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

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              <pb o="38" file="0058" n="58" rhead="GEOMETRIÆ"/>
            bus, quæ ſunt regulæ homologarum earundem, poſſunt reperiri duæ in-
              <lb/>
            cidentes earundem, quarum altera ſit iam ducta; </s>
            <s xml:id="echoid-s1014" xml:space="preserve">veluti, acta, HP, vt-
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            cumque inuentæ ſunt duæ incidentes, KN, HP, quarum altera fuit,
              <lb/>
            HP. </s>
            <s xml:id="echoid-s1015" xml:space="preserve">Et quia bomologarum in eaſdem incidentes productarum, & </s>
            <s xml:id="echoid-s1016" xml:space="preserve">ad
              <lb/>
            eas terminatarum, portiones, eodem ordine ſumpcæ, ſunt proportiona-
              <lb/>
            les, ſunt enim, vt ipſæ incidentes, ideò per homologarum productarum,
              <lb/>
            talia extremaſemper tranſeunt aliquæ incidentes.</s>
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        <div xml:id="echoid-div123" type="section" level="1" n="86">
          <head xml:id="echoid-head97" xml:space="preserve">THEOREMA XVII. PROPOS. XX.</head>
          <p>
            <s xml:id="echoid-s1018" xml:space="preserve">SI conicus ſecetur quomodocumq; </s>
            <s xml:id="echoid-s1019" xml:space="preserve">planis parallelis, cum
              <lb/>
            omnibus eiuſdem lateribus coincidentibus, conceptæ
              <lb/>
            in ipſo figuræ erunt inter ſe ſimiles, & </s>
            <s xml:id="echoid-s1020" xml:space="preserve">ſimiliter poſitæ.</s>
            <s xml:id="echoid-s1021" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1022" xml:space="preserve">Sit conicus, cuius baſis, FHG, ver-
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              <figure xlink:label="fig-0058-01" xlink:href="fig-0058-01a" number="29">
                <image file="0058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0058-01"/>
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            tex, A, ſecetur autein vtcumque planis
              <lb/>
            parallelis, quæ cum omnibus eiuſdem la-
              <lb/>
            teribus coincidant, & </s>
            <s xml:id="echoid-s1023" xml:space="preserve">ſint conceptæ in
              <lb/>
            ipſo figuræ, DME, BNC. </s>
            <s xml:id="echoid-s1024" xml:space="preserve">Dico has
              <lb/>
            eſſe ſimiles, & </s>
            <s xml:id="echoid-s1025" xml:space="preserve">ſimiliter poſitas: </s>
            <s xml:id="echoid-s1026" xml:space="preserve">Nam
              <lb/>
            quia planum figuræ, DME, coincidit
              <lb/>
            omnibus lateribus conici, AFHG, ideo
              <lb/>
              <note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">17. Huius.</note>
            eſt etiam conicus ipſe, ADME, ſecatur
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            autem plano eius baſi, DME, æquidi-
              <lb/>
              <note position="left" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">Exantec.</note>
            ſtante, eo ſcilicet, quod producit figu-
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            ram, BNC, ergo figura, BNC, erit ſi-
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            milis baſi, DME, & </s>
            <s xml:id="echoid-s1027" xml:space="preserve">eidem ſimiliter po-
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            ſita, quod erat demonſtrandum.</s>
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        <div xml:id="echoid-div125" type="section" level="1" n="87">
          <head xml:id="echoid-head98" xml:space="preserve">THE OREMA XVIII. PROPOS. XXI.</head>
          <p>
            <s xml:id="echoid-s1029" xml:space="preserve">SI quilibet conicus ſecetur plano per verticem, ſiue ab
              <lb/>
            eodem tangatur in plano, nempe in triangulo, veltrian-
              <lb/>
            gulis, ſecetur autem alijs planis vtcumq; </s>
            <s xml:id="echoid-s1030" xml:space="preserve">baſi parallelis, com-
              <lb/>
            munes ſectiones, quæ ab eodem plano ſecante ſiunt in dictis
              <lb/>
            planis baſi parallelis, erunt homologę lineę, vel latera figu-
              <lb/>
            rarum, quæ ab eiſdem æquidiſtantibus planis in eodem co-
              <lb/>
            nico producuntur.</s>
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