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

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        <div xml:id="echoid-div215" type="section" level="1" n="139">
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            <s xml:id="echoid-s2195" xml:space="preserve">
              <pb o="89" file="0109" n="109" rhead="LIBER I."/>
            de conſtituta conoides, & </s>
            <s xml:id="echoid-s2196" xml:space="preserve">ſphæroides, in quibus planis per eorum
              <lb/>
            axes ductis, productæ ſint figuræ iam dictæ, ſecentur deinde planis
              <lb/>
            ad axem obliquis, ſed erectis ad dictas figuras, & </s>
            <s xml:id="echoid-s2197" xml:space="preserve">ſint eadem plana
              <lb/>
            deſcriptarum ellipſium dicta ſolida ſecantia, erunt ergo ex his ſecan-
              <lb/>
            tibus planis conceptæ in ipſis figuræ pariter ellipſes, quarum diame-
              <lb/>
            trierunt, BD, quidem prima, ſecunda autem in ſpha roide æqualis
              <lb/>
            ductæ à puncto, B, parallelæ tangenti ellipſim in, S, interiectæ in-
              <lb/>
            ter ipſam, BD, & </s>
            <s xml:id="echoid-s2198" xml:space="preserve">ductam à puncto, D, parallelam iungenti pun-
              <lb/>
            cta, S, A, (in cęteris autem ſolidis eadem ſuo modo verificabuntun)
              <lb/>
              <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">44. huius.</note>
            ergo in ſphæroide ipſa, BD, eſt prima diameter dictæ ellipſis, quæ
              <lb/>
            à dicto ſecante plano producitur, & </s>
            <s xml:id="echoid-s2199" xml:space="preserve">eſt etiam prima diameter ellipſis,
              <lb/>
            quę deſcribitur modo ſupradicto, ſunt autem ſecundę diametri vtriuſ-
              <lb/>
            que ellipſis ęquales, immo communes, quia ad rectos angulos ſecant
              <lb/>
            ipſam, BD, ergo habemus in eodem plano duas ellipſes circa ea-
              <lb/>
            ſdem diametros coniugatas, ergo neceſſario erunt congruentes, ſed
              <lb/>
            linea ellipſis, quę eſt communis ſectio dicti plani, & </s>
            <s xml:id="echoid-s2200" xml:space="preserve">ſuperſiciei ſphe-
              <lb/>
              <note position="right" xlink:label="note-0109-02" xlink:href="note-0109-02a" xml:space="preserve">Elicietur
                <lb/>
              ex Corol.
                <lb/>
              25. huius.</note>
            roidis eſt in ſuperficie ſphæroidis, ergo, & </s>
            <s xml:id="echoid-s2201" xml:space="preserve">linea ellipſis vt ſupra de-
              <lb/>
            ſcriptæ erit in ſuperficie dicti ſphæroidis. </s>
            <s xml:id="echoid-s2202" xml:space="preserve">Eodem modo idem de cæ-
              <lb/>
            teris ellipſibus ſimiliter deſcriptis demonſtrabimus tum in ſphæroide,
              <lb/>
            tum etiam in conoidibus parabolicis, & </s>
            <s xml:id="echoid-s2203" xml:space="preserve">hyperbolicis, quę oſtendere
              <lb/>
            opus erat.</s>
            <s xml:id="echoid-s2204" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div217" type="section" level="1" n="140">
          <head xml:id="echoid-head151" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2205" xml:space="preserve">_H_Inc patet propoſito aliquo ex ſupradictis ſolidis, eoq; </s>
            <s xml:id="echoid-s2206" xml:space="preserve">ſecto planis
              <lb/>
            vtcumque parallelis ad axem rectis, ſiue obliquis figuras, quæ ex
              <lb/>
            ſectione planorum in ipſis ſolidis producuntur, eaſdem eſſe illis, quæ de-
              <lb/>
            ſcribuntur lineis rectis, tamquam homologis diametris, & </s>
            <s xml:id="echoid-s2207" xml:space="preserve">primis, ijs,
              <lb/>
            inquam, quæ-ſunt communes ſectiones dictarum æquidiſtantium figura-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s2208" xml:space="preserve">figuræ, quæ produceretur ducto plano per axem rectè eas ſecan-
              <lb/>
            te, quæ deſcribentes eſſent, quæ ondinatim applicantur ad axes, vel dia-
              <lb/>
            metros dictarum figurarum, ſecundis autem diametris deſcriptarum fi-
              <lb/>
            gurarum exiſtentibus, ijs, quæ ſupradictæ ſunt, prout poſtul at varietas
              <lb/>
            ſolidorum, iuxta Prop.</s>
            <s xml:id="echoid-s2209" xml:space="preserve">42. </s>
            <s xml:id="echoid-s2210" xml:space="preserve">43. </s>
            <s xml:id="echoid-s2211" xml:space="preserve">& </s>
            <s xml:id="echoid-s2212" xml:space="preserve">44. </s>
            <s xml:id="echoid-s2213" xml:space="preserve">huius.</s>
            <s xml:id="echoid-s2214" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div218" type="section" level="1" n="141">
          <head xml:id="echoid-head152" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2215" xml:space="preserve">_A_Duerte tamen licet ſupra vocentur diametri, quæ dictas figuras de-
              <lb/>
            ſcribunt, deberetamen intelligi ſemper eſſe axes deſeriptarum fi-
              <lb/>
            gurarum, cum .</s>
            <s xml:id="echoid-s2216" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2217" xml:space="preserve">nomen diametri ſit commune diametro, & </s>
            <s xml:id="echoid-s2218" xml:space="preserve">axi, @li-
              <lb/>
            quando vice axis vtimur nomine diametri, vt in circulo apparet, cuius
              <lb/>
            tamen omnes diametri ſunt axes: </s>
            <s xml:id="echoid-s2219" xml:space="preserve">Inſuper ſciendum eſt etiam, quæ </s>
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