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

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              <pb o="59" file="0079" n="79" rhead="LIBER I."/>
            lelas, ac (ſi ſint inclinatę, incidantque ipſis in punctis, C, N, iun-
              <lb/>
            ganturque, CB, CD, NP, NO,) pyramides, ACDB, HNO
              <lb/>
            P, ſimiles eſſe. </s>
            <s xml:id="echoid-s1548" xml:space="preserve">Sumatur ergo in, AD, etiam quantumuis protenſa
              <lb/>
            vbicumq; </s>
            <s xml:id="echoid-s1549" xml:space="preserve">punctum, F, & </s>
            <s xml:id="echoid-s1550" xml:space="preserve">accipiatur in, HO, producta, ſi opus ſit,
              <lb/>
            HL, ęqualis, AF, & </s>
            <s xml:id="echoid-s1551" xml:space="preserve">indefinitè extenſis lineis, AC, AB, HN, H
              <lb/>
              <note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">Vidi dicta
                <lb/>
              lib.7. An-
                <lb/>
              not. Pro-
                <lb/>
              poſ.3.</note>
            P, ducantur in planis, FAC, FAG, LHN, LHP, à punctis, F,
              <lb/>
              <figure xlink:label="fig-0079-01" xlink:href="fig-0079-01a" number="41">
                <image file="0079-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0079-01"/>
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            L, ipſis, AF, HL, per-
              <lb/>
            pendiculares, FE, FG,
              <lb/>
            LI, LM, occurrentes
              <lb/>
            ipſis, AE, AG, HI, H
              <lb/>
            M, in punctis, E, G, I,
              <lb/>
            M, & </s>
            <s xml:id="echoid-s1552" xml:space="preserve">iungantur, EG,
              <lb/>
            IM. </s>
            <s xml:id="echoid-s1553" xml:space="preserve">Quoniam ergo duo
              <lb/>
            anguli, AFG, HLM,
              <lb/>
            recti, &</s>
            <s xml:id="echoid-s1554" xml:space="preserve">, FAG, LH
              <lb/>
            M, ſunt æquales, & </s>
            <s xml:id="echoid-s1555" xml:space="preserve">la-
              <lb/>
            tera, AF, HL, ęqua-
              <lb/>
            lia, erunt etiam, FG,
              <lb/>
              <note position="right" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve">26.Primi
                <lb/>
              Elem.</note>
            LM, GA, MH, ęqua-
              <lb/>
            lia; </s>
            <s xml:id="echoid-s1556" xml:space="preserve">eodem modo oſten-
              <lb/>
            demus æqualia eſſe, F
              <lb/>
            E, LI, EA, IH, vnde cum ſint ęquales, EA, IH, AG, HM, & </s>
            <s xml:id="echoid-s1557" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0079-03" xlink:href="note-0079-03a" xml:space="preserve">4. Primi
                <lb/>
              Elem.</note>
            anguli, EAG, IHM, pariter ęquales, etiam baſes, EG, IM, æ-
              <lb/>
            quales erunt, & </s>
            <s xml:id="echoid-s1558" xml:space="preserve">pyramides, AEFG, HILM, ſimiles, & </s>
            <s xml:id="echoid-s1559" xml:space="preserve">ęquales
              <lb/>
            ad inuicem exiſtent. </s>
            <s xml:id="echoid-s1560" xml:space="preserve">Suſpendatur nunc pyramis, AEFG, & </s>
            <s xml:id="echoid-s1561" xml:space="preserve">pona-
              <lb/>
              <note position="right" xlink:label="note-0079-04" xlink:href="note-0079-04a" xml:space="preserve">Defin. 10.
                <lb/>
              vndec. El.</note>
            tur punctum, F, in, L, demittaturque, FG, ſuper, LM, cui con-
              <lb/>
            gruet, ſed & </s>
            <s xml:id="echoid-s1562" xml:space="preserve">triangulo, EFG, cadente ſuper, ILM, punctum, F,
              <lb/>
            erit in, I, ac latus, AF, in, HL, alioquin duę eidem plano, ILM,
              <lb/>
              <note position="right" xlink:label="note-0079-05" xlink:href="note-0079-05a" xml:space="preserve">7. Pri. El.</note>
            perpendiculares eſſent eductæ ab eodem puncto, L, quod eſt abſur-
              <lb/>
            dum (ſunt autem, AF, HL, perpendiculares planis, EFG, ILM,
              <lb/>
              <note position="right" xlink:label="note-0079-06" xlink:href="note-0079-06a" xml:space="preserve">13. Vnd.
                <lb/>
              Elem.</note>
            hoc eſt ſolo plano, ILM, cum ſuperponuntur, ex eo, quod duabus,
              <lb/>
            IL, IM, ſint perpendiculares in puncto, L,) ergo, FA, cadet ſu-
              <lb/>
            per, LH, & </s>
            <s xml:id="echoid-s1563" xml:space="preserve">punctum, A, in, H, vnde etiam, EA, cadet in, IH,
              <lb/>
              <note position="right" xlink:label="note-0079-07" xlink:href="note-0079-07a" xml:space="preserve">4. Vnd. El.</note>
            &</s>
            <s xml:id="echoid-s1564" xml:space="preserve">, AG, in, HM, punctum, B, verò eſto, quod ſit in, T, D, in,
              <lb/>
            S, &</s>
            <s xml:id="echoid-s1565" xml:space="preserve">, C, in, V, erit et@am, DB, congruens ipſi, ST, CD, VS,
              <lb/>
            &</s>
            <s xml:id="echoid-s1566" xml:space="preserve">, CB, ipſi, VT, & </s>
            <s xml:id="echoid-s1567" xml:space="preserve">quia angulus, ABD, æquatur ipſi, HPO,
              <lb/>
            ABD, autem eſt etiam æqualis, HTS, ergo, HTS, HPO, ſunt
              <lb/>
            æquales, &</s>
            <s xml:id="echoid-s1568" xml:space="preserve">, ST, parallela, OP. </s>
            <s xml:id="echoid-s1569" xml:space="preserve">Dico etiam triangulum, VST,
              <lb/>
              <note position="right" xlink:label="note-0079-08" xlink:href="note-0079-08a" xml:space="preserve">4. Primi
                <lb/>
              Elem.</note>
            æquidiſtare ipſi, NOP, ſi .</s>
            <s xml:id="echoid-s1570" xml:space="preserve">n. </s>
            <s xml:id="echoid-s1571" xml:space="preserve">hoc non ſit, quia, ST, eſt parallela
              <lb/>
            ipſi, OP, poterit per, ST, duci planum ipſi, NOP, parallelum,
              <lb/>
            ducatur, & </s>
            <s xml:id="echoid-s1572" xml:space="preserve">producat in pyramide triangulum, KST, acta autem à
              <lb/>
            puncto, H, ipſi, OP, perpendiculari, quę ſit, HQ, ſecante, </s>
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