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

Table of contents

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[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)
[491.] COROLLARIVM I.
Page: 366 (346)
[492.] COROLLARIVM II.
Page: 366 (346)
[493.] COROLLARIVM III.
Page: 367 (347)
[494.] COROLLARIVM IV.
Page: 367 (347)
[495.] COROLL. V. SECTIO I.
Page: 368 (348)
[496.] SECTIO II.
Page: 369 (349)
[497.] SECTIO III.
Page: 369 (349)
[498.] COROLLARIVM VI.
Page: 370 (350)
[499.] APPENDIX.
Page: 371 (351)
[500.] A. COROLL. VII. SECTIO I.
Page: 372 (352)
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          <head xml:id="echoid-head496" xml:space="preserve">THEOREMA XXXVII. PROP. XXXIX.</head>
          <p>
            <s xml:id="echoid-s8161" xml:space="preserve">IN Schemate adhuc Prop. </s>
            <s xml:id="echoid-s8162" xml:space="preserve">antec. </s>
            <s xml:id="echoid-s8163" xml:space="preserve">oſtendemus omnia qua-
              <lb/>
            quadrata figuræ, HBDM, demptis omnibus quadratis
              <lb/>
            figuræ, BHMF, eſſe ad omnia quadrata ſemiparabolæ, B
              <lb/>
            DE, vt, DM, MF, ad @ {3/6}. </s>
            <s xml:id="echoid-s8164" xml:space="preserve">ipſius, FD.</s>
            <s xml:id="echoid-s8165" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8166" xml:space="preserve">Nam omnia quadrata figuræ, HBDM, demptis omnibus qua-
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            dratis figuræ, BHMF, ad omnia quadrata figuræ, CBDF, dem-
              <lb/>
              <note position="left" xlink:label="note-0354-01" xlink:href="note-0354-01a" xml:space="preserve">37. huius 1</note>
            ptis omnibus quadratis trilinei, BCF, oſtenſa ſunt eſſe, vt, DM, M
              <lb/>
            F, ad, FD, hæc autem ad omnia quadrata ſemiparabolæ, BDE,
              <lb/>
            ſunt vt {2/3}. </s>
            <s xml:id="echoid-s8167" xml:space="preserve">FD, ad {1/8}. </s>
            <s xml:id="echoid-s8168" xml:space="preserve">ipſius, FD, .</s>
            <s xml:id="echoid-s8169" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8170" xml:space="preserve">vt, FD, ad @ {3/6}. </s>
            <s xml:id="echoid-s8171" xml:space="preserve">FD, ergo, ex æ-
              <lb/>
            quali, omnia quadrata figuræ, HBDM, demptis omnibus qua-
              <lb/>
            dratis figuræ, BHMF, ad omnia quadrata ſemiparabolæ, BDE.
              <lb/>
            </s>
            <s xml:id="echoid-s8172" xml:space="preserve">erunt vt, DM, MF, ad @ {3/6}. </s>
            <s xml:id="echoid-s8173" xml:space="preserve">ipſius, FD, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s8174" xml:space="preserve"/>
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          <head xml:id="echoid-head497" xml:space="preserve">THEOREMA XXXVIII. PROP. XL.</head>
          <p>
            <s xml:id="echoid-s8175" xml:space="preserve">SI in figuris Propoſ. </s>
            <s xml:id="echoid-s8176" xml:space="preserve">32. </s>
            <s xml:id="echoid-s8177" xml:space="preserve">& </s>
            <s xml:id="echoid-s8178" xml:space="preserve">34. </s>
            <s xml:id="echoid-s8179" xml:space="preserve">ducantur, GP, GV, regu-
              <lb/>
            lis, DF, DM, parallelæ, oſtendemus (ſi ipſę ſecauerint
              <lb/>
            parabolam, DBF,) omnia quadrata figuræ, CBDF, dem
              <lb/>
            ptis omnibus quadratis trilinei, BCF, ad omnia quadrata
              <lb/>
            figuræ, CBNP, demptis omnibus quadratis quadrilinei,
              <lb/>
            BCPO. </s>
            <s xml:id="echoid-s8180" xml:space="preserve">Vel omnia quadrata figuræ, HBDM, demptis
              <lb/>
            omnibus quadratis figuræ, BHMF, ad omnia quadrata fi-
              <lb/>
            guræ, HBNV, demptis omnibus quadratis figuræ, HVO
              <lb/>
            B, eſſe vt parabolam, DBF, ad parabolam, NBO.</s>
            <s xml:id="echoid-s8181" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8182" xml:space="preserve">Demonſtratio præſentis, Theor. </s>
            <s xml:id="echoid-s8183" xml:space="preserve">erit conformis demonſtratio.
              <lb/>
            </s>
            <s xml:id="echoid-s8184" xml:space="preserve">nibus Prop. </s>
            <s xml:id="echoid-s8185" xml:space="preserve">19. </s>
            <s xml:id="echoid-s8186" xml:space="preserve">20. </s>
            <s xml:id="echoid-s8187" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s8188" xml:space="preserve">3. </s>
            <s xml:id="echoid-s8189" xml:space="preserve">quapropter inde petatur.</s>
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          <head xml:id="echoid-head498" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s8191" xml:space="preserve">_H_Inc colligemus omnia quadrata ſiguræ, HBDM, demptis omni-
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            bus quadratis figuræ, BHMF, ad omnia quadrata figuræ, HBN
              <lb/>
            V, demptis omnibus quadratis figuræ, BHVO, eſſe vt omnia quadra-
              <lb/>
            ta figuræ, CBDF, demptis omnibus quadratis trilinei, BCF, ad </s>
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