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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            E, ideſt rectangulum bis ſub, MF, & </s>
            <s xml:id="echoid-s8023" xml:space="preserve">ſub {1/3}. </s>
            <s xml:id="echoid-s8024" xml:space="preserve">FE, remanebitrectangu-
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            lum bis ſub, MF, & </s>
            <s xml:id="echoid-s8025" xml:space="preserve">{2/3}. </s>
            <s xml:id="echoid-s8026" xml:space="preserve">FE, idtſt ſemel ſub, MF, & </s>
            <s xml:id="echoid-s8027" xml:space="preserve">ſexquitertia, FE:
              <lb/>
            </s>
            <s xml:id="echoid-s8028" xml:space="preserve">Tandem ablato {1/6}. </s>
            <s xml:id="echoid-s8029" xml:space="preserve">aquadrato, FE, remanent {5/6}. </s>
            <s xml:id="echoid-s8030" xml:space="preserve">eiuſdem quadrati, vnde
              <lb/>
            omnia quadrata, BM, ad reſiduum, demptis omnibus quadratis figuræ,
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            BFMH, erunt vt quadratum, EM, ad rectangulum ſub, MF, & </s>
            <s xml:id="echoid-s8031" xml:space="preserve">ſex-
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            quitertia, FE, cum {5/6}. </s>
            <s xml:id="echoid-s8032" xml:space="preserve">quadrati, FE.</s>
            <s xml:id="echoid-s8033" xml:space="preserve"/>
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        <div xml:id="echoid-div799" type="section" level="1" n="473">
          <head xml:id="echoid-head493" xml:space="preserve">THEOREMA XXXIV. PROPOS. XXXVI.</head>
          <p>
            <s xml:id="echoid-s8034" xml:space="preserve">INeodem Schemate Theor. </s>
            <s xml:id="echoid-s8035" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s8036" xml:space="preserve">34. </s>
            <s xml:id="echoid-s8037" xml:space="preserve">oſtendemus omnia
              <lb/>
            quadrata figuræ, BDMH, demptis omnibus quadra-
              <lb/>
            tis, BM, ad omnia quadrata, BM, demptis omnibus qua-
              <lb/>
            dratis figuræ, BFMH, eſſe vt, EM, cum {1/2}. </s>
            <s xml:id="echoid-s8038" xml:space="preserve">EM, & </s>
            <s xml:id="echoid-s8039" xml:space="preserve">{1/2}. </s>
            <s xml:id="echoid-s8040" xml:space="preserve">ED,
              <lb/>
            ad, MF, cum {1/3}. </s>
            <s xml:id="echoid-s8041" xml:space="preserve">MF, & </s>
            <s xml:id="echoid-s8042" xml:space="preserve">{5/6}. </s>
            <s xml:id="echoid-s8043" xml:space="preserve">FE.</s>
            <s xml:id="echoid-s8044" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s8045" xml:space="preserve">Omnia enim quadrata, AM, ad omnia quadrata figuræ, DBH
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                <image file="0351-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0351-01"/>
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            M, oſtendimus eſſe,
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              <note position="right" xlink:label="note-0351-01" xlink:href="note-0351-01a" xml:space="preserve">34. huius.</note>
            vt quadratum, D
              <lb/>
            M, ad quadratum,
              <lb/>
            ME, rectangulum
              <lb/>
            ſub, ME, & </s>
            <s xml:id="echoid-s8046" xml:space="preserve">ſexqui-
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            tertia, ED, cum {1/2}.
              <lb/>
            </s>
            <s xml:id="echoid-s8047" xml:space="preserve">quadrati, ED, ea-
              <lb/>
            dem verò ad omnia
              <lb/>
            quadrata, BM, ſunt
              <lb/>
            vt quadratum, DM, ad quadratum, ME, ergo omnia quadrata, A
              <lb/>
            M, ad omnia quadrata figuræ, HBDM, demptis omnibus qua-
              <lb/>
            Matis, BM, erunt vt quadratum, DM, ad rectangulum ſub, ME,
              <lb/>
            & </s>
            <s xml:id="echoid-s8048" xml:space="preserve">ſexquitertia, ED, cum {1/2}. </s>
            <s xml:id="echoid-s8049" xml:space="preserve">quadrati, ED, &</s>
            <s xml:id="echoid-s8050" xml:space="preserve">, conuertendo, hæc
              <lb/>
            ad illa erunt, vt rectangulum ſub ſexquitertia, ED, cum {1/2}. </s>
            <s xml:id="echoid-s8051" xml:space="preserve">quadra-
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            ti, ED, ad quadratum, DM: </s>
            <s xml:id="echoid-s8052" xml:space="preserve">Omnia verò quadrata, AM, ad om-
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            nia quadrata. </s>
            <s xml:id="echoid-s8053" xml:space="preserve">BM, ſunt vt quadratum, DM, ad quadratum, ME,
              <lb/>
            & </s>
            <s xml:id="echoid-s8054" xml:space="preserve">tandem omnia quadrata, BM, adeorum reſiduum, demptis
              <lb/>
            omnibus quadratis figuræ, BHMF, ſunt vt quadratum, EM,
              <lb/>
              <note position="right" xlink:label="note-0351-02" xlink:href="note-0351-02a" xml:space="preserve">Ex corol.
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              autec.</note>
            ad rectangulum ſub, MF, & </s>
            <s xml:id="echoid-s8055" xml:space="preserve">ſexquitertia, FE, cum {5/6}. </s>
            <s xml:id="echoid-s8056" xml:space="preserve">quadrati,
              <lb/>
            FE, ergo, ex æquali, omnia quadrata figuræ, BDMH,
              <lb/>
            demptis omnibus quadratis, BM, ad omnia quadrata, BM,
              <lb/>
            demptis omnibus quadratis figuræ, BFMH, erunt vt rectangu-
              <lb/>
            lum ſub, ME, & </s>
            <s xml:id="echoid-s8057" xml:space="preserve">ſexquitertia, ED, cum {1/2}. </s>
            <s xml:id="echoid-s8058" xml:space="preserve">quadrati, ED, ad re-
              <lb/>
            ctangulum ſub, MF, & </s>
            <s xml:id="echoid-s8059" xml:space="preserve">ſexquitertia, FE, cum {5/6}. </s>
            <s xml:id="echoid-s8060" xml:space="preserve">quadrati, FE;
              <lb/>
            </s>
            <s xml:id="echoid-s8061" xml:space="preserve">quia verò rectangulum ſub, ME, & </s>
            <s xml:id="echoid-s8062" xml:space="preserve">ſexquitertia, ED, </s>
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