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

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          <p>
            <s xml:id="echoid-s1614" xml:space="preserve">
              <pb o="62" file="0082" n="82" rhead="GEOMETRIÆ"/>
            punctis, P, O, occurrentes, ductis autem duobus planis quomodo-
              <lb/>
            cumque baſibus parallelis, & </s>
            <s xml:id="echoid-s1615" xml:space="preserve">ſecantibus altitudines, FC, PO, ſimi-
              <lb/>
            liter ad eandem partem in punctis, Λ Γ, eadem ſecent latera homo-
              <lb/>
            loga ex. </s>
            <s xml:id="echoid-s1616" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s1617" xml:space="preserve">IH, QS, in punctis, Π Z. </s>
            <s xml:id="echoid-s1618" xml:space="preserve">Dico in eiſdem ſecari ſimi-
              <lb/>
            liter ad eandem partem. </s>
            <s xml:id="echoid-s1619" xml:space="preserve">Producantur ergo, HI, SQ, hinc inde,
              <lb/>
            ita vt (niſi hocipſis contingat abſque eo, quod producantur) ad pla-
              <lb/>
            na baſium, DAB, KMN, & </s>
            <s xml:id="echoid-s1620" xml:space="preserve">eiſdem æquidiſtantia plana per ver-
              <lb/>
            tices, F, P, ducta, terminentur, vt in punctis, L, T, G, R, à pun-
              <lb/>
            ctis verò, G, R, demittantur ad plana dictarum baſium perpendicu-
              <lb/>
            lares, GE, RX, illis incidentes in, E, X, & </s>
            <s xml:id="echoid-s1621" xml:space="preserve">iungantur, L, E, TX.
              <lb/>
            </s>
            <s xml:id="echoid-s1622" xml:space="preserve">Sìmiliter à verticibus, F, P, ad puncta baſium, B, N, ducantur, F
              <lb/>
            B, PN, & </s>
            <s xml:id="echoid-s1623" xml:space="preserve">iungantur, BC, NO. </s>
            <s xml:id="echoid-s1624" xml:space="preserve">Quoniam ergo latera homolo-
              <lb/>
            ga, HI, SQ, continent cumhomologis lateribus ſimilium trian-
              <lb/>
            gulorum, AID, MQK, ad eandem partem baſibus, DAB, KM
              <lb/>
            N, inclinatorum (quia, IADB, QMNK, eſſent ſimiles pyrami-
              <lb/>
            des) angulos ęquales, & </s>
            <s xml:id="echoid-s1625" xml:space="preserve">producta incidunt in plana dictarum baſium
              <lb/>
              <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">Ex Lem.
                <lb/>
              5.</note>
            in, L, T, erunt eiſdem æqualiter inclinata, ergo anguli, GLE, R
              <lb/>
              <figure xlink:label="fig-0082-01" xlink:href="fig-0082-01a" number="43">
                <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0082-01"/>
              </figure>
            TX, erunt ęquales,
              <lb/>
            &</s>
            <s xml:id="echoid-s1626" xml:space="preserve">, GEL, RXT,
              <lb/>
            ſunt recti, ergo triã-
              <lb/>
            gula, GLE, RT
              <lb/>
            X, ſimilia erunt, er-
              <lb/>
            go, GL, ad, RT,
              <lb/>
            erit vt, GE, ad, R
              <lb/>
            X, ideſt vt, FC, ad
              <lb/>
            PO. </s>
            <s xml:id="echoid-s1627" xml:space="preserve">Vlterius ſi iun-
              <lb/>
            geremus, FA, FD,
              <lb/>
            PM, PK, fierent
              <lb/>
            ſimiles pyramides,
              <lb/>
            FDAB, PKMN, vnde pateret, FB, PN, eſſe ad plana baſium,
              <lb/>
              <note position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">Ex Lem.
                <lb/>
              4.</note>
            DAB, KMN, ſimiliter inclinata, & </s>
            <s xml:id="echoid-s1628" xml:space="preserve">ſubinde angulos, FBC, P
              <lb/>
            NO, eſſe ęquales, & </s>
            <s xml:id="echoid-s1629" xml:space="preserve">cum ſint recti, FCB, PNO, triangula, FB
              <lb/>
            C, PNO, eſſe æquiangula, & </s>
            <s xml:id="echoid-s1630" xml:space="preserve">vt, FC, ad, PO, ita eſſe, FB, ad,
              <lb/>
            PN, etiam manifeſtum eſſet, ſed vt, FC, ad, PO, ita eſt, GL, ad,
              <lb/>
            RT, & </s>
            <s xml:id="echoid-s1631" xml:space="preserve">vt, FB, ad, PN, ita, BD, ad, NK, & </s>
            <s xml:id="echoid-s1632" xml:space="preserve">ita quodcunque
              <lb/>
            latus in ſolido, FHB, ad latus ſibi homologum in ſolido, PSN,
              <lb/>
            ideſt ita, IH, ad, QS, ergo vt, GL, ad, RT, ita, HI, ad, SQ,
              <lb/>
              <note position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve">19. Quin.
                <lb/>
              Elem.</note>
            & </s>
            <s xml:id="echoid-s1633" xml:space="preserve">ita compoſitum ex reſiduis, LH, IG, ad compoſitum ex reſiduis,
              <lb/>
            TS, QR, ſunt autem, LH, TS, latera homologa ſimilium pyra-
              <lb/>
              <note position="left" xlink:label="note-0082-04" xlink:href="note-0082-04a" xml:space="preserve">Ex Lem.
                <lb/>
              5.</note>
            midum, HLAD, STMK, ergo vt, HA, ad, SM, velvt, HI,
              <lb/>
            ad, SQ, ita, HL, ad, ST, ergo etiam reliqua, IG, ad reliquam,
              <lb/>
            QR, eſt vt, HI, ad, SQ, vel vt altitudo, FC, ad, PO, vel vt, </s>
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