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

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        <div xml:id="echoid-div31" type="section" level="1" n="28">
          <p>
            <s xml:id="echoid-s315" xml:space="preserve">
              <pb o="5" file="0025" n="25" rhead="LIBERI."/>
            nomina fectionum conicorum latera recta, ſeu tranſuerſa,
              <lb/>
            ſumantur, prout ab Apollonio definiuntur, hoctantum ani-
              <lb/>
            maduerſo, me in ſequentibus aliquando abuti eiſdem no-
              <lb/>
            minibus ſectionum coni, Parabolæ .</s>
            <s xml:id="echoid-s316" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s317" xml:space="preserve">Hyperbolæ, Ellipſis,
              <lb/>
            & </s>
            <s xml:id="echoid-s318" xml:space="preserve">oppoſitarum ſectionum, ſpatia videlicet intelligens ſub
              <lb/>
            illis, & </s>
            <s xml:id="echoid-s319" xml:space="preserve">earum baſibus, compręhenſa, quod ex modo lo-
              <lb/>
            quendi tunc euidenter cognoſcitur. </s>
            <s xml:id="echoid-s320" xml:space="preserve">Cætera deniq Apol-
              <lb/>
            lonij, & </s>
            <s xml:id="echoid-s321" xml:space="preserve">quæ ab Archimede circa Sphęroides, & </s>
            <s xml:id="echoid-s322" xml:space="preserve">Conoides,
              <lb/>
            definiuntur, niſi alia afferatur à me definitio, ſumantur,
              <lb/>
            prout ab ipſis vſurpantur.</s>
            <s xml:id="echoid-s323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div32" type="section" level="1" n="29">
          <head xml:id="echoid-head39" xml:space="preserve">VI.</head>
          <p>
            <s xml:id="echoid-s324" xml:space="preserve">FIguram planam circa diametrum, vocat Apollonius,
              <lb/>
            Conicorum, cum in ea ductis quotuis lineis cuidam
              <lb/>
            æquidiſtantibus, omnes bifariam à quadam recta linea di-
              <lb/>
            uiduntur, quam vocat diametrum, ſieas oblique ſecet, & </s>
            <s xml:id="echoid-s325" xml:space="preserve">
              <lb/>
            axem, ſi eas rectè diuidat, & </s>
            <s xml:id="echoid-s326" xml:space="preserve">ipſam figuram circa diame-
              <lb/>
            trum, vel axem.</s>
            <s xml:id="echoid-s327" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s328" xml:space="preserve">Siergo figura circa axem, reuoluatur circa eundem do-
              <lb/>
            nec redeat, vnde diſceſſit, deſcripta in tali reuolutione ab
              <lb/>
            eadem ſolida figura dicatur: </s>
            <s xml:id="echoid-s329" xml:space="preserve">ſolidum rotundum, eiuſdem
              <lb/>
            verò axis, circa quem fit reuolutio.</s>
            <s xml:id="echoid-s330" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div33" type="section" level="1" n="30">
          <head xml:id="echoid-head40" xml:space="preserve">VII.</head>
          <p>
            <s xml:id="echoid-s331" xml:space="preserve">SImiles Cylindrici, & </s>
            <s xml:id="echoid-s332" xml:space="preserve">Conicidicantur, quorum baſes
              <lb/>
            ſunt ſimiles (iuxta definitionem 10. </s>
            <s xml:id="echoid-s333" xml:space="preserve">ſimilium figura-
              <lb/>
            rum infra poſitam, ſubint ellige, veliuxta aliorum defini-
              <lb/>
            tiones, quas cum prędictam concordare infra oſtendemus)
              <lb/>
            in quibus ſumptis duabus homologis lineis, vel lateribus
              <lb/>
            vtcumque, & </s>
            <s xml:id="echoid-s334" xml:space="preserve">per ipſas, & </s>
            <s xml:id="echoid-s335" xml:space="preserve">latera extenſis planis ipſa ad ean-
              <lb/>
            dem partem ęquè ad baſes inclinantur, horumq. </s>
            <s xml:id="echoid-s336" xml:space="preserve">conceptę
              <lb/>
            in eiſdem figurę ſunt ſimiles, nempè ſimilia parallelogram-
              <lb/>
            ma in cylindricis, & </s>
            <s xml:id="echoid-s337" xml:space="preserve">ſimilia triangula in conicis, quorum ho-
              <lb/>
            mologa latera ſint ſumptę in baſibus homologę.</s>
            <s xml:id="echoid-s338" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div34" type="section" level="1" n="31">
          <head xml:id="echoid-head41" xml:space="preserve">VIII.</head>
          <p>
            <s xml:id="echoid-s339" xml:space="preserve">SImiles ſphęroides dieentur, quę ex ſimilium ellipſium
              <lb/>
            reuolutione oriuntur.</s>
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          </p>
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