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

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        <div xml:id="echoid-div331" type="section" level="1" n="203">
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            <s xml:id="echoid-s3095" xml:space="preserve">
              <pb o="131" file="0151" n="151" rhead="LIBER II."/>
            tione ipſius, MP, ad, Ω &</s>
            <s xml:id="echoid-s3096" xml:space="preserve">, ideò figura, MZP, ad figuram, Ω ℟
              <lb/>
              <note position="right" xlink:label="note-0151-01" xlink:href="note-0151-01a" xml:space="preserve">Defnilo,
                <lb/>
              Quin. El.</note>
            & </s>
            <s xml:id="echoid-s3097" xml:space="preserve">habebit rationem compofitam ex duabus rationibus ipſius, MP,
              <lb/>
            ad, Ω &</s>
            <s xml:id="echoid-s3098" xml:space="preserve">, . </s>
            <s xml:id="echoid-s3099" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3100" xml:space="preserve">duplam eius, quam habet, MP, ad, Ω &</s>
            <s xml:id="echoid-s3101" xml:space="preserve">, ſiue, KM,
              <lb/>
            ad, Π Ω, quæ illis ſunt æquales, ſed & </s>
            <s xml:id="echoid-s3102" xml:space="preserve">figuræ, ABD, φ Σ Λ, ſunt
              <lb/>
            æquales figuris, MZP, Ω ℟ &</s>
            <s xml:id="echoid-s3103" xml:space="preserve">, ergo ſigura, ABD, ad figuram, Φ
              <lb/>
            Σ Λ, duplam rationem habebit eius, quam habet, KM, ad, Π Ω,
              <lb/>
            quia vero, KM, &</s>
            <s xml:id="echoid-s3104" xml:space="preserve">, Π Ω, ſunt incidentes ſimilium figurarum, AB
              <lb/>
              <note position="right" xlink:label="note-0151-02" xlink:href="note-0151-02a" xml:space="preserve">B. Def. 10.
                <lb/>
              lib. 1.</note>
            D, Φ Σ Λ, ideò, vt, KM, ad, Π Ω, ita erit, BEID, ſimul ad, Σ 2,
              <lb/>
            3 Λ, ſimul, vel ita, BE, ad, Σ 2, ſiue, ID, ad, 3 Λ, ergo figura,
              <lb/>
              <note position="right" xlink:label="note-0151-03" xlink:href="note-0151-03a" xml:space="preserve">Coroll. 1.
                <lb/>
              22. lib. @.</note>
            ABD, ad figuram, Φ Σ Λ, duplam rationem habebit eius, quam
              <lb/>
            habet, BE, ad, Σ 2, vel, ID, ad, 3 Λ, .</s>
            <s xml:id="echoid-s3105" xml:space="preserve">i. </s>
            <s xml:id="echoid-s3106" xml:space="preserve">erunt iſtæ ſimiles figuræ
              <lb/>
            in dupla ratione linearum, vel laterum homologorum, BE, Σ 2, vel,
              <lb/>
            ID, 3 Λ, vel aliarum quarumcumque homologarum præfatis regu-
              <lb/>
            lis æquidiſtantium, quod oſtendere opus erat.</s>
            <s xml:id="echoid-s3107" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div333" type="section" level="1" n="204">
          <head xml:id="echoid-head219" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s3108" xml:space="preserve">_E_T quia dictæ figuræ planæ ſimiles oſtenſæ ſunt eſſe in dupla ratione
              <lb/>
            linearum, vel laterum homologorum, quæ æquidiſtant regulis vt-
              <lb/>
            cunque ſumptis, patet eaſdem eſſe in dupla ratione quarumuis homolo-
              <lb/>
            garum, & </s>
            <s xml:id="echoid-s3109" xml:space="preserve">duas quaſdam homologas ſumptas cum quibuſdam regulis, eſſe
              <lb/>
            inter ſe, vt alias quaslibet duas homologas, cum alijs quibuſuis regulis, eſſe
              <lb/>
            aſſumptas, quod etiam in Corollario Lemmatis 48. </s>
            <s xml:id="echoid-s3110" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s3111" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3112" xml:space="preserve">aliunde dedu-
              <lb/>
            ctum eſt.</s>
            <s xml:id="echoid-s3113" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div334" type="section" level="1" n="205">
          <head xml:id="echoid-head220" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s3114" xml:space="preserve">_V_Niuersè inſuper manifeſtum eſt, ſitres rectæ lineæ deinceps pro-
              <lb/>
            portionales fuerint, vt prima ad tertiam, ita eſſe figuram planam
              <lb/>
            deſcriptam à prima ad eam, quæ à ſecunda de ſcribitur; </s>
            <s xml:id="echoid-s3115" xml:space="preserve">& </s>
            <s xml:id="echoid-s3116" xml:space="preserve">huius conuer-
              <lb/>
            ſum, dummodò deſcribentes ſint ſimilium deſcriptarum figurarum lineæ,
              <lb/>
            ſiue latera homologa.</s>
            <s xml:id="echoid-s3117" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div335" type="section" level="1" n="206">
          <head xml:id="echoid-head221" xml:space="preserve">THEOREMA XVI. PROPOS. XVI.</head>
          <p>
            <s xml:id="echoid-s3118" xml:space="preserve">SI quatuor rectæ lineæ proportionales fuerint, prima au-
              <lb/>
            tem, & </s>
            <s xml:id="echoid-s3119" xml:space="preserve">ſecunda ſimiles figuras planas deſcripſerint, & </s>
            <s xml:id="echoid-s3120" xml:space="preserve">
              <lb/>
            tertia, & </s>
            <s xml:id="echoid-s3121" xml:space="preserve">quarta alias figuras planas ſimiles, licet etiam præ-
              <lb/>
            dictis diſſimiles eſſent, ita vt deſcribentes ſint earum lineæ,
              <lb/>
            vel latera homologa, figura primæ ad figuram lecundæ </s>
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