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

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        <div xml:id="echoid-div219" type="section" level="1" n="142">
          <p>
            <s xml:id="echoid-s2268" xml:space="preserve">
              <pb o="92" file="0112" n="112" rhead="GEOMETRIÆ"/>
            &</s>
            <s xml:id="echoid-s2269" xml:space="preserve">. Modòetiam ſi ad illa puncta non terminentur dico tamen, ls,
              <lb/>
            ad, E4, eſſe vt, 47, ad, ℟ &</s>
            <s xml:id="echoid-s2270" xml:space="preserve">, etenim, ls, ad, 47, eſt vt, AC,
              <lb/>
            ad, FK, ideſt vt, LO, ad, uY, vel vt, E4, ad, ℟ &</s>
            <s xml:id="echoid-s2271" xml:space="preserve">, vt probatum
              <lb/>
            eſt, ergo permutando, ls, ad, E4, erit vt, 47, ad, ℟ &</s>
            <s xml:id="echoid-s2272" xml:space="preserve">, quod o-
              <lb/>
            ſtendere oportebat.</s>
            <s xml:id="echoid-s2273" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div221" type="section" level="1" n="143">
          <head xml:id="echoid-head154" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2274" xml:space="preserve">_E_T quoniam probatum eſt, l s, ad, 4 7, eſſe vt, E 4, ad, ℟ &</s>
            <s xml:id="echoid-s2275" xml:space="preserve">, ſeu
              <lb/>
            vt, LO, ad, u γ, vt autem, LO, ad, u γ, ita duæ homologæ, QP,
              <lb/>
            ad, 83, ideò duæ homologæ, ls, 47, ſunt inter ſe, vt duæ homologæ,
              <lb/>
            QP, 8R, & </s>
            <s xml:id="echoid-s2276" xml:space="preserve">cum oppoſitæ tangentes, DL, dO, pu, g γ, ductæ ſint vt-
              <lb/>
            cumque, licet ad eundem angulum cx eadem parte cum ipſis, E4, ℟ &</s>
            <s xml:id="echoid-s2277" xml:space="preserve">,
              <lb/>
            ideò duæhomologæ, ls, 4 7, erunt vt quæcumq; </s>
            <s xml:id="echoid-s2278" xml:space="preserve">aliæ duæ homologæ qui-
              <lb/>
            buſuis regulis aſſimptæ, vel vt ecrum incidentes, immo & </s>
            <s xml:id="echoid-s2279" xml:space="preserve">ipſæ inciden-
              <lb/>
            tes, crunt inter ſe, vt quæuis aliæ duæ incidentes, oſtenſum. </s>
            <s xml:id="echoid-s2280" xml:space="preserve">n. </s>
            <s xml:id="echoid-s2281" xml:space="preserve">eſt, A
              <lb/>
            C, ad, FK, eſſe vt, LO, ad, u γ.</s>
            <s xml:id="echoid-s2282" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div222" type="section" level="1" n="144">
          <head xml:id="echoid-head155" xml:space="preserve">THEOREMA XLV. PROPOS. XLVIII.</head>
          <p>
            <s xml:id="echoid-s2283" xml:space="preserve">SI ſint duæ ſimiles figuræ planæ, quarum ſint ductæ oppo-
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            ſitæ tangentes, quæ ſunt homologarum earundem regu-
              <lb/>
            læ, per quas extendantur duo plana vtcumque inuicem pa-
              <lb/>
            rallela ęquè ad eandem partem ijſdem inclinata, deinde ſum-
              <lb/>
            ptis duabus quibuslibet homologis illæ deſcribere intelli-
              <lb/>
            gantur figuras planas ſimiles, ductis primò planis æquidi-
              <lb/>
            ſtantes, ita vt ſint ſimiliter deſcriptæ, & </s>
            <s xml:id="echoid-s2284" xml:space="preserve">deſcribentes earum
              <lb/>
            lineæ, vel latera homologa, idem autem contingat cæteris
              <lb/>
            homologis, etiam ſi omnes figuræ deſcriptæ ſeorſim in vna-
              <lb/>
            quaque propoſitarum figurarum non eſſent ſimiles; </s>
            <s xml:id="echoid-s2285" xml:space="preserve">Solida,
              <lb/>
            quę ab ijſdem tanguntur oppoſitis planis, in quibus ex traie-
              <lb/>
            ctione planorum præfatis oppoſitis tangentibus æquidiſtan-
              <lb/>
            tium eædem figuræ produci poſſunt, erunt ſimilia, & </s>
            <s xml:id="echoid-s2286" xml:space="preserve">figuræ
              <lb/>
            deſcriptæ eorundem homologæ figuræ, & </s>
            <s xml:id="echoid-s2287" xml:space="preserve">earum regulę ipſa
              <lb/>
            oppoſita tangentia plana, quorum & </s>
            <s xml:id="echoid-s2288" xml:space="preserve">dictorum ſolidorum fi-
              <lb/>
            guræ incidentes erunt primò propoſitæ figuræ.</s>
            <s xml:id="echoid-s2289" xml:space="preserve"/>
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