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

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          <pb o="42" file="0062" n="62" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div130" type="section" level="1" n="90">
          <head xml:id="echoid-head101" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s1114" xml:space="preserve">QVoniam oſtendimus, tum, DC, BR, tum etiam, EF, IO, eſſe vt
              <lb/>
            ipſas incidentes, PH, NK, habetur ſimilium figurar um homo-
              <lb/>
            logas pariter eſſe, vt incidentes earundem, & </s>
            <s xml:id="echoid-s1115" xml:space="preserve">oppoſitarum tangentium,
              <lb/>
            quæ ſunt earundem regulæ, quod in diffinitione aſſumitur contingere
              <lb/>
            tantum ijs, quæ inter circuicum figurarum, & </s>
            <s xml:id="echoid-s1116" xml:space="preserve">ipſas incidentes, eodem
              <lb/>
            ordine ſumptæ, continentur.</s>
            <s xml:id="echoid-s1117" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div131" type="section" level="1" n="91">
          <head xml:id="echoid-head102" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s1118" xml:space="preserve">PAtet etiam ex hac, & </s>
            <s xml:id="echoid-s1119" xml:space="preserve">14. </s>
            <s xml:id="echoid-s1120" xml:space="preserve">huius, omnes ſimiles figuras planas poſſe
              <lb/>
            eſſe alicuius cylindrici, vel fruſti conici, oppoſitas baſes; </s>
            <s xml:id="echoid-s1121" xml:space="preserve">vnde qua
              <lb/>
            pro illis in Coroll. </s>
            <s xml:id="echoid-s1122" xml:space="preserve">2. </s>
            <s xml:id="echoid-s1123" xml:space="preserve">19. </s>
            <s xml:id="echoid-s1124" xml:space="preserve">huius colliguntur, pro omnibus ſimilibus figu-
              <lb/>
            ris planis etiam colligi poſſunt.</s>
            <s xml:id="echoid-s1125" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div132" type="section" level="1" n="92">
          <head xml:id="echoid-head103" xml:space="preserve">LEMMA PRO ANTECED. PROP.</head>
          <p>
            <s xml:id="echoid-s1126" xml:space="preserve">SI in recta linea ſignenturtria puncta, primum, medium, & </s>
            <s xml:id="echoid-s1127" xml:space="preserve">po-
              <lb/>
            ſtremum, à primo autem, & </s>
            <s xml:id="echoid-s1128" xml:space="preserve">medio ducantur ad eandem par-
              <lb/>
            tem duę inuicem parallelę ita ſe habentes, vt educta à primo ad edu-
              <lb/>
            ctam à ſecundo, ſit veluti recta inter primum, & </s>
            <s xml:id="echoid-s1129" xml:space="preserve">poſtremum pun-
              <lb/>
            ctum poſita, ad eam, quę inter medium, & </s>
            <s xml:id="echoid-s1130" xml:space="preserve">idem poſtremum ſita eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s1131" xml:space="preserve">Extrema puncta parallelarum, quę non ſunt in propoſita linea, & </s>
            <s xml:id="echoid-s1132" xml:space="preserve">
              <lb/>
            illius poſtremum, eruntin recta linea.</s>
            <s xml:id="echoid-s1133" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1134" xml:space="preserve">Sit propoſita recta, AC, in qua ſignatis vt-
              <lb/>
              <figure xlink:label="fig-0062-01" xlink:href="fig-0062-01a" number="31">
                <image file="0062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0062-01"/>
              </figure>
            cumque tribus punctis, C, primo, B, medio,
              <lb/>
            &</s>
            <s xml:id="echoid-s1135" xml:space="preserve">, A, poſtremo, à punctis, C, B, educantur
              <lb/>
            ad eandem partem duę inuicem parallelę, quę
              <lb/>
            ſint, CE, BD, ita ſe habentes, vt, CE, ad,
              <lb/>
            BD, ſit, vt, CA, ad, AB. </s>
            <s xml:id="echoid-s1136" xml:space="preserve">Dico puncta,
              <lb/>
            A, D, E, eſſe in recta linea, ſi enim (iuncta,
              <lb/>
            ED,) ipſa, ED, producta non tranſit per,
              <lb/>
            A, tranſibit ſupra, vel infra, A, ſecans, CA,
              <lb/>
            (nam, BD, eſt minor ipſa, CE, vt eſt, AB,
              <lb/>
            minor, AC,) tranſeat, vt per, M, quia igi-
              <lb/>
            tur, EDM, eſt recta erit, MCE, triangu-
              <lb/>
            lus, in quo lateri, CE, ducitur parallela, B
              <lb/>
            D, ergo trianguli, ECM, DBM, erunt æ-
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">4. Sexti
                <lb/>
              Elem.</note>
            quianguli, & </s>
            <s xml:id="echoid-s1137" xml:space="preserve">circa æquales angulos latera proportionalia, ergo, per-
              <lb/>
            mutando, CE, ad, BD, erit vt, CM, ad, MB, eſt autem vt, </s>
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