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

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        <div xml:id="echoid-div143" type="section" level="1" n="98">
          <p style="it">
            <s xml:id="echoid-s1211" xml:space="preserve">
              <pb o="47" file="0067" n="67" rhead="LIBERI."/>
            in Prop. </s>
            <s xml:id="echoid-s1212" xml:space="preserve">demonſtratum eſt. </s>
            <s xml:id="echoid-s1213" xml:space="preserve">Et vice verſaſi figuræ ſint ſimiles, & </s>
            <s xml:id="echoid-s1214" xml:space="preserve">æqua-
              <lb/>
            les, etiam homologas æquales eſſe, ſi enim inæquales eſſent, etiam ipſæ
              <lb/>
            figuræ inæquales eſſent, quod eſt abſurdum. </s>
            <s xml:id="echoid-s1215" xml:space="preserve">Vlterius autem patet, ſi
              <lb/>
            ſint inuicem ſuperpoſitæ, ita vt ſimiliter ſint conſtitutæ, ac duæ quæuis
              <lb/>
            homologæ inuicem fuerint congruentes, etiam ipſas figuras fore con-
              <lb/>
            gruentes, alioquin ſequerentur abſurda ſuperius demonſtrata, cum quę-
              <lb/>
            uis aliæ homologæ neceſſariò quoque ſint æquales, quæ enim congruerunt
              <lb/>
            ſunt æquales, & </s>
            <s xml:id="echoid-s1216" xml:space="preserve">ſubinde etiam incidentes, & </s>
            <s xml:id="echoid-s1217" xml:space="preserve">quæuis aliæ homologæ in-
              <lb/>
            ter ſe ſunt æquales.</s>
            <s xml:id="echoid-s1218" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div144" type="section" level="1" n="99">
          <head xml:id="echoid-head110" xml:space="preserve">THEOREMA XXIII. PROPOS. XXVI.</head>
          <p>
            <s xml:id="echoid-s1219" xml:space="preserve">SI duobus parallelis quibuſcumque planis inciderint duo
              <lb/>
            plana ſe ſe interſecantia, primum nempè, & </s>
            <s xml:id="echoid-s1220" xml:space="preserve">ſecundum;
              <lb/>
            </s>
            <s xml:id="echoid-s1221" xml:space="preserve">fuerint autem alia duo parallela quæcumque plana, quibus
              <lb/>
            pariter incidant duo alia plana ſe ſe diuidentia, primum ſi-
              <lb/>
            militer, & </s>
            <s xml:id="echoid-s1222" xml:space="preserve">ſecundum: </s>
            <s xml:id="echoid-s1223" xml:space="preserve">Eorum autem cum paralielis planis
              <lb/>
            communes ſectiones angulos ęquales comprehenderint, nec-
              <lb/>
            non primorum, ac ſecundorum planorum mutuæ ſectiones
              <lb/>
            ad communes ſectiones primorum planorum cum planis pa-
              <lb/>
            rallelis effe ct as angulos æquales conſtituerint, ipſa verò pri-
              <lb/>
            ma plana ad plana parallela æquè fuerint ad eandem partem
              <lb/>
            inclinata: </s>
            <s xml:id="echoid-s1224" xml:space="preserve">Eędem communes ſectiones ad communes ſectio-
              <lb/>
            nes ſecundorum planorum cum planis parallelis effe ctas an-
              <lb/>
            gulos pariter conſtituent æquales, necnon ſecunda plana e-
              <lb/>
            runt ad eadem plana parallela æqualiter ad eandem partem
              <lb/>
            inclinata.</s>
            <s xml:id="echoid-s1225" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1226" xml:space="preserve">Sint duo parallela quæcunque plana, BD, HV, quibus incidat
              <lb/>
            duo plana, HA, primum, AV, ſecundum ſe ſe ſecantia in recta,
              <lb/>
            AG. </s>
            <s xml:id="echoid-s1227" xml:space="preserve">Sint nunc alia duo plana quęcunq; </s>
            <s xml:id="echoid-s1228" xml:space="preserve">parallela, LQ, & </s>
            <s xml:id="echoid-s1229" xml:space="preserve">Λ, qui-
              <lb/>
            bus pariter incidant alia duo plana, LY, primum, &</s>
            <s xml:id="echoid-s1230" xml:space="preserve">, Κ Λ, ſecun-
              <lb/>
            dum, ſe ſe pariter ſecantia in recta, KY, communes vero ſectiones,
              <lb/>
            BA, AD; </s>
            <s xml:id="echoid-s1231" xml:space="preserve">LK, KQ, incidentium planorum cum planis paralle-
              <lb/>
            lis contineant angulos æquales, ſit nempè, BAD, angulus æqua-
              <lb/>
            lis angulo, LKQ, (erit. </s>
            <s xml:id="echoid-s1232" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1233" xml:space="preserve">&</s>
            <s xml:id="echoid-s1234" xml:space="preserve">, HGV, ęqualis ipſi, & </s>
            <s xml:id="echoid-s1235" xml:space="preserve">Υ Λ,) ſimili-
              <lb/>
              <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">10. Vnde.
                <lb/>
              cimi El.</note>
            ter ipſæ, AG, KY, cum ipſis, GH, Y &</s>
            <s xml:id="echoid-s1236" xml:space="preserve">, angulos conſtituant æ-
              <lb/>
            quales, & </s>
            <s xml:id="echoid-s1237" xml:space="preserve">prima plana, BG, LY, ad plana parallela, BD, HV;
              <lb/>
            </s>
            <s xml:id="echoid-s1238" xml:space="preserve">LQ, & </s>
            <s xml:id="echoid-s1239" xml:space="preserve">Λ, ſint æquè ad eandem partem inclinata. </s>
            <s xml:id="echoid-s1240" xml:space="preserve">Dico angulos,
              <lb/>
            AGV, Κ Υ Λ, ęquales eſſe, necnonſecunda plana, AV, Κ Λ, </s>
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