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

Table of contents

< >
[421.] THEOREMA X. PROPOS. XI.
Page: 318 (298)
[422.] COROLLARIV M.
Page: 320 (300)
[423.] THEOREMA XI. PROPOS. XII.
Page: 320 (300)
[424.] THEOREMA XII. PROPOS. XIII.
Page: 321 (301)
[425.] THEOREMA XIII. PROPOS. XIV.
Page: 323 (303)
[426.] THEOREMA XIV. PROPOS. XV.
Page: 324 (304)
[427.] THEOREMA XV. PROPOS. XVI.
Page: 325 (305)
[428.] THEOREMA XVI. PROPOS. XVII.
Page: 325 (305)
[429.] COROLLARIVM.
Page: 327 (307)
[430.] THEOREMA XVII. PROPOS. XVIII.
Page: 327 (307)
[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
< >
page |< < (307) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div729" type="section" level="1" n="428">
          <p>
            <s xml:id="echoid-s7394" xml:space="preserve">
              <pb o="307" file="0327" n="327" rhead="LIBER IV."/>
            eorundem cubi ſunt æquales, ergo parabola, DAF, erit æqualis
              <lb/>
            parabolæ, MHFC, quod oſtendere opuserat.</s>
            <s xml:id="echoid-s7395" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div731" type="section" level="1" n="429">
          <head xml:id="echoid-head449" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7396" xml:space="preserve">_H_Inc patet, ſi diametri, AR, HO, vel axis, & </s>
            <s xml:id="echoid-s7397" xml:space="preserve">diameter ſint æquà-
              <lb/>
            les, etiam, DF, XC, eſſe ęquales, nam oſtenſum eſt, QC, eſſe æqualem
              <lb/>
            ipſi, RF, eſt autem, XC, dupla, CQ &</s>
            <s xml:id="echoid-s7398" xml:space="preserve">, DF, dupla, FR, ideò etiam,
              <lb/>
            XC, DF, ſunt, æquales.</s>
            <s xml:id="echoid-s7399" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div732" type="section" level="1" n="430">
          <head xml:id="echoid-head450" xml:space="preserve">THEOREMA XVII. PROPOS. XVIII.</head>
          <p>
            <s xml:id="echoid-s7400" xml:space="preserve">EXpoſita ſemiparabola cum dimidia baſi, & </s>
            <s xml:id="echoid-s7401" xml:space="preserve">axi, vel
              <lb/>
            diametro totius, & </s>
            <s xml:id="echoid-s7402" xml:space="preserve">completo parallelogrammo ſub
              <lb/>
            dicto axi, vel diametro. </s>
            <s xml:id="echoid-s7403" xml:space="preserve">& </s>
            <s xml:id="echoid-s7404" xml:space="preserve">ſemibaſi, deſcriptaque ellipſis
              <lb/>
            quarta, vel circuli circa axem vel diametrum, & </s>
            <s xml:id="echoid-s7405" xml:space="preserve">ſemi-
              <lb/>
            baſim dictam, tanquam circa ſemiaxes, vel ſemidiame-
              <lb/>
            tros coniugatas integræ ellipſis, vel circuli; </s>
            <s xml:id="echoid-s7406" xml:space="preserve">ſi deinde ſu-
              <lb/>
            matur vtcunque punctum in ſemibaſi, per quod ducatur
              <lb/>
            recta linea ad oppoſitum latus parallelogrammi paralle-
              <lb/>
            la dictæ axi, vel diametro, portio huius inter ſemibaſim,
              <lb/>
            & </s>
            <s xml:id="echoid-s7407" xml:space="preserve">curuam ellipſis, vel circuli incluſa, erit media propor-
              <lb/>
            tionalis inter incluſam oppoſitis lateribus parallelogram-
              <lb/>
            mi iam dicti, & </s>
            <s xml:id="echoid-s7408" xml:space="preserve">eadem ſemibaſi, ac curua parabolæ. </s>
            <s xml:id="echoid-s7409" xml:space="preserve">Si
              <lb/>
            verò ſumatur punctum in axi, vel diametro iam dicta,
              <lb/>
            & </s>
            <s xml:id="echoid-s7410" xml:space="preserve">per ipſum ducatur ſemibaſi parallela, producta vſq; </s>
            <s xml:id="echoid-s7411" xml:space="preserve">ad
              <lb/>
            latus oppoſitum parallelogrammi iam dicti, & </s>
            <s xml:id="echoid-s7412" xml:space="preserve">iungantur
              <lb/>
            extrema puncta curuæ parabolæ recta linea, huius portio
              <lb/>
            incluſa inter axim, vel diametrum dictam, & </s>
            <s xml:id="echoid-s7413" xml:space="preserve">curuam pa-
              <lb/>
            rabolæ, erit media proportionalis inter eam, quæ inclu-
              <lb/>
            ditur lateribus oppoſitis dicti parallelogrammi, & </s>
            <s xml:id="echoid-s7414" xml:space="preserve">eam,
              <lb/>
            quæ includitur lateribus trianguli ſub dicta axi, vel diame-
              <lb/>
            tro, & </s>
            <s xml:id="echoid-s7415" xml:space="preserve">dicta ſemibaſi conſtituti.</s>
            <s xml:id="echoid-s7416" xml:space="preserve"/>
          </p>
          <figure number="219">
            <image file="0327-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0327-01"/>
          </figure>
        </div>
      </text>
    </echo>
Impressum