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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            quadrata ſemiparabolæ, BDC, ad omnia quadrata figuræ, CBD
              <lb/>
            F, demptis omnibus quadratis trilinei, BCF, erunt vt dimidium
              <lb/>
            quadrati, DE, .</s>
            <s xml:id="echoid-s8124" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8125" xml:space="preserve">vt rectangulum ſub {1/8}. </s>
            <s xml:id="echoid-s8126" xml:space="preserve">DF, & </s>
            <s xml:id="echoid-s8127" xml:space="preserve">ſub, DF, ad rectã-
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            gulum ſub {2/3}. </s>
            <s xml:id="echoid-s8128" xml:space="preserve">DF, & </s>
            <s xml:id="echoid-s8129" xml:space="preserve">ſub, DF, .</s>
            <s xml:id="echoid-s8130" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8131" xml:space="preserve">vt {1/8}. </s>
            <s xml:id="echoid-s8132" xml:space="preserve">DF, ad {1/3}. </s>
            <s xml:id="echoid-s8133" xml:space="preserve">DF, .</s>
            <s xml:id="echoid-s8134" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8135" xml:space="preserve">vt {1/2} {3/4}. </s>
            <s xml:id="echoid-s8136" xml:space="preserve">D
              <lb/>
            F, ad {1/2} {6/4}. </s>
            <s xml:id="echoid-s8137" xml:space="preserve">DF, .</s>
            <s xml:id="echoid-s8138" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8139" xml:space="preserve">vt 3. </s>
            <s xml:id="echoid-s8140" xml:space="preserve">ad 16. </s>
            <s xml:id="echoid-s8141" xml:space="preserve">quod oſtendere opus erat.</s>
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          <head xml:id="echoid-head495" xml:space="preserve">THEOREMA XXXVI. PROP. XXXVIII.</head>
          <p>
            <s xml:id="echoid-s8143" xml:space="preserve">IN figura Prop. </s>
            <s xml:id="echoid-s8144" xml:space="preserve">34. </s>
            <s xml:id="echoid-s8145" xml:space="preserve">adhuc oſtendemus omnia quadrata
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            figuræ, HBDM, demptis omnibus quadratis figuræ, B
              <lb/>
            HMF, ad omnia quadrata figuræ, CBDF, demptis omni-
              <lb/>
            bus quadratis trilinei, BCF, eſſe vt, D/M, MF, ad, FD.</s>
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            <s xml:id="echoid-s8147" xml:space="preserve">Quoniam .</s>
            <s xml:id="echoid-s8148" xml:space="preserve">n. </s>
            <s xml:id="echoid-s8149" xml:space="preserve">omnia quadrata, AM, demptis omnibus quadra-
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            tis, CM, ſunt ad omnia quadrata figuræ, HBDM, demptis om-
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            nibus quadratis figu-
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            ræ, BHMF, vt, AF,
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            ad parabolam, DBF,
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              <note position="right" xlink:label="note-0353-01" xlink:href="note-0353-01a" xml:space="preserve">34. huius.</note>
            .</s>
            <s xml:id="echoid-s8150" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8151" xml:space="preserve">vt omnia quadrata,
              <lb/>
            A F, ad omnia quadra.
              <lb/>
            </s>
            <s xml:id="echoid-s8152" xml:space="preserve">ta figuræ, CBDF,
              <lb/>
            demptis omnibus qua
              <lb/>
            dratis trilinei, BCF,
              <lb/>
            ergo, permutando,
              <lb/>
            omnia quadrata, A
              <lb/>
            M, demptis omnibus
              <lb/>
            quadratis, CM, ad omnia quadrata, AF, erunt vt omnia quadra-
              <lb/>
            ta figuræ, HBDM, demptis omnibus quadratis figuræ, HBFM,
              <lb/>
            ad omnia quadrata figuræ, CBDF, dem ptis omnibus quadratis
              <lb/>
            trilinei, BCF, ſunt autem omnia quadrata, AM, demptis omnibus
              <lb/>
            quadratis, CM, ad omnia quadrata, AF, vt rectangulum bis ſub,
              <lb/>
            MF, FD, cum quadrato, FD, .</s>
            <s xml:id="echoid-s8153" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8154" xml:space="preserve">rectangulum ſub compoſita ex,
              <lb/>
            DM, MF, & </s>
            <s xml:id="echoid-s8155" xml:space="preserve">ſub; </s>
            <s xml:id="echoid-s8156" xml:space="preserve">FD, ad quadratum, FD, .</s>
            <s xml:id="echoid-s8157" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8158" xml:space="preserve">vt compoſita ex,
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            DM, MF, ad, FD, ergo omnia quadrata figuræ, DM, HB, dem-
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            ptis omnibus quadratis figuræ CBDF, demptis omnibus quadra. </s>
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            tis trilinei, BCF, erunt vt, DM, MF, ad, FD, quod oſtendere
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            opus erat.</s>
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