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

Table of contents

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[141.] SCHOLIVM.
Page: 109 (89)
[142.] LEMMA.
Page: 110 (90)
[143.] COROLLARIVM.
Page: 112 (92)
[144.] THEOREMA XLV. PROPOS. XLVIII.
Page: 112 (92)
[145.] COROLLARIVM.
Page: 113 (93)
[146.] THEOREMA XLVI. PROPOS. XLIX.
Page: 114 (94)
[147.] THEOREMA XLVII. PROPOS. L:
Page: 115 (95)
[148.] COROLLARIVM I.
Page: 117 (97)
[149.] COROLLARIVM II.
Page: 117 (97)
[150.] SCHOLIVM.
Page: 118 (98)
[151.] Finis Primi Libri.
Page: 118 (98)
[152.] CAVALER II LIBER SECVNDVS.
Page: 119 (99)
[153.] DIFINITIONES. I.
Page: 119 (99)
[154.] COROLLARIVM.
Page: 120 (100)
[155.] II.
Page: 120 (100)
[156.] COROLLARIVM.
Page: 120 (100)
[157.] III.
Page: 120 (100)
[158.] COROLLARIVM.
Page: 121 (101)
[159.] IV.
Page: 121 (101)
[160.] V.
Page: 121 (101)
[161.] COROLLARIVM.
Page: 122 (102)
[162.] VI.
Page: 122 (102)
[163.] COROLLARIVM.
Page: 122 (102)
[164.] VII.
Page: 122 (102)
[165.] A. VIII.
Page: 123 (103)
[166.] B.
Page: 123 (103)
[167.] C.
Page: 123 (103)
[168.] D.
Page: 124 (104)
[169.] E.
Page: 124 (104)
[170.] APPENDIX. Pro antecedentium Definitionum explicatione.
Page: 124 (104)
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          <pb o="231" file="0251" n="251" rhead="LIBER III."/>
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        <div xml:id="echoid-div566" type="section" level="1" n="335">
          <head xml:id="echoid-head352" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s5673" xml:space="preserve">_P_ATET autem omnia quadrata, HT, ad omnia quadrata figure,
              <lb/>
            BMCP, eſſe pariter, vt quadratum, BP, ad rectangulum ſub,
              <lb/>
            BP, PA, vna cum rectangulo ſub, PA, & </s>
            <s xml:id="echoid-s5674" xml:space="preserve">ſub exceſſu, quo dupla,
              <lb/>
            EI, ſuperat, EF, cum, {2/3}, quadrati, BA. </s>
            <s xml:id="echoid-s5675" xml:space="preserve">Et quoniam, iuncta, BM,
              <lb/>
            oſtenſum eſt omnia quadrata, HP, ad omnia quadrata trapezij, MB,
              <lb/>
              <note position="right" xlink:label="note-0251-01" xlink:href="note-0251-01a" xml:space="preserve">_28. Lib. 2._</note>
            PC, eſſe vt quadratum, BP, adrectangulum, BPA, vna cum {1/3}, qua-
              <lb/>
            drati, AB, ideò eadem omnia quadrata, HP, ad reſiduum omnium
              <lb/>
            quadratorum figuræ, quæ eiſdem, MCPB, & </s>
            <s xml:id="echoid-s5676" xml:space="preserve">curua, MB, contine-
              <lb/>
            tur, demptis ab ijſdem omnibus quadratis trapezij, BMCP, erunt vt
              <lb/>
            idem quadratum, BP, ad rectangulum ſub, AP, & </s>
            <s xml:id="echoid-s5677" xml:space="preserve">ſub exceſſu du-
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            pla, EI, ſuper, EF, vnacum, {2/3}, quadrati, BA.</s>
            <s xml:id="echoid-s5678" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div568" type="section" level="1" n="336">
          <head xml:id="echoid-head353" xml:space="preserve">THEOREMA XVIII. PROPOS. XIX.</head>
          <p>
            <s xml:id="echoid-s5679" xml:space="preserve">EXpoſita adhuc figura Propof. </s>
            <s xml:id="echoid-s5680" xml:space="preserve">15. </s>
            <s xml:id="echoid-s5681" xml:space="preserve">& </s>
            <s xml:id="echoid-s5682" xml:space="preserve">intra circulum, vel
              <lb/>
            ellipſim, MBEG, ducta, RV, vtcunq; </s>
            <s xml:id="echoid-s5683" xml:space="preserve">regulę, DF,
              <lb/>
            parallela, diuidente ipſum circulum, vel ellipſim in duas vt-
              <lb/>
            cunque portiones, SMT, SET. </s>
            <s xml:id="echoid-s5684" xml:space="preserve">Dico omnia quadrata
              <lb/>
            portionis, SMT, cumrectangulis bis ſub eadem portione,
              <lb/>
            & </s>
            <s xml:id="echoid-s5685" xml:space="preserve">ſub quadrilineo, MTVN, ad omnia quadrata portionis,
              <lb/>
            SET, cum rectangulis bis ſub eadem portione, & </s>
            <s xml:id="echoid-s5686" xml:space="preserve">ſub tri-
              <lb/>
            lineis, TGV, GEF, eſſe vt portio, SMT, ad portionem,
              <lb/>
            SET.</s>
            <s xml:id="echoid-s5687" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5688" xml:space="preserve">Quoniam .</s>
            <s xml:id="echoid-s5689" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5690" xml:space="preserve">rectangula ſub portione, SMT, & </s>
            <s xml:id="echoid-s5691" xml:space="preserve">parallelogram-
              <lb/>
              <note position="right" xlink:label="note-0251-02" xlink:href="note-0251-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. lib. 2.
                <lb/>
              per A. 23.
                <lb/>
              lib. 2.</note>
            mo, HV, ad omnia quadrata, HV, ſunt vt portio, SMT, ad
              <lb/>
            parallelogrammum, HV, rectangula verò ſub, SMT, & </s>
            <s xml:id="echoid-s5692" xml:space="preserve">paralle-
              <lb/>
            logrammo, HV, diuiduntur in rectangula ſub, SMT, & </s>
            <s xml:id="echoid-s5693" xml:space="preserve">ſub, SM
              <lb/>
            T, ideſt in omnia quadrata, SMT, & </s>
            <s xml:id="echoid-s5694" xml:space="preserve">in rectangula ſub, SMT, & </s>
            <s xml:id="echoid-s5695" xml:space="preserve">
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            ſub quadrilineis, HRSM, MTVN, ideſt bis ſub, SMT, & </s>
            <s xml:id="echoid-s5696" xml:space="preserve">ſub
              <lb/>
            quadrilineo, MTVN; </s>
            <s xml:id="echoid-s5697" xml:space="preserve">namcum, ME, ſit diameter, bifariam di-
              <lb/>
            uidit tum ordinatim applicatas in parallelogrammo, HF, tum in
              <lb/>
            circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5698" xml:space="preserve">ideò exceſſus earundem linearum
              <lb/>
            hinc inde relinquuntur æquales, vndein quadrilineis, HRSM, M
              <lb/>
            TVN, lineæ in eadem rectitudine ſumptæ ſunt æquales, ideò om-
              <lb/>
            nia quadrata portionis, SMT, & </s>
            <s xml:id="echoid-s5699" xml:space="preserve">rectangula ſub eadem, & </s>
            <s xml:id="echoid-s5700" xml:space="preserve">ſub </s>
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