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

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            <s xml:id="echoid-s1240" xml:space="preserve">
              <pb o="48" file="0068" n="68" rhead="GEOMETRIÆ"/>
            eadem parallela plana eſſe æqualiter ad eandem partem inclinata.
              <lb/>
            </s>
            <s xml:id="echoid-s1241" xml:space="preserve">
              <note position="left" xlink:label="note-0068-01" xlink:href="note-0068-01a" xml:space="preserve">Defin. 3.
                <lb/>
              Vndec. El.</note>
            Siigitur, AG, KY, eſſent dictis planis parallelis perpendiculares,
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              <note position="left" xlink:label="note-0068-02" xlink:href="note-0068-02a" xml:space="preserve">18. Vnde-
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              cimi El.</note>
            manifeſtum eſt, quod anguli, AGV, Κ Υ Λ, eſſent æquales, ideſt
              <lb/>
            recti, & </s>
            <s xml:id="echoid-s1242" xml:space="preserve">plana, AV, Κ Λ, eiſdem planis parallelis erecta; </s>
            <s xml:id="echoid-s1243" xml:space="preserve">ſed non
              <lb/>
            ſint perpendiculares, & </s>
            <s xml:id="echoid-s1244" xml:space="preserve">à punctis, A, K, demittanturipſę, AE, K
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              <figure xlink:label="fig-0068-01" xlink:href="fig-0068-01a" number="34">
                <image file="0068-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0068-01"/>
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            T, quæ eiſdem
              <lb/>
            ſint perpẽdicu-
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            lares, incidant
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            autem ſubiectis
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            planis in pun-
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            ctis, E, T; </s>
            <s xml:id="echoid-s1245" xml:space="preserve">de-
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            inde à puncto,
              <lb/>
            A, ad, HG, V
              <lb/>
            G, productas,
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            ducantur per-
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            pendiculares, A
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            F, quidem ipſi;
              <lb/>
            </s>
            <s xml:id="echoid-s1246" xml:space="preserve">HG, & </s>
            <s xml:id="echoid-s1247" xml:space="preserve">AP,
              <lb/>
              <note position="left" xlink:label="note-0068-03" xlink:href="note-0068-03a" xml:space="preserve">Vide di-
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              cta lib. 7.
                <lb/>
              annot.</note>
            ipſi, VG, inci-
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            dentes in pun-
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              <note position="left" xlink:label="note-0068-04" xlink:href="note-0068-04a" xml:space="preserve">Prop. 3.</note>
            ctis, V, P, niſi
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            fortè, AG, eſſet
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            alteri earũ per-
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            pendicularis, vt
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            contingere po-
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            teſt, & </s>
            <s xml:id="echoid-s1248" xml:space="preserve">iungan-
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            tur, EP, EG,
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            EF; </s>
            <s xml:id="echoid-s1249" xml:space="preserve">ſimiliter in
              <lb/>
            alia figura ca-
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            dant à puncto,
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            K, perpendicu-
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            lariter ſuper ip-
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            ſas, & </s>
            <s xml:id="echoid-s1250" xml:space="preserve">Y, Λ Υ,
              <lb/>
            productas, ſi o-
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            pus ſit, ipſæ, K
              <lb/>
            Z, KX, & </s>
            <s xml:id="echoid-s1251" xml:space="preserve">iun-
              <lb/>
              <note position="left" xlink:label="note-0068-05" xlink:href="note-0068-05a" xml:space="preserve">47. Primi
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              Elem.</note>
            gantur ſimiliter, TX, TY, &</s>
            <s xml:id="echoid-s1252" xml:space="preserve">, TZ. </s>
            <s xml:id="echoid-s1253" xml:space="preserve">Quoniam ergo anguli, AF
              <lb/>
            G, KZY, ſunt recti, ideò quadratum, AG, erit æquales duobus
              <lb/>
            quadratis, AF, FG, ſicut quadratum, KY, æquale duobus, KZ,
              <lb/>
            ZY, eſt autem etiam quadratum, AF, ęquale duobus quadratis, A
              <lb/>
            E, EF, quia angulus, AEF. </s>
            <s xml:id="echoid-s1254" xml:space="preserve">rectus eſt, & </s>
            <s xml:id="echoid-s1255" xml:space="preserve">quadratum, KZ, pari-
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            teræquale quadratis, KT, TZ, ergo quadratum, AG, ideſt </s>
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