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

Table of contents

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[231.] D. SECTIO IV.
Page: 174 (154)
[232.] E. SECTIO V.
Page: 175 (155)
[233.] F. SECTIO VI.
Page: 175 (155)
[234.] THEOR EMA XXIII. PROPOS. XXIII.
Page: 175 (155)
[235.] A. COROLLARII SECTIO I.
Page: 176 (156)
[236.] B. SECTIO II.
Page: 177 (157)
[237.] C. SECTIO III.
Page: 177 (157)
[238.] D. SECTIO IV.
Page: 177 (157)
[239.] E. SECTIO V.
Page: 177 (157)
[240.] F. SECTIO VI.
Page: 177 (157)
[241.] G. SECTIO VII.
Page: 177 (157)
[242.] H. SECTIO VIII.
Page: 178 (158)
[243.] I. SECTIO IX.
Page: 178 (158)
[244.] K. SECTIO X.
Page: 178 (158)
[245.] L. SECTIO XI.
Page: 178 (158)
[246.] THEOREMA XXIV. PROPOS. XXIV.
Page: 179 (159)
[247.] COROLLARIVM.
Page: 180 (160)
[248.] THEOREMA XXV. PROPOS. XXV.
Page: 181 (161)
[249.] THE OREMA XXVI. PROPOS. XXVI.
Page: 183 (163)
[250.] COROLLARIVM I.
Page: 185 (165)
[251.] COROLLARIVM II.
Page: 186 (166)
[252.] COROLLARIVM III.
Page: 186 (166)
[253.] THEOREMA XXVII. PROPOS. XXVII.
Page: 187 (167)
[254.] THEOREMA XXVIII. PROPOS. XXVIII:
Page: 188 (168)
[255.] COROLLARIVM.
Page: 189 (169)
[256.] THEOREMA XXIX. PROPOS. XXIX.
Page: 190 (170)
[257.] COROLLARIVM.
Page: 190 (170)
[258.] THEOREMA XXX. PROPOS. XXX.
Page: 191 (171)
[259.] COROLLARIVM.
Page: 192 (172)
[260.] THEOREMA XXXI. PROPOS. XXXI.
Page: 193 (173)
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            <s xml:id="echoid-s5211" xml:space="preserve">
              <pb o="214" file="0234" n="234" rhead="GEOMETRIÆ"/>
            licet non ſint rectangula, tamen erunt æquiangula, vndeæquiangu-
              <lb/>
            lum erit parallelogrammi, HP, ipſi, FG, & </s>
            <s xml:id="echoid-s5212" xml:space="preserve">ellipſes, ABCD, K
              <lb/>
              <figure xlink:label="fig-0234-01" xlink:href="fig-0234-01a" number="146">
                <image file="0234-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0234-01"/>
              </figure>
            TMI, erunt circa, AC, KM,
              <lb/>
            æquales diametros, ita vt ſi ſuper-
              <lb/>
            ponerentur ad inuicem iſti ellipſes,
              <lb/>
            vt, KM, eſſet in, AC, ipſa, TI,
              <lb/>
            eſſet in, BD, & </s>
            <s xml:id="echoid-s5213" xml:space="preserve">ideò eodem mo-
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            do oſtendemus, vt ſupra ellipſes,
              <lb/>
            ABCD, STVI, eſſe inter ſe, vt
              <lb/>
            parallelogramma illis eircumſcri-
              <lb/>
            pta, FG, ER, & </s>
            <s xml:id="echoid-s5214" xml:space="preserve">quia illa ſunt
              <lb/>
            ęquiangula habebunt rationem ex
              <lb/>
            ratione laterum compoſitam, ſed
              <lb/>
            etiam parallelogramma rectangu-
              <lb/>
              <note position="left" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">6.Lib.2.</note>
            la ſub eiſdem lateribus habent ra-
              <lb/>
            tionem cõpoſitam ex ratione eo-
              <lb/>
            rundem laterum, ergo ellipſis, A
              <lb/>
            BCD, ad ellipſim, STVI, erit
              <lb/>
            vt parallelogrammum, FG, ad
              <lb/>
            parallelogrammum, ER, ſibiæ-
              <lb/>
            quiangulum. </s>
            <s xml:id="echoid-s5215" xml:space="preserve">.</s>
            <s xml:id="echoid-s5216" xml:space="preserve">vt rectangulum ſub,
              <lb/>
            FL, LG, vel ſub, BD, AC, dia-
              <lb/>
            metris, ad rectangulum ſub, TI,
              <lb/>
            SV, diametris, patetigitur circu-
              <lb/>
            lum, vel ellipſim, ABCD, ad cir-
              <lb/>
            eulum, vel cllipſim, STVI, eſſe vt rectangulum ſub axibus, vel dia-
              <lb/>
            metris, AC, BD, ad rectangulum ſub axibus, vel diametris, SV,
              <lb/>
            TI, quæ diametri æquè ad inuicem inclinantur, quod oſtendere
              <lb/>
            opuserat.</s>
            <s xml:id="echoid-s5217" xml:space="preserve"/>
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        <div xml:id="echoid-div531" type="section" level="1" n="316">
          <head xml:id="echoid-head333" xml:space="preserve">COROLLARIVM I.</head>
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            <s xml:id="echoid-s5218" xml:space="preserve">_H_INC ergo colligitur, quod quando circulos comparatur ad cir-
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            culum, illi ſunt interſe, vt rectangula ſub eorum axibus. </s>
            <s xml:id="echoid-s5219" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5220" xml:space="preserve">vt
              <lb/>
            quadrata axium, & </s>
            <s xml:id="echoid-s5221" xml:space="preserve">ideò ſunt in dupla ratione axium, ſiue diametro-
              <lb/>
            rum, quando verò circulus comparatur ad ellipſim, erit ad illum, vt
              <lb/>
            ſui axis quadratum adrectangulum ſub axibus ellipſis. </s>
            <s xml:id="echoid-s5222" xml:space="preserve">Denique, ſiel-
              <lb/>
            lipſis comparetur ad ellipſim, erit ad illum, vt rectangulum ſub axibus
              <lb/>
            illius ad rectangulum ſub axibus alterius, vel vt rectangulum ſub dia-
              <lb/>
            metris (coniugatis ſemper intellige, niſi aliud addatur) illius ad rectan-
              <lb/>
            gulum ſub diametris alterins, quæ vt prædicti æqualiter ad inuicem
              <lb/>
            ſunt inclinatæ; </s>
            <s xml:id="echoid-s5223" xml:space="preserve">vel tandem, vt parallelogramma illis </s>
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