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

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              <pb o="97" file="0117" n="117" rhead="LIBER I."/>
            oppoſitis tangentibus baſium, FGHN, BDCE, iam dictis, om-
              <lb/>
            nes æquidiſtant, ergo ſolida, FMH, BAC, ſunt ſimilia iuxta de-
              <lb/>
            fin. </s>
            <s xml:id="echoid-s2379" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2380" xml:space="preserve">huius, & </s>
            <s xml:id="echoid-s2381" xml:space="preserve">earum, ac oppoſitorum tangentium planorum iam
              <lb/>
            dictorum, figuræ incidentes ſunt ipſæ, FMH, BAC, quod erat o-
              <lb/>
            ſtendendum.</s>
            <s xml:id="echoid-s2382" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div230" type="section" level="1" n="148">
          <head xml:id="echoid-head159" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s2383" xml:space="preserve">_H_Inc etiam non difficile intelligi poteſt, propoſitis duabus coniſi-
              <lb/>
            milibus ſectionibus, FMH, BAC, quarum axes, vel diametri
              <lb/>
            ſint, MO, AX, ac poſito ipſas, FH, BC, tanquam axes deſcribere cir-
              <lb/>
            culos, ſeu ſimiles ellipſes erectas planis figurarum, FMH, BAC, & </s>
            <s xml:id="echoid-s2384" xml:space="preserve">
              <lb/>
            cæteras omnes ordinatim applicatas ad ipſas, MO, AX, vel circulos,
              <lb/>
            vel ſemper ſimiles ellipſes deſcribere, vt dictum eſt, ſolida in cuius ſu-
              <lb/>
            perficie capiuntur omnes peripbæriæ circulorum, vel ſimilium ellipſi-
              <lb/>
            um, eſſe ſimiles portiones ſphærarum, vel ſimiles ſphæroides, vel conoi-
              <lb/>
            des, earumuè portiones, ſimiles inquam nedum iuxta defin. </s>
            <s xml:id="echoid-s2385" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2386" xml:space="preserve">huius,
              <lb/>
            hoc. </s>
            <s xml:id="echoid-s2387" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2388" xml:space="preserve">habetur ex 48. </s>
            <s xml:id="echoid-s2389" xml:space="preserve">huius, ſed etiam iuxta defin. </s>
            <s xml:id="echoid-s2390" xml:space="preserve">9. </s>
            <s xml:id="echoid-s2391" xml:space="preserve">habentur. </s>
            <s xml:id="echoid-s2392" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2393" xml:space="preserve">hic
              <lb/>
            omnes iſtius conditiones, vt examinanti facilè apparebit, quod eſt con-
              <lb/>
            uerſum eius, quod in præſenti Theor. </s>
            <s xml:id="echoid-s2394" xml:space="preserve">propoſitum fuit. </s>
            <s xml:id="echoid-s2395" xml:space="preserve">Hoc autem con-
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            uerſum etiam in reliquis Theorematibus, in quibus definitiones particu-
              <lb/>
            lares ſimilium planarum, vel ſolidarum figurarum cum generalibus o-
              <lb/>
            ſtendimus cencordare, poterat demonſtrari, ſedcum in ſequentibus libris
              <lb/>
            vel nullam, vel ſaltem non neceſſariam occaſionem viderem me huius
              <lb/>
            habiturum eſſe, & </s>
            <s xml:id="echoid-s2396" xml:space="preserve">cum etiam facilè hoc ſtudioſus, quirectè priores pro-
              <lb/>
            poſitiones intellexit, deducere poſſit, proptereane longior fierem, con-
              <lb/>
            ſultò hoc prætermiſi, quod tamen verum eſſe minimè dubito, & </s>
            <s xml:id="echoid-s2397" xml:space="preserve">propte-
              <lb/>
            rea hoc etiam pro vero ſuppoſito infraſcriptum Coroll. </s>
            <s xml:id="echoid-s2398" xml:space="preserve">ſubiungere volui.</s>
            <s xml:id="echoid-s2399" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div231" type="section" level="1" n="149">
          <head xml:id="echoid-head160" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s2400" xml:space="preserve">_V_Lterius ergo cum hucuſque ſatis manifeſtum ſit, definitiones par-
              <lb/>
            ticulares ſimilium planarum, vel ſolidarum figurarum, cum de-
              <lb/>
            finitionibus generalibus 10. </s>
            <s xml:id="echoid-s2401" xml:space="preserve">nempè, & </s>
            <s xml:id="echoid-s2402" xml:space="preserve">11. </s>
            <s xml:id="echoid-s2403" xml:space="preserve">huius concordare, ideò in ſe-
              <lb/>
            quentibus vtriuſq; </s>
            <s xml:id="echoid-s2404" xml:space="preserve">definitionis, tam particularis ſcilicet quam generalis,
              <lb/>
            prout libuerit, hypoteſi nos vti poſſe ex hoc colligemus.</s>
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