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

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        <div xml:id="echoid-div102" type="section" level="1" n="73">
          <pb o="30" file="0050" n="50" rhead="GEOMETRIÆ"/>
        </div>
        <div xml:id="echoid-div104" type="section" level="1" n="74">
          <head xml:id="echoid-head85" xml:space="preserve">THEOREMA XI. PROPOS. XIV.</head>
          <p>
            <s xml:id="echoid-s842" xml:space="preserve">SI duæ figuræ planæ non exiſtentes in eodem plano fue-
              <lb/>
            rint ſimiles, æquales, & </s>
            <s xml:id="echoid-s843" xml:space="preserve">ſim iliter poſitæ, illæ erunt cu-
              <lb/>
            iuſdam cylindrici oppoſitæ baſes.</s>
            <s xml:id="echoid-s844" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s845" xml:space="preserve">Sint duæ ſimiles figuræ planæ, & </s>
            <s xml:id="echoid-s846" xml:space="preserve">æquales, AQTO, FDNC,
              <lb/>
            non exiſtentes in eodem plano, & </s>
            <s xml:id="echoid-s847" xml:space="preserve">ſimiliter poſitæ. </s>
            <s xml:id="echoid-s848" xml:space="preserve">Dico eas eſſe
              <lb/>
            cuiuſdam cylindrici oppoſitas baſes. </s>
            <s xml:id="echoid-s849" xml:space="preserve">Quoniam enim ſunt ſimiliter
              <lb/>
            poſitæ erunt inter ſe æquidiſtantes, & </s>
            <s xml:id="echoid-s850" xml:space="preserve">earum incidentes pariter inter
              <lb/>
              <note position="left" xlink:label="note-0050-01" xlink:href="note-0050-01a" xml:space="preserve">D. Def. 10</note>
            ſe æquidiſtantes, ducantur oppoſitæ tangentes figuræ, AQTO,
              <lb/>
            quæ ſint, TP, AB, & </s>
            <s xml:id="echoid-s851" xml:space="preserve">figuræ, FDNC, quæ ſint, FH, NL,
              <lb/>
              <note position="left" xlink:label="note-0050-02" xlink:href="note-0050-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              huius.</note>
            quæque ſint regulæ homologarum earumdem ſimilium figurarum,
              <lb/>
            & </s>
            <s xml:id="echoid-s852" xml:space="preserve">ſint incidentes earum, & </s>
            <s xml:id="echoid-s853" xml:space="preserve">ſimilium figurarum ipſę, BP, HL, quę
              <lb/>
            erunt parallelæ, & </s>
            <s xml:id="echoid-s854" xml:space="preserve">quia ſunt incidentes ſimilium figurarum, AT,
              <lb/>
              <note position="left" xlink:label="note-0050-03" xlink:href="note-0050-03a" xml:space="preserve">D. Def. 10.</note>
            FN, & </s>
            <s xml:id="echoid-s855" xml:space="preserve">oppoſitarum tangentium iam ductarum, ideò ad eaſdem ex
              <lb/>
            eadem parte efficient angulos æquales, igitur angulus, BPT, erit
              <lb/>
              <note position="left" xlink:label="note-0050-04" xlink:href="note-0050-04a" xml:space="preserve">B. Def. 10.</note>
            æqualis angulo, HLN, & </s>
            <s xml:id="echoid-s856" xml:space="preserve">ideò etiam, PT, ęquidiſtabitipſi, LN,
              <lb/>
              <note position="left" xlink:label="note-0050-05" xlink:href="note-0050-05a" xml:space="preserve">Excõuer.
                <lb/>
              ſa 10. Vn-
                <lb/>
              dec. Ele.</note>
              <figure xlink:label="fig-0050-01" xlink:href="fig-0050-01a" number="23">
                <image file="0050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0050-01"/>
              </figure>
            &</s>
            <s xml:id="echoid-s857" xml:space="preserve">, BA, ipſi, FH, iungantur, BH, PL,
              <lb/>
            quoniam ergo, AT, FN, ſunt ſimiles,
              <lb/>
            & </s>
            <s xml:id="echoid-s858" xml:space="preserve">æquales, earum homologæ erunt pa-
              <lb/>
            riter æquales, ſunt autem incidentes, BP,
              <lb/>
            HL, vt ipſæ homologæ, vt colligitur in
              <lb/>
            Coroll. </s>
            <s xml:id="echoid-s859" xml:space="preserve">1. </s>
            <s xml:id="echoid-s860" xml:space="preserve">ſequentis Propoſit. </s>
            <s xml:id="echoid-s861" xml:space="preserve">22. </s>
            <s xml:id="echoid-s862" xml:space="preserve">indepen-
              <lb/>
            denter ab hac Propoſitione, ergo, BP, H
              <lb/>
            L, erunt æquales, & </s>
            <s xml:id="echoid-s863" xml:space="preserve">ſunt æquidiſtantes,
              <lb/>
            ergo eas iungentes, BH, PL, erunt ęqua-
              <lb/>
            les, & </s>
            <s xml:id="echoid-s864" xml:space="preserve">æquidiſtantes. </s>
            <s xml:id="echoid-s865" xml:space="preserve">Diuidantur ipſę in-
              <lb/>
            cidentes, BP, HL, ſimiliter ad eandem
              <lb/>
              <note position="left" xlink:label="note-0050-06" xlink:href="note-0050-06a" xml:space="preserve">10. Sexti
                <lb/>
              Elem.</note>
            partem in punctis, E, M, G, K, & </s>
            <s xml:id="echoid-s866" xml:space="preserve">iun-
              <lb/>
            gantur, EG, MK, erit ergo, MP, ęqua-
              <lb/>
            lis ipſi, KL, &</s>
            <s xml:id="echoid-s867" xml:space="preserve">, EM, ipſi, GK, &</s>
            <s xml:id="echoid-s868" xml:space="preserve">, BE,
              <lb/>
            ipſi, HG, nam quia, BP, HL, ſimiliter
              <lb/>
            diuiduntur in his punctis, earum partes ſunt, vt ipſæ integræ, illæ
              <lb/>
            verò ſunt æquales, & </s>
            <s xml:id="echoid-s869" xml:space="preserve">ideò etiam homologæ partes ſunt æquales, & </s>
            <s xml:id="echoid-s870" xml:space="preserve">
              <lb/>
            eas iungentes, PL, MK, EG, BH, erunt æquales, & </s>
            <s xml:id="echoid-s871" xml:space="preserve">æquidiſtan-
              <lb/>
              <note position="left" xlink:label="note-0050-07" xlink:href="note-0050-07a" xml:space="preserve">15. Vnde-
                <lb/>
              cimi El.</note>
            tes, ducatur à puncto, K, verſus figuram, FN, ipſa, KR, æquidi-
              <lb/>
            ſtans ipſi, NL, quia ergo, MK, æquidiſtat ipſi, PL, &</s>
            <s xml:id="echoid-s872" xml:space="preserve">, RK,
              <lb/>
            ipſi, NL, planum per, MK, KR, tranſiens æquidiſtat tranſeunti
              <lb/>
            per, PL, LN, ſecet hoc planum tranſiens per, MK, KR, pla-
              <lb/>
            num, AT, productum, in recta, SM, & </s>
            <s xml:id="echoid-s873" xml:space="preserve">iungantur, SR, VI, </s>
          </p>
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