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

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        <div xml:id="echoid-div826" type="section" level="1" n="488">
          <p>
            <s xml:id="echoid-s8669" xml:space="preserve">
              <pb o="345" file="0365" n="365" rhead="LIBER IV."/>
            ea, quam habet rectangulum, ZPG, cum {1/2}. </s>
            <s xml:id="echoid-s8670" xml:space="preserve">quadrati, PG, ad re-
              <lb/>
            ctangulum, STI, cum {1/2}. </s>
            <s xml:id="echoid-s8671" xml:space="preserve">quadrati, TI, & </s>
            <s xml:id="echoid-s8672" xml:space="preserve">ex ea, quam habet qua-
              <lb/>
            dratum, PG, ad quadratum, TI, quod, &</s>
            <s xml:id="echoid-s8673" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8674" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div828" type="section" level="1" n="489">
          <head xml:id="echoid-head509" xml:space="preserve">THEOREMA XLIX. PROPOS. LI.</head>
          <p>
            <s xml:id="echoid-s8675" xml:space="preserve">IN omnibus huius Libri 4. </s>
            <s xml:id="echoid-s8676" xml:space="preserve">Propoſitionibus, in quibus
              <lb/>
            duarum quarumcunque fi grarum notificata fuit ratio
              <lb/>
            omnium quadratorum, iuxta regulas in eiſdem aſſumptas,
              <lb/>
            nota etiam euadit ratio ſimilarium ſolidorum, quæ ex illis
              <lb/>
            gignuntur figuris, iuxta eaſdem regulas.</s>
            <s xml:id="echoid-s8677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8678" xml:space="preserve">Quoniam enim oſtenſum eſt Lib. </s>
            <s xml:id="echoid-s8679" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8680" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s8681" xml:space="preserve">33. </s>
            <s xml:id="echoid-s8682" xml:space="preserve">vt omnia quadra-
              <lb/>
            ta duarum figurarum inter ſe ſumpta cum datis regulis, ita effe ſo-
              <lb/>
            lida ſimilaria genita ex ijſdem figuris iuxta eaſdem regulas, ideò
              <lb/>
            cum in Propoſitionibus huius Libri inuenta eſt ratio omnium qua-
              <lb/>
            dratorum duarum figurarum cum quibuſdam regulis, colligemus
              <lb/>
            etiam nunc eandem eſſe rationem duorum ſimilarium ſolidorum,
              <lb/>
            quæ ex illis figuris iuxta eaſdem regulas, genita dicuntur. </s>
            <s xml:id="echoid-s8683" xml:space="preserve">Vtex. </s>
            <s xml:id="echoid-s8684" xml:space="preserve">g.
              <lb/>
            </s>
            <s xml:id="echoid-s8685" xml:space="preserve">in Prop. </s>
            <s xml:id="echoid-s8686" xml:space="preserve">21. </s>
            <s xml:id="echoid-s8687" xml:space="preserve">conſpecta denuò illius figura, cum oſtenſum eſt omnia
              <lb/>
            quadrata, AF, eſſe dupla omnium quadratorum parabolæ, VEF,
              <lb/>
            regula ſumpta, VF; </s>
            <s xml:id="echoid-s8688" xml:space="preserve">& </s>
            <s xml:id="echoid-s8689" xml:space="preserve">item omnia quadrata parabolæ, VEF, eſ-
              <lb/>
            ſe ſexquialtera omnium quadratorum trianguli, VEF, conclude-
              <lb/>
            mus pariter ſolidum fimilare genitum ex, AF, ad ſibi ſimilare geni-
              <lb/>
            tum ex parabola, VEF, duplam habere rationem; </s>
            <s xml:id="echoid-s8690" xml:space="preserve">hoc verò ad ſo-
              <lb/>
            lidum ſibiſimilare genitum ex triangulo, VEF, habere rationem
              <lb/>
            ſexquialteram, genita autem dicta ſolida intellige iuxta dictam re-
              <lb/>
            gulam, VF; </s>
            <s xml:id="echoid-s8691" xml:space="preserve">pater ergo propoſitum.</s>
            <s xml:id="echoid-s8692" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div829" type="section" level="1" n="490">
          <head xml:id="echoid-head510" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s8693" xml:space="preserve">_Q_V oniam autem apertè colligitur ex Lib. </s>
            <s xml:id="echoid-s8694" xml:space="preserve">I. </s>
            <s xml:id="echoid-s8695" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s8696" xml:space="preserve">46. </s>
            <s xml:id="echoid-s8697" xml:space="preserve">& </s>
            <s xml:id="echoid-s8698" xml:space="preserve">47 ſi onæ-
              <lb/>
            nes figuræ ſimiles parabolæ, quæ ſumantur regula eiuſdem baſi,
              <lb/>
            ſint circuli, diame tros in eadem parabola ſitos babentes, cui ſint ere-
              <lb/>
            cti, ſolidum ſimilare genitum ex dicta parabola eſſe conoides parabo-
              <lb/>
            licum, cuius baſis rectè ſecat axim; </s>
            <s xml:id="echoid-s8699" xml:space="preserve">ſi verò ſint ellipſes homologas
              <lb/>
            diametros in eadem parabola ſitos babentes eidem erectæ, quarum ſe-
              <lb/>
            cunda diametri ſint æquales diſtantia parallelarum, qua ducuntur ab
              <lb/>
            extremis primæ diametri æquidiſtanter axi, eſſe pariter conoides pa-
              <lb/>
            rabolicum, cuius baſis tunc obliquè axim ſecat. </s>
            <s xml:id="echoid-s8700" xml:space="preserve">Ideò ex bis </s>
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