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

Table of contents

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[61.] COROLLARIVM.
Page: 40 (20)
[62.] THEOREMA IV. PROPOS. VII.
Page: 40 (20)
[63.] THEOREMA V. PROPOS. VIII.
Page: 41 (21)
[64.] COROLLARIV M.
Page: 42 (22)
[65.] THEOREMA VI. PROPOS. IX.
Page: 42 (22)
[66.] COROLLARIVM.
Page: 43 (23)
[67.] THEOREMA VII. PROPOS. X.
Page: 43 (23)
[68.] THEOREMA VIII. PROPOS. XI.
Page: 44 (24)
[69.] COROLLARIV M.
Page: 46 (26)
[70.] LEMMA PRO ANTECED. PROP.
Page: 47 (27)
[71.] THEOREMA IX. PROPOS. XII.
Page: 47 (27)
[72.] COROLLARIV M.
Page: 48 (28)
[73.] THEOREMA X. PROPOS. XIII.
Page: 48 (28)
[74.] THEOREMA XI. PROPOS. XIV.
Page: 50 (30)
[75.] THEOREMA XII. PROPOS. XV.
Page: 51 (31)
[76.] SCHOLIVM.
Page: 52 (32)
[77.] THEOREMA XIII. PROPOS. XVI.
Page: 52 (32)
[78.] COROLLARIVM.
Page: 52 (32)
[79.] THEOREMA XIV. PROPOS. XVII.
Page: 53 (33)
[80.] COROLLARIVM.
Page: 53 (33)
[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)
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              <pb o="43" file="0063" n="63" rhead="LIBERI."/>
            E, ad, BD, ita, CA, ad, AB, ergo vt, CM, ad, MB, ita erit, C
              <lb/>
            A, ad, AB, diuidendo, CB, ad, BM, erit vt, CB, ad, BA, er-
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            go, MB, erit æqualis ipſi, BA, totum parti, quod eſt abiurdum,
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            non igitur, ED, producta tranſit ſupra, A, eodem modo oſtende-
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            mus non tranfire infra, A, ergo tranſibit per, A, ergo tria puncta,
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            A, D, E, erunt in recta linea, AE, quod erat oſtendendum.</s>
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        <div xml:id="echoid-div134" type="section" level="1" n="93">
          <head xml:id="echoid-head104" xml:space="preserve">THEOREMA XX. PROPOS. XXIII.</head>
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            <s xml:id="echoid-s1139" xml:space="preserve">SI duarum quarumlibet ſimilium figurarum habeamus
              <lb/>
            homologas cum duabus quibuſdam regulis, habebi-
              <lb/>
            mus etiam homologas earundem cum duabus quibuſuis a-
              <lb/>
            lijs, cum prædictis angulos æquales ad eandem partem fa-
              <lb/>
            cientibus.</s>
            <s xml:id="echoid-s1140" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1141" xml:space="preserve">Patet hęc propoſitio, nam quæcunq; </s>
            <s xml:id="echoid-s1142" xml:space="preserve">figuræ planę ſimiles, ſi ſint
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s1143" xml:space="preserve">ſimiliter poſitæ, poſſunt eſſe cuiuſdam cylindrici oppo-
              <lb/>
              <note position="right" xlink:label="note-0063-01" xlink:href="note-0063-01a" xml:space="preserve">14. Huius.</note>
            ſitæ baſes, ſi ſint inæquales, oppoſitæ bales fruſti conici, in his au-
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              <note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">22. Huius</note>
            tem contingit, ſi habeamus homologas cum duabus quibuſdam re-
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              <note position="right" xlink:label="note-0063-03" xlink:href="note-0063-03a" xml:space="preserve">Corol. 9.
                <lb/>
              & 11. hus
                <lb/>
              ius.</note>
            gulis, nos eaſdem habere cum alijs duabus quibuſcumque cum præ-
              <lb/>
            dictis angulos æquales ad eandem partem conſtituentibus, ergo hoc
              <lb/>
            in quibuſcumque planis ſimilibus figuris verificatur, quod eſt pro-
              <lb/>
            poſitum.</s>
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        <div xml:id="echoid-div136" type="section" level="1" n="94">
          <head xml:id="echoid-head105" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s1145" xml:space="preserve">_E_T quia incidentes ad homologarum ſimilium figurarum regulas an-
              <lb/>
              <note position="right" xlink:label="note-0063-04" xlink:href="note-0063-04a" xml:space="preserve">_B. Def. 10._</note>
            gulos ad eandem partem efficiunt æquales, ideò & </s>
            <s xml:id="echoid-s1146" xml:space="preserve">ipſæ incidentes
              <lb/>
            erunt homologarum earundem ſimilium figurarum regulæ, & </s>
            <s xml:id="echoid-s1147" xml:space="preserve">vice verſa
              <lb/>
            in quibuſdam regulis homologarum poterunt ſumi earum incidentes.</s>
            <s xml:id="echoid-s1148" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div138" type="section" level="1" n="95">
          <head xml:id="echoid-head106" xml:space="preserve">THEOREMA XXI. PROPOS. XXIV.</head>
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            <s xml:id="echoid-s1149" xml:space="preserve">SI in duarum ſimilium figurarum oppoſitas tangentes, quę
              <lb/>
            earundem homologarum ſint regulæ, incidant duæ re-
              <lb/>
            ctæ lineæ ad eundem angulum ex eadem parte eaſdem ſe-
              <lb/>
            cantes, ductis verò quibuſdam duabus, prædictis tangenti-
              <lb/>
            bus parallelis, in dictis figuris, quæ ſecantes diuidant ſimi-
              <lb/>
            liter ad eandem partem, vel aſſumptis ipſis oppoſitis tangen-
              <lb/>
            tibus, reperiamus harum portiones inter incidentes, & </s>
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