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

Table of contents

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[121.] THEOREMA XXX. PROPOS. XXXIII.
Page: 95 (75)
[122.] THEOREMA XXXI. PROPOS. XXXIV.
Page: 96 (76)
[123.] COROLLARIVM.
Page: 97 (77)
[124.] THEOREMA XXXII. PROPOS. XXXV.
Page: 97 (77)
[125.] COROLLARIVM.
Page: 98 (78)
[126.] THEOREMA XXXIII. PROPOS. XXXVI.
Page: 98 (78)
[127.] THEOREMA XXXIV. PROPOS. XXXVII.
Page: 99 (79)
[128.] COROLLARIVM.
Page: 101 (81)
[129.] THEOREMA XXXV. PROPOS. XXXVIII.
Page: 101 (81)
[130.] THEOREMA XXXVI. PROPOS. XXXIX.
Page: 103 (83)
[131.] THEOREMA XXXVII. PROPOS. XL.
Page: 103 (83)
[132.] SCHOLIVM.
Page: 104 (84)
[133.] THEOREMA XXXVIII. PROPOS. XLI.
Page: 105 (85)
[134.] THEOREMA XXXIX PROPOS. XLII.
Page: 105 (85)
[135.] THEOREMA XL. PROPOS. XLIII.
Page: 105 (85)
[136.] THEOREMA XLI. PROPOS. XLIV.
Page: 106 (86)
[137.] THEOREMA XLII. PROPOS. XLV.
Page: 107 (87)
[138.] THEOREMA XLIII. PROPOS. XLVI.
Page: 107 (87)
[139.] THEOREMA XLIV. PROPOS. XLVII.
Page: 108 (88)
[140.] COROLLARIVM.
Page: 109 (89)
[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)
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          <head xml:id="echoid-head324" xml:space="preserve">THEOREMA VI. PROPOS. VI.</head>
          <p>
            <s xml:id="echoid-s5070" xml:space="preserve">SI in circulo, vel ellipſiad axim, vel diametrum eiuſdem
              <lb/>
            ordinatim applicetur vtcumque recta linea, quæ ſuma-
              <lb/>
            tur pro regula; </s>
            <s xml:id="echoid-s5071" xml:space="preserve">Omnia quadrata eiuſdem ad omnia quadra-
              <lb/>
            ta alterutrius portionis peream conſtitutæ, erunt vt paralle-
              <lb/>
            lepipedum ſub quadrato totius axis, vel diametri, altitudi-
              <lb/>
            ne eiuſdem dimidia, ad parallele pipedum ſub quadrato aſ-
              <lb/>
            ſumptæ portionis, altitudine autem linea compoſita ex reli-
              <lb/>
            quæ portionis axi, vel diametro, & </s>
            <s xml:id="echoid-s5072" xml:space="preserve">dimidia totius: </s>
            <s xml:id="echoid-s5073" xml:space="preserve">Vel e-
              <lb/>
            runt, vt cubus totius axis, vel diametri ad parallelepipe-
              <lb/>
            dum ſub quadrato aſſumptæ portionis axis, vel diametri, & </s>
            <s xml:id="echoid-s5074" xml:space="preserve">
              <lb/>
            ſub altitudine linea compoſita ex tripla axis, vel diametri
              <lb/>
            reliquæ portionis, cum cubo axis, vel diametri reliquæ por-
              <lb/>
            tionis.</s>
            <s xml:id="echoid-s5075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5076" xml:space="preserve">Sit circulus, vel ellipſis, ABCD, cuius axis, vel diameter, AC,
              <lb/>
            centrum, O, & </s>
            <s xml:id="echoid-s5077" xml:space="preserve">ordinatim vtcunq; </s>
            <s xml:id="echoid-s5078" xml:space="preserve">ad ipſam applicata, BD, con-
              <lb/>
            ſtituens duas portiones, BAD, BCD, quæ quoque ſit regula.
              <lb/>
            </s>
            <s xml:id="echoid-s5079" xml:space="preserve">Dico ergo omnia quadrata circuli, vel ellipſis, ABCD, ad omnia
              <lb/>
            quadrata portionis, BAD, ex duabus portionibus, BAD, BC
              <lb/>
            D, ad libitum ſumptæ, eſſe, vt parallelepipedum ſub baſi quadra-
              <lb/>
              <figure xlink:label="fig-0226-01" xlink:href="fig-0226-01a" number="139">
                <image file="0226-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0226-01"/>
              </figure>
            to, AC, altitudine, CO, vel, CX, quæ ſit
              <lb/>
            æqualis, CO, & </s>
            <s xml:id="echoid-s5080" xml:space="preserve">illi in directum conſtituta, ad
              <lb/>
            parallelepipedum ſub baſi quadrato, AE, al-
              <lb/>
            titudine, EX, vel vt cubus, AC, ad parallele-
              <lb/>
            pipedum ſub baſi quadrato, AE, altitudine tri-
              <lb/>
            pla. </s>
            <s xml:id="echoid-s5081" xml:space="preserve">EC, cum cubo, AE; </s>
            <s xml:id="echoid-s5082" xml:space="preserve">iungantur, BA, A
              <lb/>
            D, BC, CD: </s>
            <s xml:id="echoid-s5083" xml:space="preserve">Omnia ergo quadrata portio-
              <lb/>
            nis, BCD, ad omnia quadrata portion@s, BA
              <lb/>
              <note position="left" xlink:label="note-0226-01" xlink:href="note-0226-01a" xml:space="preserve">Diff. 12.
                <lb/>
              lib. 1.</note>
            D, habent rationem compoſitam ex ea, quam
              <lb/>
            habent omnia quadrata portionis, BCD, ad
              <lb/>
            omnia quadrata trianguli, BCD, & </s>
            <s xml:id="echoid-s5084" xml:space="preserve">ex ea,
              <lb/>
            quam habent hæc ad omnia quadrata trianguli, BAD, & </s>
            <s xml:id="echoid-s5085" xml:space="preserve">ex ratio-
              <lb/>
            ne iſtorum ad omnia quadrata portionis, BAD: </s>
            <s xml:id="echoid-s5086" xml:space="preserve">Omnia verò qua-
              <lb/>
              <note position="left" xlink:label="note-0226-02" xlink:href="note-0226-02a" xml:space="preserve">1. huius.</note>
            drata portionis, BCD, ad omnia quadrata trianguli, BCD, ſunt
              <lb/>
              <note position="left" xlink:label="note-0226-03" xlink:href="note-0226-03a" xml:space="preserve">PerC. Co
                <lb/>
              rollar. 22.
                <lb/>
              lib. 2.</note>
            vt compoſita ex, OA, AE, ad, AE: </s>
            <s xml:id="echoid-s5087" xml:space="preserve">Omnia item quadrata trian-
              <lb/>
            guli, BCD, ad omnia quadrata trianguli, BAD, (quia triangula
              <lb/>
            ſunt in eadem baſi, BD,) ſunt vt, CE, ad, EA: </s>
            <s xml:id="echoid-s5088" xml:space="preserve">Omnia </s>
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