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

Table of contents

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[351.] THEOREMA XXX. PROPOS. XXXI.
Page: 272 (252)
[352.] COROLLARIVM.
Page: 274 (254)
[353.] THEOREMA XXXI. PROPOS. XXXII.
Page: 274 (254)
[354.] COROLLARIVM.
Page: 275 (255)
[355.] THEOREMA XXXII. PROPOS. XXXIII.
Page: 275 (255)
[356.] COROLLARIVM.
Page: 276 (256)
[357.] THEOREMA XXXIII. PROPOS. XXXIV.
Page: 276 (256)
[358.] SCHOLIVM.
Page: 277 (257)
[359.] COROLLARIVMI.
Page: 279 (259)
[360.] COROLLARIVM II.
Page: 281 (261)
[361.] COROLLARIVM III.
Page: 282 (262)
[362.] COROLLARIVM IV.
Page: 282 (262)
[363.] COROLLARIVM V.
Page: 283 (263)
[364.] COROLL. VI. SECTIO PRIOR.
Page: 284 (264)
[365.] SECTIO POSTERIOR.
Page: 284 (264)
[366.] COROLLARIVM VII.
Page: 284 (264)
[367.] COROLLARIVM VIII.
Page: 285 (265)
[368.] COROLL. IX. SECTIO PRIOR.
Page: 285 (265)
[369.] SECTIO POSTERIOR.
Page: 285 (265)
[370.] COROLL. X. SECTIO PRIMA.
Page: 286 (266)
[371.] SECTIO II.
Page: 286 (266)
[372.] SECTIO III.
Page: 287 (267)
[373.] SECTIO IV.
Page: 287 (267)
[374.] SECTIO V.
Page: 287 (267)
[375.] COROLLARIVM XI.
Page: 287 (267)
[376.] COROLLARIVM XII.
Page: 288 (268)
[377.] COROLLARIVM XIII.
Page: 289 (269)
[378.] COROLLARIVM XIV.
Page: 289 (269)
[379.] COROLL. XV. SECTIO PRIMA.
Page: 290 (270)
[380.] SECTIO II.
Page: 291 (271)
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          <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,
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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-
              <lb/>
            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
              <lb/>
            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-
              <lb/>
            gulam, ZG.</s>
            <s xml:id="echoid-s9214" xml:space="preserve"/>
          </p>
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          <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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            <s xml:id="echoid-s9219" xml:space="preserve">minus parabolæ, quod eſt, DGP, quodque ſecatur per rectam,
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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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