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

Table of handwritten notes

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            <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
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            parabolæ, MHFC, quod oſtendere opuserat.</s>
            <s xml:id="echoid-s7395" xml:space="preserve"/>
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        <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-
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            les, etiam, DF, XC, eſſe ęquales, nam oſtenſum eſt, QC, eſſe æqualem
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            ipſi, RF, eſt autem, XC, dupla, CQ &</s>
            <s xml:id="echoid-s7398" xml:space="preserve">, DF, dupla, FR, ideò etiam,
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            XC, DF, ſunt, æquales.</s>
            <s xml:id="echoid-s7399" xml:space="preserve"/>
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        <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
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            diametro totius, & </s>
            <s xml:id="echoid-s7402" xml:space="preserve">completo parallelogrammo ſub
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            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
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            quarta, vel circuli circa axem vel diametrum, & </s>
            <s xml:id="echoid-s7405" xml:space="preserve">ſemi-
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            baſim dictam, tanquam circa ſemiaxes, vel ſemidiame-
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            tros coniugatas integræ ellipſis, vel circuli; </s>
            <s xml:id="echoid-s7406" xml:space="preserve">ſi deinde ſu-
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            matur vtcunque punctum in ſemibaſi, per quod ducatur
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            recta linea ad oppoſitum latus parallelogrammi paralle-
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            la dictæ axi, vel diametro, portio huius inter ſemibaſim,
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            & </s>
            <s xml:id="echoid-s7407" xml:space="preserve">curuam ellipſis, vel circuli incluſa, erit media propor-
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            tionalis inter incluſam oppoſitis lateribus parallelogram-
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            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
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            verò ſumatur punctum in axi, vel diametro iam dicta,
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            & </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
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            latus oppoſitum parallelogrammi iam dicti, & </s>
            <s xml:id="echoid-s7412" xml:space="preserve">iungantur
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            extrema puncta curuæ parabolæ recta linea, huius portio
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            incluſa inter axim, vel diametrum dictam, & </s>
            <s xml:id="echoid-s7413" xml:space="preserve">curuam pa-
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            rabolæ, erit media proportionalis inter eam, quæ inclu-
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            ditur lateribus oppoſitis dicti parallelogrammi, & </s>
            <s xml:id="echoid-s7414" xml:space="preserve">eam,
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            quæ includitur lateribus trianguli ſub dicta axi, vel diame-
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            tro, & </s>
            <s xml:id="echoid-s7415" xml:space="preserve">dicta ſemibaſi conſtituti.</s>
            <s xml:id="echoid-s7416" xml:space="preserve"/>
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            <image file="0327-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0327-01"/>
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