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

Table of contents

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[461.] B. SECTIO II.
Page: 344 (324)
[462.] C. SECTIO III.
Page: 344 (324)
[463.] D. SECTIO IV.
Page: 344 (324)
[464.] E. SECTIO V.
Page: 345 (325)
[465.] THEOREMA XXIX. PROPOS. XXXI.
Page: 345 (325)
[466.] THEOREMA XXX. PROPOS. XXXII.
Page: 346 (326)
[467.] COROLLARIVM.
Page: 347 (327)
[468.] THEOREMA XXXI. PROPOS. XXXIII.
Page: 347 (327)
[469.] THEOREMA XXXII. PROPOS. XXXIV.
Page: 348 (328)
[470.] COROLLARIVM.
Page: 349 (329)
[471.] THEOREMA XXXIII. PROPOS. XXXV.
Page: 349 (329)
[472.] COROLLARIVM.
Page: 350 (330)
[473.] THEOREMA XXXIV. PROPOS. XXXVI.
Page: 351 (331)
[474.] THEOREMA XXXV. PROPOS. XXXVII.
Page: 352 (332)
[475.] THEOREMA XXXVI. PROP. XXXVIII.
Page: 353 (333)
[476.] THEOREMA XXXVII. PROP. XXXIX.
Page: 354 (334)
[477.] THEOREMA XXXVIII. PROP. XL.
Page: 354 (334)
[478.] COROLLARIVM.
Page: 354 (334)
[479.] THEOREMA XXXIX. PROPOS. XLI
Page: 355 (335)
[480.] THEOREMA XL. PROPOS. XLII.
Page: 356 (336)
[481.] THEOREMA XLI. PROPOS. XLIII.
Page: 357 (337)
[482.] THEOREMA XLII. PROPOS. XLIV.
Page: 358 (338)
[483.] THEOREMA XLIII. PROP. XLV.
Page: 358 (338)
[484.] THEOREMA XLIV. PROP. XLVI.
Page: 359 (339)
[485.] THEOREMA XLV. PROP. XLVII.
Page: 360 (340)
[486.] THEOREMA XLVI. PROPOS. XLVIII.
Page: 361 (341)
[487.] THEOREMA XLVII. PROPOS. XLIX.
Page: 362 (342)
[488.] THEOREMA XLVIII. PROPOS. L.
Page: 364 (344)
[489.] THEOREMA XLIX. PROPOS. LI.
Page: 365 (345)
[490.] SCHOLIVM.
Page: 365 (345)
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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-
              <lb/>
            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
              <lb/>
            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>
            <s xml:id="echoid-s8146" xml:space="preserve"/>
          </p>
          <p>
            <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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              <figure xlink:label="fig-0353-01" xlink:href="fig-0353-01a" number="239">
                <image file="0353-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0353-01"/>
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            nibus quadratis figu-
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            ræ, BHMF, vt, AF,
              <lb/>
            ad parabolam, DBF,
              <lb/>
              <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,
              <lb/>
            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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              <lb/>
            tis trilinei, BCF, erunt vt, DM, MF, ad, FD, quod oſtendere
              <lb/>
            opus erat.</s>
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