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

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        <div xml:id="echoid-div611" type="section" level="1" n="355">
          <p>
            <s xml:id="echoid-s6412" xml:space="preserve">
              <pb o="256" file="0276" n="276" rhead="GEOMETRIÆ"/>
            rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6413" xml:space="preserve">ſub quadrilineo, BGMXT, erunt vt,
              <lb/>
            AR, ad ellipſim, BDMG. </s>
            <s xml:id="echoid-s6414" xml:space="preserve">Sic etiam fiet demonſtratio, ſi produ-
              <lb/>
            cantur, FA, RC, ſimiliter ac productę ſunt, AC, FR, quarum al-
              <lb/>
            tera pro regula ſumatur.</s>
            <s xml:id="echoid-s6415" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div613" type="section" level="1" n="356">
          <head xml:id="echoid-head373" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6416" xml:space="preserve">_H_Inc patet, ſi, BDMG, non eſſet ellipſis, ſed alia vtcunque figu-
              <lb/>
            ra plana parallelogrammo, AR, inſcripta, dummodo portiones
              <lb/>
            laterum coalternè tangentes eſſent æquales, & </s>
            <s xml:id="echoid-s6417" xml:space="preserve">rectangula ſumpta ad
              <lb/>
            coalternè tangentes, eo modo, quo dictum eſt in heor. </s>
            <s xml:id="echoid-s6418" xml:space="preserve">antecedenti, eſ-
              <lb/>
            ſent quoque æqualia, quod omnia quadrata, AR, ad omnia quadrata,
              <lb/>
            talis figuræ, cum rectangulis bis ſub eadem, & </s>
            <s xml:id="echoid-s6419" xml:space="preserve">ſub trilineis adiacenti-
              <lb/>
            bus lateri, quod non ſumitur pro regula, erunt vt, AR, ad talem figu-
              <lb/>
            ram; </s>
            <s xml:id="echoid-s6420" xml:space="preserve">V eluti erunt etiam omnia quadrata, AR, cumrectangu
              <unsure/>
            lis bis ſub,
              <lb/>
            AR, RT, ad omnia quadrata talis figuræ, cum rectangulis bis ſub ea-
              <lb/>
            dem, & </s>
            <s xml:id="echoid-s6421" xml:space="preserve">ſub quadrilineo ſimili ipſi, BGMXT, bæc. </s>
            <s xml:id="echoid-s6422" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6423" xml:space="preserve">eodem modo col-
              <lb/>
            ligentur, quo pro ellipſi, BDMG, per demonſtrationem collecta ſunt,
              <lb/>
            aderunt enim eadem principia, ex quibus demonſtratio pro ellipſi pende-
              <lb/>
            bat: </s>
            <s xml:id="echoid-s6424" xml:space="preserve">Exemplum facile baberi poteſt in figura ex duabus æqualibus cir-
              <lb/>
            culi, vel ellipſis portionibus minoribus compoſita tali pacto, vt baſis v-
              <lb/>
            nius portionis alterius baſi congruat, quæ quidem figura ſit inſoripta di-
              <lb/>
            cto rectangulo, cuiuſque latera eam tangant non in punctis extremis
              <lb/>
            axium, ſed in quatuor alijs vtcunq, vnde, &</s>
            <s xml:id="echoid-s6425" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6426" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div614" type="section" level="1" n="357">
          <head xml:id="echoid-head374" xml:space="preserve">THEOREMA XXXIII. PROPOS. XXXIV.</head>
          <p>
            <s xml:id="echoid-s6427" xml:space="preserve">QVæcunque ſolida ad inuicem ſimilaria, genita ex figu-
              <lb/>
            ris ſuperius in hoc Libro Tertio conſideratis, iuxta re-
              <lb/>
            gulas ibidem aſſumptas, quarum patefacta eſt ra-
              <lb/>
            tio omnium quadratorum, habent inter ſe rationem notam.</s>
            <s xml:id="echoid-s6428" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6429" xml:space="preserve">Quoniam enim alibi oſtenſum eſt, vt omnia quadrata duarum fi-
              <lb/>
            gurarum inter ſe ſumpta cum da
              <unsure/>
            tis regulis, ita eſſe ſoli
              <unsure/>
            da ad inuicem
              <lb/>
              <note position="left" xlink:label="note-0276-01" xlink:href="note-0276-01a" xml:space="preserve">33. Lib. 2.</note>
            ſimilaria genita ex ijldem ſiguris, iuxta eaſdem regulas, ideò cum in
              <lb/>
            Theorematibus huius Libri inuenta eſt ratio omnium quadratorum
              <lb/>
            duarum quarundam figurarum cum talibus regulis, colligimus etiam
              <lb/>
            nunc eandem eſſe rationem duorum ad inuicem ſimilarium ſolido-
              <lb/>
            rum, quæ ex illis figuris iuxta eaſdem regulas genita dicuntur; </s>
            <s xml:id="echoid-s6430" xml:space="preserve">Vt
              <lb/>
            exempli gratia in Propoſ. </s>
            <s xml:id="echoid-s6431" xml:space="preserve">I. </s>
            <s xml:id="echoid-s6432" xml:space="preserve">conſpectis, iterum eiuſdem figuris, </s>
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