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

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        <div xml:id="echoid-div222" type="section" level="1" n="144">
          <pb o="93" file="0113" n="113" rhead="LIBER I."/>
          <p>
            <s xml:id="echoid-s2290" xml:space="preserve">Hæc Propoſitio manifeſta eſt, inuoluit. </s>
            <s xml:id="echoid-s2291" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2292" xml:space="preserve">requiſita omnia defini-
              <lb/>
              <note position="right" xlink:label="note-0113-01" xlink:href="note-0113-01a" xml:space="preserve">Defin. 21.
                <lb/>
              huius.</note>
            tionis ſimilium ſolidorum; </s>
            <s xml:id="echoid-s2293" xml:space="preserve">nam hic habemus duo ſolida, ea nempè,
              <lb/>
            quæ ſecantur planis dictarum figurarum, quorum duo extrema ſiue
              <lb/>
            primo ducta æquidiſtantia plana talia ſunt, vt illis incidant duo pla-
              <lb/>
            na (in quibus nempè reperiuntur propoſitæ figuræ ſimiles, quarum
              <lb/>
            homologarum regulę ſunt communes ſectiones earum, & </s>
            <s xml:id="echoid-s2294" xml:space="preserve">dictorum
              <lb/>
            oppoſitorum planorum tangentium) ad eundem angulum ex eadem
              <lb/>
            parte, ſunt autem figuræ planę deſcriptæ lineis, vel lateribus homo-
              <lb/>
            logis propoſitarum figurarum inter ſe ſimiles, illæ. </s>
            <s xml:id="echoid-s2295" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s2296" xml:space="preserve">quæ ſecant in-
              <lb/>
            cidentes propoſitarum figurarum, & </s>
            <s xml:id="echoid-s2297" xml:space="preserve">ſubinde altitudines dictorum ſc-
              <lb/>
              <note position="right" xlink:label="note-0113-02" xlink:href="note-0113-02a" xml:space="preserve">17. Vnd.
                <lb/>
              Elem.</note>
            lidorum ſimiliter ad eandem partem, & </s>
            <s xml:id="echoid-s2298" xml:space="preserve">æquidiſtant dictis tangenti-
              <lb/>
            bus planis, reſpectu quorum altitudines dictas aſſumptas intelligo;
              <lb/>
            </s>
            <s xml:id="echoid-s2299" xml:space="preserve">& </s>
            <s xml:id="echoid-s2300" xml:space="preserve">quia ſupponimus omnium deſcriptarum ſimilium figurarum late-
              <lb/>
            ra homologa deſcribentia eſſe lineas, vel latera homologa ſimilium
              <lb/>
            figurarum, quæ omnia ſunt inter ſe æquidiſtantia, ideò omnes ea-
              <lb/>
              <note position="right" xlink:label="note-0113-03" xlink:href="note-0113-03a" xml:space="preserve">Corol. 23.
                <lb/>
              huius.</note>
            rum lineæ homologæ duabus quibuſdam regulis æquidiſtabunt, & </s>
            <s xml:id="echoid-s2301" xml:space="preserve">
              <lb/>
            ipſa latera deſcribentia erunt etiam lineæ incidentes, vel in eiſdem
              <lb/>
            productis ſaltem reperiri poterunt incidentes deſcriptarum ſimilium
              <lb/>
            figurarum, & </s>
            <s xml:id="echoid-s2302" xml:space="preserve">oppoſitarum tangentium duabus quibuſdam ſemper
              <lb/>
            ęquidiſtantium, ſcilicet eis, quę cum dictis incidentibus angulos con-
              <lb/>
            tinent ęquales (erunt autem dicta latera homologa incidentes, ſi di-
              <lb/>
            ctæ tangentes tranſeant per extrema laterum deſcribentium, ſi au-
              <lb/>
            tem non, poterunt tamen in ipſis lateribus productis aſſumi earun-
              <lb/>
              <note position="right" xlink:label="note-0113-04" xlink:href="note-0113-04a" xml:space="preserve">Ex Lem.
                <lb/>
              antec.</note>
            dem incidentes, quæ erunt, vtipſa latera homologa) & </s>
            <s xml:id="echoid-s2303" xml:space="preserve">cum ipſæ
              <lb/>
            propoſitæ figuræ ſint ſimiles, ſubinde etiam erunt ſimiles illæ, quæ
              <lb/>
            capient omnes dictas incidentes, ſi fortè accidat ipſa latera homolo-
              <lb/>
            ga deſcribentia non eſſe incidentes, vt dictum eſt, igitur adſunt hic
              <lb/>
            omnes conditiones definitionis meæ ſimilium ſolidorum, ergo ſoli-
              <lb/>
            da, in quibus dictæ ſimiles deſcriptæ figuræ ex traiectione dictorum
              <lb/>
            planorum producuntur, erunt ſimilia, & </s>
            <s xml:id="echoid-s2304" xml:space="preserve">regulæ figurarum homo-
              <lb/>
            logarum erunt dicta plana tangentia, & </s>
            <s xml:id="echoid-s2305" xml:space="preserve">eorum, ac dictorum ſolido-
              <lb/>
            rum figuræ incidentes, propoſitæ primò figuræ, vel aliæ in eiſdem
              <lb/>
            planis inuentæ, illæ ſcilicet, in quibus iacent omnium ſimilium de-
              <lb/>
            ſcriptarum figurarum lineæ incidentes, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s2306" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div224" type="section" level="1" n="145">
          <head xml:id="echoid-head156" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2307" xml:space="preserve">_H_Inc apparet ſi deſcriptæ figuræ omnes ſint inter ſe ſimiles, dicta,
              <lb/>
            ſolida pariter eſſe ſimilia. </s>
            <s xml:id="echoid-s2308" xml:space="preserve">Vnde ſi intelligamus ſimiles coni ſe-
              <lb/>
            ctionum portiones, ſiue eaſdem integras, circa axes, vel diametros, & </s>
            <s xml:id="echoid-s2309" xml:space="preserve">
              <lb/>
            ab ordinatim applicatis ad axim, vel diametrum, earundem deſcribi ſi-
              <lb/>
            mil. </s>
            <s xml:id="echoid-s2310" xml:space="preserve">s figuras planas eiſdem ſectionum portionibus erectas, tanquam </s>
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