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

Table of contents

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[261.] COROLLARIVM.
Page: 194 (174)
[262.] THEOREMA XXXII. PROPOS. XXXII.
Page: 195 (175)
[263.] COROLLARIVM.
Page: 196 (176)
[264.] THEOREMA XXXIII. PROPOS. XXXIII.
Page: 197 (177)
[265.] COROLLARIVM I.
Page: 198 (178)
[266.] COROLLARIVM II.
Page: 199 (179)
[267.] THEOREMA XXXIV. PROPOS. XXXIV.
Page: 199 (179)
[268.] COROLLARIVM I.
Page: 201 (181)
[269.] COROLLARIVM II.
Page: 201 (181)
[270.] COROLLARIVM III.
Page: 201 (181)
[271.] A. COROLLARII IV. GENERALIS. SECTIO I.
Page: 203 (183)
[272.] B. SECTIO II.
Page: 203 (183)
[273.] C. SECTIO III.
Page: 203 (183)
[274.] D. SECTIO IV.
Page: 204 (184)
[275.] E. SECTIO V.
Page: 204 (184)
[276.] F. SECTIO VI.
Page: 204 (184)
[277.] G. SECTIO VII.
Page: 204 (184)
[278.] H. SECTIO VIII.
Page: 204 (184)
[279.] I. SECTIO IX.
Page: 205 (185)
[280.] K. SECTIO X.
Page: 205 (185)
[281.] L. SECTIO XI.
Page: 206 (186)
[282.] M. SECTIO XII.
Page: 206 (186)
[283.] N. SECTIO XIII.
Page: 207 (187)
[284.] THEOREMA XXXV. PROPOS. XXXV.
Page: 207 (187)
[285.] SCHOLIV M.
Page: 208 (188)
[286.] THEOREMA XXXVI. PROPOS. XXXVI.
Page: 208 (188)
[287.] THEOREMA XXXVII. PROPOS. XXXVII.
Page: 209 (189)
[288.] COROLLARIVM.
Page: 210 (190)
[289.] THEOREMA XXXVIII. PROPOS. XXXVIII.
Page: 210 (190)
[290.] SCHOLIVM.
Page: 211 (191)
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          <head xml:id="echoid-head362" xml:space="preserve">THEOREMA XXIV. PROPOS. XXV.</head>
          <p>
            <s xml:id="echoid-s6033" xml:space="preserve">IN figura circuli, & </s>
            <s xml:id="echoid-s6034" xml:space="preserve">ellipſis eiuſdem Theor. </s>
            <s xml:id="echoid-s6035" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6036" xml:space="preserve">oſtenden-
              <lb/>
            dum eſt, ibi appoſitis retentis, ſumpta tamen vtcunque
              <lb/>
            portione minori, RFV, & </s>
            <s xml:id="echoid-s6037" xml:space="preserve">regula diametro eiuſdem portio-
              <lb/>
            nis. </s>
            <s xml:id="echoid-s6038" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6039" xml:space="preserve">FM; </s>
            <s xml:id="echoid-s6040" xml:space="preserve">omnia quadrata parallelogrammi, Δ V, ad omnia
              <lb/>
            quadrata portionis, RFV, eſſe vt quadratum, FM, ad ſpa-
              <lb/>
            tium, quod remanet, dempto rectangulo ſub, IM, & </s>
            <s xml:id="echoid-s6041" xml:space="preserve">ſub, F
              <lb/>
            M, (ad quam, FM, ſit, vt, Δ V, ad portionem, RFV,) à re-
              <lb/>
            ctangulo ſub, FM, & </s>
            <s xml:id="echoid-s6042" xml:space="preserve">ſub, {2/3}, ipſius, MH.</s>
            <s xml:id="echoid-s6043" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6044" xml:space="preserve">Sit igitur vt, Δ V, ad, RFV, ita, FM, ad, MI; </s>
            <s xml:id="echoid-s6045" xml:space="preserve">omnia ergo qua-
              <lb/>
            drata, Δ V, adrectangula ſub, Δ V, VT, ſunt vt quadratum, FM,
              <lb/>
            ad rectangulum, FMI, rectangula inſuper ſub, Δ V, VT, ad re-
              <lb/>
              <note position="left" xlink:label="note-0264-01" xlink:href="note-0264-01a" xml:space="preserve">14. Lib. 2.</note>
            ctangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s6046" xml:space="preserve">ſub, VT, ſunt vt, Δ V, ad portionem,
              <lb/>
              <figure xlink:label="fig-0264-01" xlink:href="fig-0264-01a" number="163">
                <image file="0264-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0264-01"/>
              </figure>
            RFV, .</s>
            <s xml:id="echoid-s6047" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6048" xml:space="preserve">vt, FM, ad, MT, .</s>
            <s xml:id="echoid-s6049" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6050" xml:space="preserve">ſumpta, MI,
              <lb/>
              <note position="left" xlink:label="note-0264-02" xlink:href="note-0264-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. lib. 2.</note>
            communi altitudine, vt rectangulum, F
              <lb/>
            MI, ad rectangulum, r MI, ergo ex æ-
              <lb/>
              <note position="left" xlink:label="note-0264-03" xlink:href="note-0264-03a" xml:space="preserve">@. Lib. 2.</note>
            quali omnia quadrata, Δ V, ad rectangu-
              <lb/>
            la ſub portione, RFV, & </s>
            <s xml:id="echoid-s6051" xml:space="preserve">ſub, VT, erunt
              <lb/>
            vt quadratum, FM, ad rectangulum,
              <lb/>
            Γ Μ Ι, quod ſerua.</s>
            <s xml:id="echoid-s6052" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6053" xml:space="preserve">Vlterius omnia quadrata, ΔV, ad om-
              <lb/>
              <note position="right" xlink:label="note-0264-04" xlink:href="note-0264-04a" xml:space="preserve">@. Lib. 2.</note>
            nia quadrata, VII, ſunt vt quadratum, F
              <lb/>
            M, ad quadratum, MO, vel ad quadra-
              <lb/>
            tum, RV, .</s>
            <s xml:id="echoid-s6054" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6055" xml:space="preserve">ad quatuor rectangula ſub,
              <lb/>
            R M, MV: </s>
            <s xml:id="echoid-s6056" xml:space="preserve">Omnia inſuper quadrata,
              <lb/>
            V II, ad rectangula ſub portione, RFV,
              <lb/>
            & </s>
            <s xml:id="echoid-s6057" xml:space="preserve">quadrilineo, RTHY V, ſunt vt ſex
              <lb/>
            quadrata, CE, ad quadratũ, FH, nam in
              <lb/>
            circulo omnia quadrata, RZ, ſunt ſex-
              <lb/>
              <note position="left" xlink:label="note-0264-05" xlink:href="note-0264-05a" xml:space="preserve">Elicitur
                <lb/>
              èx 21.hu-
                <lb/>
              ius.</note>
            cupla rectangulorum ſub portione, RF
              <lb/>
            V, & </s>
            <s xml:id="echoid-s6058" xml:space="preserve">quadrilineo, RTHYV, & </s>
            <s xml:id="echoid-s6059" xml:space="preserve">ideo ſunt
              <lb/>
            ad illa, vt ſex quadrata, CE, ad quadra-
              <lb/>
            tum, CE, vel ad quadratum, FH, in ellipſi
              <lb/>
            verò omnia quadrata, RZ, ſunt ad re-
              <lb/>
            ctangula ſub portione, RFV, & </s>
            <s xml:id="echoid-s6060" xml:space="preserve">quadrilineo, RTHYV, vt ſex quadra-
              <lb/>
            ta, CE, ad quadratum, FH, quod elicitur ex Prop. </s>
            <s xml:id="echoid-s6061" xml:space="preserve">21. </s>
            <s xml:id="echoid-s6062" xml:space="preserve">huius. </s>
            <s xml:id="echoid-s6063" xml:space="preserve">Quia
              <lb/>
            vero rectangulum, RMV, ad rectangulum, FMH, (tum in cir-
              <lb/>
              <note position="left" xlink:label="note-0264-06" xlink:href="note-0264-06a" xml:space="preserve">17. 3. Con.</note>
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