO POSTERIOR.
Page: 378 (358)
[523.] COROLLARIVM XIX.
Page: 379 (359)
[524.] COROLLARIVM XX.
Page: 379 (359)
[525.] COROLLARIVM XXI.
Page: 380 (360)
[526.] COROLLARIVM XXII.
Page: 380 (360)
[527.] COROLLARIVM XXIII.
Page: 381 (361)
[528.] COROLLARIVM XXIV.
Page: 381 (361)
[529.] COROLLARIVM XXV.
Page: 382 (362)
[530.] COROLLARIVM XXVI.
Page: 383 (363)
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          <pb o="361" file="0381" n="381" rhead="LIBER IV."/>
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        <div xml:id="echoid-div880" type="section" level="1" n="527">
          <head xml:id="echoid-head547" xml:space="preserve">COROLLARIVM XXIII.</head>
          <p>
            <s xml:id="echoid-s9115" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s9116" xml:space="preserve">45. </s>
            <s xml:id="echoid-s9117" xml:space="preserve">viſa adhuc anteced. </s>
            <s xml:id="echoid-s9118" xml:space="preserve">figura, patet aceruum maio-
              <lb/>
            rem parabolicum, HBEON, ad conoidem parabolicam geni-
              <lb/>
            tam ex ſemiparabola, BHG, eſſe vt reliquum parallelepiped@ſub,
              <lb/>
            GB, & </s>
            <s xml:id="echoid-s9119" xml:space="preserve">his ſpatis ſ. </s>
            <s xml:id="echoid-s9120" xml:space="preserve">quadrato, FG, {1/2}. </s>
            <s xml:id="echoid-s9121" xml:space="preserve">quadrati, GH, & </s>
            <s xml:id="echoid-s9122" xml:space="preserve">rectãgulo ſub,
              <lb/>
            FG, & </s>
            <s xml:id="echoid-s9123" xml:space="preserve">ſexquitertia, GH, ab eedẽ dẽpto {1/6}. </s>
            <s xml:id="echoid-s9124" xml:space="preserve">parallelepipediſub, CE, & </s>
            <s xml:id="echoid-s9125" xml:space="preserve">
              <lb/>
            quadrato, FG, ad dimidiũ parallepepidiſub, @BG, & </s>
            <s xml:id="echoid-s9126" xml:space="preserve">quadrato, GH;
              <lb/>
            </s>
            <s xml:id="echoid-s9127" xml:space="preserve">vt etiã erit quodlibet ſolidũ ſimilare genitũ ex figura, CBHF, dem-
              <lb/>
            pto ſolido ſimilari genito ex trilineo, BCE, ad ſolidum ſibi ſimilare
              <lb/>
            genitum ex ſemiparabola, BHG, iuxta communem regulam, HF.</s>
            <s xml:id="echoid-s9128" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div881" type="section" level="1" n="528">
          <head xml:id="echoid-head548" xml:space="preserve">COROLLARIVM XXIV.</head>
          <p>
            <s xml:id="echoid-s9129" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s9130" xml:space="preserve">47. </s>
            <s xml:id="echoid-s9131" xml:space="preserve">ſumatur ex figura Prop. </s>
            <s xml:id="echoid-s9132" xml:space="preserve">46. </s>
            <s xml:id="echoid-s9133" xml:space="preserve">fruſtum minus parabo-
              <lb/>
            læ, quod eſt, DPG, cum Parallelogrammo, DG, & </s>
            <s xml:id="echoid-s9134" xml:space="preserve">integra
              <lb/>
              <figure xlink:label="fig-0381-01" xlink:href="fig-0381-01a" number="260">
                <image file="0381-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0381-01"/>
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            baſi parabolæ,
              <lb/>
            ZAG, quæ eſt,
              <lb/>
            ZG, &</s>
            <s xml:id="echoid-s9135" xml:space="preserve">, vt fiat
              <lb/>
            ſolitum exem-
              <lb/>
            plum, reuolua-
              <lb/>
            tur, DG, circa
              <lb/>
            manentẽ axim,
              <lb/>
            DP, & </s>
            <s xml:id="echoid-s9136" xml:space="preserve">iterum
              <lb/>
            circa manentẽ
              <lb/>
            axim, EG, fiet ergo ex reuolutione circa, DP, à parallelogrammo,
              <lb/>
            DG, cylindrus, RG, & </s>
            <s xml:id="echoid-s9137" xml:space="preserve">à fruſto parabolæ minori, PDG, ſolidum,
              <lb/>
            quod ſit, HDG, quodque vocetur, Aceruus minor parabolicus; </s>
            <s xml:id="echoid-s9138" xml:space="preserve">& </s>
            <s xml:id="echoid-s9139" xml:space="preserve">
              <lb/>
            ex reuolutione circa; </s>
            <s xml:id="echoid-s9140" xml:space="preserve">EG, à parallelogrammo, DG, in alia figura
              <lb/>
            cylindrus, DV, & </s>
            <s xml:id="echoid-s9141" xml:space="preserve">à trilineo extra fruſtum minus parabolæ conſti-
              <lb/>
            tuto ſolidum, DGX@, quod eſt fruſtum apicis parabolici refectum
              <lb/>
            per circulum. </s>
            <s xml:id="echoid-s9142" xml:space="preserve">DX, quodque vocetur Fruſtum apicis parabolici. </s>
            <s xml:id="echoid-s9143" xml:space="preserve">Pa-
              <lb/>
            tet ergo cylindrum, RG, ad aceruum minorem parabolicu, HDG,
              <lb/>
            eſſe vt, ZP, ad compoſitam ex {1/3}. </s>
            <s xml:id="echoid-s9144" xml:space="preserve">ZP, & </s>
            <s xml:id="echoid-s9145" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s9146" xml:space="preserve">PG, ac cylindrum, DV,
              <lb/>
            ad fruſtum apicis parabolici, DGX, eſſe vt, ZP, ad ſui reliquum,
              <lb/>
            demptis ab ea {2/3}. </s>
            <s xml:id="echoid-s9147" xml:space="preserve">ZP, cum {1/6}. </s>
            <s xml:id="echoid-s9148" xml:space="preserve">PG; </s>
            <s xml:id="echoid-s9149" xml:space="preserve">Sic autem etiam erit quodlibet
              <lb/>
            ſolidum ſimilare genitum ex, DG, ad ſolidum ſibi ſimilare genitum
              <lb/>
            ex fruſto minori, DGP, vt, inquam, in priori parte huius Theor.
              <lb/>
            </s>
            <s xml:id="echoid-s9150" xml:space="preserve">dictum eſt; </s>
            <s xml:id="echoid-s9151" xml:space="preserve">& </s>
            <s xml:id="echoid-s9152" xml:space="preserve">ſic etiam ſolidum quodlibet ſimilare genitum ex,
              <lb/>
            DG, ad ſibi ſimilare genitum ex trilineo, DEG, iuxta </s>
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