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

Table of contents

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[81.] THEOREMA XV. PROPOS. XVIII.
Page: 54 (34)
[82.] COROLLARIVM.
Page: 55 (35)
[83.] THEOREMA XVI. PROPOS. XIX.
Page: 55 (35)
[84.] COROLLARIVMI.
Page: 57 (37)
[85.] COROLLARIVM II.
Page: 57 (37)
[86.] THEOREMA XVII. PROPOS. XX.
Page: 58 (38)
[87.] THE OREMA XVIII. PROPOS. XXI.
Page: 58 (38)
[88.] COROLLARIVM.
Page: 59 (39)
[89.] THEOREMA XIX. PROPOS. XXII.
Page: 60 (40)
[90.] COROLLARIVM I.
Page: 62 (42)
[91.] COROLLARIVM II.
Page: 62 (42)
[92.] LEMMA PRO ANTECED. PROP.
Page: 62 (42)
[93.] THEOREMA XX. PROPOS. XXIII.
Page: 63 (43)
[94.] COROLLARIVM.
Page: 63 (43)
[95.] THEOREMA XXI. PROPOS. XXIV.
Page: 63 (43)
[96.] COROLLARIVM.
Page: 65 (45)
[97.] THEOREMA XXII. PROPOS. XXV.
Page: 65 (45)
[98.] COROLLARIVM.
Page: 66 (46)
[99.] THEOREMA XXIII. PROPOS. XXVI.
Page: 67 (47)
[100.] THEOREMA XXIV. PROPOS XXVII.
Page: 69 (49)
[101.] COROLLARIVM.
Page: 72 (52)
[102.] THEOREMA XXV. PROPOS. XXVIII.
Page: 72 (52)
[103.] DEFINITIO.
Page: 72 (52)
[104.] SCHOLIV M.
Page: 73 (53)
[105.] LEMMA I.
Page: 74 (54)
[106.] LEMMA II.
Page: 75 (55)
[107.] LEMMA III.
Page: 76 (56)
[108.] LEMMA IV.
Page: 77 (57)
[109.] COROLLARIVM.
Page: 78 (58)
[110.] LEMMA V.
Page: 78 (58)
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            <s xml:id="echoid-s1032" xml:space="preserve">Videatur figura Propoſ.</s>
            <s xml:id="echoid-s1033" xml:space="preserve">16. </s>
            <s xml:id="echoid-s1034" xml:space="preserve">huius, in qua conicus, ATDF, in-
              <lb/>
            telligatur ſectus plano vtcumque per verticem, A, ducto efficiente
              <lb/>
            triangulum, ſiue triangulos, ADC, AEF, intra, extra autem trian-
              <lb/>
            gulum, ACE, & </s>
            <s xml:id="echoid-s1035" xml:space="preserve">qui ex illis integratur, ADF, ſecetur autem alio
              <lb/>
            plano baſi parallelo, quod in conico producat figuram, VBO, & </s>
            <s xml:id="echoid-s1036" xml:space="preserve">
              <lb/>
            ſint earum, & </s>
            <s xml:id="echoid-s1037" xml:space="preserve">plani per verticem communes ſectiones, BR, DC,
              <lb/>
            IO, EF. </s>
            <s xml:id="echoid-s1038" xml:space="preserve">Dico eaſdem eſſe lineas homologas earundem figurarum,
              <lb/>
            VBO, TDF. </s>
            <s xml:id="echoid-s1039" xml:space="preserve">Intelligantur in baſi ductæ oppoſitæ tangentes, T
              <lb/>
            H, SP, per quas, & </s>
            <s xml:id="echoid-s1040" xml:space="preserve">verticem, A, extendantur plana, quæ pariter
              <lb/>
              <note position="right" xlink:label="note-0059-01" xlink:href="note-0059-01a" xml:space="preserve">Coroll.1.
                <lb/>
              huius.</note>
            tangent conicum, ATDF, ſint autem eorum, & </s>
            <s xml:id="echoid-s1041" xml:space="preserve">plani figurę, VB
              <lb/>
            O, producti communes ſectiones, VK, XN, quas, vt ibi, oſten-
              <lb/>
              <note position="right" xlink:label="note-0059-02" xlink:href="note-0059-02a" xml:space="preserve">18. Huius.</note>
            demus eſſe oppoſitas tangentes ipſius, VBO, reſpectu, BO, ſum-
              <lb/>
            ptas, accipiatur deinde in, TH, vtcumq; </s>
            <s xml:id="echoid-s1042" xml:space="preserve">punctum, H, à quo vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s1043" xml:space="preserve">ad aliam oppoſitam tangentem, SP, ducatur vtcumque, HP, & </s>
            <s xml:id="echoid-s1044" xml:space="preserve">
              <lb/>
            peripſam, & </s>
            <s xml:id="echoid-s1045" xml:space="preserve">punctum, A, extendatur planum, quod ſecet tangen-
              <lb/>
            tia plana in rectis, AH, AP, & </s>
            <s xml:id="echoid-s1046" xml:space="preserve">planum parallelarum, VK, XN,
              <lb/>
            in recta, KN, erunt ergo ipſæ, KN, HP, parallelæ, extendatur
              <lb/>
            planum trianguli, ADF, ita vt ſecet triangulum, APH, in recta,
              <lb/>
            AG, & </s>
            <s xml:id="echoid-s1047" xml:space="preserve">planum figuræ, TDF, productum, ſi opus ſit, in recta, D
              <lb/>
            G, Eodem modo igitur, quo vti ſumus in Propoſ. </s>
            <s xml:id="echoid-s1048" xml:space="preserve">19. </s>
            <s xml:id="echoid-s1049" xml:space="preserve">quia, KN,
              <lb/>
            HP, ſunt parallelæ, oſtendemus ipſas, KN, HP, eſſe ab ipſis, B
              <lb/>
            M, DG, (quę ſunt communes ſectiones trianguli, ADF, & </s>
            <s xml:id="echoid-s1050" xml:space="preserve">ęqui-
              <lb/>
            diſtantium planorum, VBO, TDF, & </s>
            <s xml:id="echoid-s1051" xml:space="preserve">ideò ſunt parallelæ) ſimi-
              <lb/>
            liter diuiſas, & </s>
            <s xml:id="echoid-s1052" xml:space="preserve">ad eandem partem in punctis, M, G, vnde, vt ibi
              <lb/>
            oſtendemus figuras, VBO, TDF, eſſe ſimiles, & </s>
            <s xml:id="echoid-s1053" xml:space="preserve">earum, & </s>
            <s xml:id="echoid-s1054" xml:space="preserve">tan-
              <lb/>
            gentium oppoſitarum, XN, VK; </s>
            <s xml:id="echoid-s1055" xml:space="preserve">SP, TH, incidentes eſſe ipſas,
              <lb/>
            KN, HP, & </s>
            <s xml:id="echoid-s1056" xml:space="preserve">tangentes eſſe regulas homologarum earundem, qua-
              <lb/>
            rum duæ ſunt ipſæ, BRIO, DCEF, coniunctæ, ſiue ipſæ, BR,
              <lb/>
            DC; </s>
            <s xml:id="echoid-s1057" xml:space="preserve">IO, EF. </s>
            <s xml:id="echoid-s1058" xml:space="preserve">Eodem modo, ſi propoſitus conicus fuiſſet, cuius
              <lb/>
            vertex, A, baſis altera figurarum a bafi, TDF, per rectam, DF,
              <lb/>
            abſciſſarum, vt ipſa, DTF, oſtenſum eſſet ipſas, BR, DC; </s>
            <s xml:id="echoid-s1059" xml:space="preserve">IO,
              <lb/>
            EF, communes ſectiones plani conicum tangentis in triangulis, A
              <lb/>
              <note position="right" xlink:label="note-0059-03" xlink:href="note-0059-03a" xml:space="preserve">Sed hoc
                <lb/>
              etiam per
                <lb/>
              modũ Co-
                <lb/>
              rollar. ex
                <lb/>
              Prop. 19.
                <lb/>
              deducipo
                <lb/>
              tuiſſet.</note>
            DC, AEF, & </s>
            <s xml:id="echoid-s1060" xml:space="preserve">planorum æquidiſtantium, BVO, DTF, eſſe ea-
              <lb/>
            rundem homologas, erunt autem in hoc caſu latera homologa, ve-
              <lb/>
            lut cum ſunt intra figuras ſunt lineæ homologæ earumdem, quode-
              <lb/>
            rat oſtendendum.</s>
            <s xml:id="echoid-s1061" xml:space="preserve"/>
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        <div xml:id="echoid-div127" type="section" level="1" n="88">
          <head xml:id="echoid-head99" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s1062" xml:space="preserve">_H_Inc habetur, ſi propoſitum fuiſſet fruſtum conici, BTF, quod eius
              <lb/>
            omnia latera producta coincidiſſent in vno puncto, A vnde,
              <lb/>
            oſtenſum pariter fuiſſet communes ſectiones plani per eius latera </s>
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