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

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[531.] COROLLARIVM XXVII.
[532.] SCHOLIV M.
[533.] Finis quarti Libri.
[534.] GEOMETRIÆ CAVALERII. LIBER QVINTVS. In quo de Hyperbola, Oppoſitis Sectionib us, ac ſolidis ab eiſdem genitis, babetur contemplatio. THEOREMA I. PROPOS. I.
[535.] THEOREMA II. PROPOS. II.
[536.] THEOREMA III. PROPOS. III.
[537.] THEOREMA IV. PROPOS. IV.
[538.] THEOREMA V. PROPOS. V.
[539.] PROBLEMA I. PROPOS. VI.
[540.] THEOREMA VI. PROPOS. VII.
[541.] THEOREMA VII. PROPOS. VIII.
[542.] THEOREMA VIII. PROPOS. IX.
[543.] THEOREMA IX. PROPOS. X.
[544.] THEOREMA X. PROPOS. XI.
[545.] THEOREMA XI. PROPOS. XII.
[546.] THEOREMA XII. PROPOS. XIII.
[547.] THEOREMA XIII, PROPOS. XIV.
[548.] SCHOLIVM.
[549.] THEOREMA XIV. PROPOS. XV.
[550.] THEOREMA XV. PROPOS. XVI.
[551.] COROLLARIVM.
[552.] THEOREMA XVI. PROPOS. XVII.
[553.] THE OREMA XVII. PROPOS. XVIII.
[554.] THEOREMA XVIII. PROPOS. XIX.
[555.] COROLLARIVM.
[556.] SCHOLIVM.
[557.] THEOREMA XIX. PROPOS. XX.
[558.] THEOREMA XX. PROPOS. XXI.
[559.] A@@ter ſupradictam rationem explicare.
[560.] COROLLARIVM:
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          <pb o="363" file="0383" n="383" rhead="LIBER IV."/>
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        <div xml:id="echoid-div885" type="section" level="1" n="530">
          <head xml:id="echoid-head550" xml:space="preserve">COROLLARIVM XXVI.</head>
          <p>
            <s xml:id="echoid-s9188" xml:space="preserve">N Propoſitione 49. </s>
            <s xml:id="echoid-s9189" xml:space="preserve">aſſumpta de figura Propoſit. </s>
            <s xml:id="echoid-s9190" xml:space="preserve">46. </s>
            <s xml:id="echoid-s9191" xml:space="preserve">parabola,</s>
          </p>
          <p>
            <s xml:id="echoid-s9192" xml:space="preserve">ZAG, cum axi, AQ, & </s>
            <s xml:id="echoid-s9193" xml:space="preserve">illi parallela, DP, abſcindatur ab axi,
              <lb/>
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                <image file="0383-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0383-01"/>
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            AQ, ipſa, AV, exceſſus, AQ,
              <lb/>
            ſuper, DP, & </s>
            <s xml:id="echoid-s9194" xml:space="preserve">vt fiat ſolitum
              <lb/>
            exemplum, reuoluantur tũ
              <lb/>
            fruſtum maius, ZADP, tum
              <lb/>
            fruſtum minus, DPG, circa
              <lb/>
            communem axem, DP, vt
              <lb/>
            ex fruſto maiori, DAZP,
              <lb/>
            fiat aceruus maior parabo
              <lb/>
            licus, ZADON, & </s>
            <s xml:id="echoid-s9195" xml:space="preserve">ex fruſto
              <lb/>
            minori, DPG, fiat aceruus
              <lb/>
            minor parabolicus, RDG: </s>
            <s xml:id="echoid-s9196" xml:space="preserve">Patet ergo ex hac Propoſ. </s>
            <s xml:id="echoid-s9197" xml:space="preserve">aceruum
              <lb/>
            minorem, RDG, ad aceruum maiorem, ZADON, habere ratio-
              <lb/>
            nem compoſitam ex ea, quam habet compoſita ex {1/3}. </s>
            <s xml:id="echoid-s9198" xml:space="preserve">ZP, & </s>
            <s xml:id="echoid-s9199" xml:space="preserve">{1/6}. </s>
            <s xml:id="echoid-s9200" xml:space="preserve">PG,
              <lb/>
            ad ZP, & </s>
            <s xml:id="echoid-s9201" xml:space="preserve">ex ratione parallelepipedi ſub, DP, & </s>
            <s xml:id="echoid-s9202" xml:space="preserve">quadrato, PG, ad
              <lb/>
            parallelepipedum ſub, AQ, & </s>
            <s xml:id="echoid-s9203" xml:space="preserve">his ſpatijs. </s>
            <s xml:id="echoid-s9204" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9205" xml:space="preserve">quadrato, PQ, {1/2}. </s>
            <s xml:id="echoid-s9206" xml:space="preserve">qua-
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            drati, QZ, & </s>
            <s xml:id="echoid-s9207" xml:space="preserve">rectangulo ſub ſexquitertia, ZQ, & </s>
            <s xml:id="echoid-s9208" xml:space="preserve">ſub, QP, dempto
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            ab eodem {1/6}. </s>
            <s xml:id="echoid-s9209" xml:space="preserve">parallelepipedi ſub, AV, & </s>
            <s xml:id="echoid-s9210" xml:space="preserve">quadrato, QP: </s>
            <s xml:id="echoid-s9211" xml:space="preserve">Sic autem
              <lb/>
            erit etiam quodlibet ſolidum ſimilare genitum ex fruſto minori,
              <lb/>
            DPG, ad ſibi ſimilare genitum ex figura, CAZP, Prop. </s>
            <s xml:id="echoid-s9212" xml:space="preserve">46. </s>
            <s xml:id="echoid-s9213" xml:space="preserve">dem-
              <lb/>
            pto ſolido ſimilari genit o ex trilineo, ACD, iuxta communem re-
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            gulam, ZG.</s>
            <s xml:id="echoid-s9214" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div887" type="section" level="1" n="531">
          <head xml:id="echoid-head551" xml:space="preserve">COROLLARIVM XXVII.</head>
          <p>
            <s xml:id="echoid-s9215" xml:space="preserve">N Propoſitione 50. </s>
            <s xml:id="echoid-s9216" xml:space="preserve">de figura Propoſit. </s>
            <s xml:id="echoid-s9217" xml:space="preserve">46. </s>
            <s xml:id="echoid-s9218" xml:space="preserve">ſumatur fruſtum</s>
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          <p>
            <s xml:id="echoid-s9219" xml:space="preserve">minus parabolæ, quod eſt, DGP, quodque ſecatur per rectam,
              <lb/>
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            TI, æquidiſtantem ipſi, PG, acci-
              <lb/>
            piantur inſuper duæ integræ, ZG,
              <lb/>
            SI, & </s>
            <s xml:id="echoid-s9220" xml:space="preserve">vt fiat noſtrum exemplum,
              <lb/>
            reuoluatur, DPG, fruſtum circa
              <lb/>
            manentem axim, DP, vt ex, DPG,
              <lb/>
            ſiat aceruus minor, RDG, & </s>
            <s xml:id="echoid-s9221" xml:space="preserve">ex,
              <lb/>
            DTI, eius fruſtum, YDI, patet er-
              <lb/>
            go ex hoc Theorem. </s>
            <s xml:id="echoid-s9222" xml:space="preserve">aceruum mi-
              <lb/>
            norem, RDG, ad reſectum fruſtum, YDI, habere rationem com-
              <lb/>
            poſitam ex ea, quam habet rectangulum, ZPG, cum {1/2}. </s>
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