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

Page concordance

< >
Scan Original
81 61
82 62
83 63
84 64
85 65
86 66
87 67
88 68
89 69
90 70
91 71
92 72
93 73
94 74
95 75
96 76
97 77
98 78
99 79
100 80
101 81
102 82
103 83
104 84
105 85
106 86
107 87
108 88
109 89
110 90
< >
page |< < (70) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div177" type="section" level="1" n="116">
          <p>
            <s xml:id="echoid-s1785" xml:space="preserve">
              <pb o="70" file="0090" n="90" rhead="GEOMETRIÆ"/>
            hos circulos eſſe ſimiles iuxta meam definitionem ſimilium plana-
              <lb/>
            rum figurarum, & </s>
            <s xml:id="echoid-s1786" xml:space="preserve">eorum, & </s>
            <s xml:id="echoid-s1787" xml:space="preserve">ductarum oppoſitarum tangentium in-
              <lb/>
            cidentes eſſe ipſas diametros, AC, OQ, quæ etiam de ſemicirculis
              <lb/>
            verificantur. </s>
            <s xml:id="echoid-s1788" xml:space="preserve">Diametri ergo, AC, OQ, diuidantur fimiliter ad ean-
              <lb/>
            dem partem in punctis, E, M, à quibus vſque ad circumferentiam
              <lb/>
            ducantur ipſæ, EB, MN, parallelæ dictis tangentibus, quæ cum
              <lb/>
            ad angulos rectos diametros diuidant, etiam ipſę, BE, NM, erunt
              <lb/>
              <figure xlink:label="fig-0090-01" xlink:href="fig-0090-01a" number="47">
                <image file="0090-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0090-01"/>
              </figure>
            illis perpendiculares, igitur quadratum,
              <lb/>
            BE, erit ęquale rectangulo, AEC, ſi-
              <lb/>
            cuti quadratum, NM, æquale rectan-
              <lb/>
            gulo, OMQ, rectangulum autem, A
              <lb/>
            EC, ad quadratum, EC, eſt vt, AE,
              <lb/>
            ad, EC, ideſt vt, OM, ad, MQ, ideſt
              <lb/>
              <note position="left" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve">1. Sex. El.</note>
            vt rectangulum, OMQ, ad quadratum,
              <lb/>
            MQ, ideſt vt quadratum, NM, ad qua-
              <lb/>
            dratum, MQ, ergo quadratum, BE,
              <lb/>
            ad quadratum, EC, eſt vt quadratum,
              <lb/>
            NM, ad quadratum, MQ, (quæ au-
              <lb/>
            tem hic ſupponuntur, vel petantur ex
              <lb/>
            Eucl. </s>
            <s xml:id="echoid-s1789" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s1790" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s1791" xml:space="preserve">vel ex ſequenti meo lib.
              <lb/>
            </s>
            <s xml:id="echoid-s1792" xml:space="preserve">
              <note position="left" xlink:label="note-0090-02" xlink:href="note-0090-02a" xml:space="preserve">8. Lib. 2.
                <lb/>
              ſequen.
                <lb/>
              vel 20.
                <lb/>
              Sex. El.</note>
            in quo, quæ hic aſſumuntur indepen-
              <lb/>
            denter ab hoc Lemmate demonſtratur)
              <lb/>
            ergo, BE, ad, EC, erit vt, NM, ad,
              <lb/>
            MQ, permutando, BE, ad, NM, e-
              <lb/>
            rit vt, EC, ad, MQ, vel vt, AC, ad, OQ, igitur, quæ æquidi-
              <lb/>
            ſtant ipſis tangentibus, FA, HO, & </s>
            <s xml:id="echoid-s1793" xml:space="preserve">ſimiliter ad eandem partem
              <lb/>
            vtcumque diuidunt ipſas, AC, OQ, & </s>
            <s xml:id="echoid-s1794" xml:space="preserve">iacent inter ipſas, & </s>
            <s xml:id="echoid-s1795" xml:space="preserve">circui-
              <lb/>
            tus ſemicirculorum, ABC, ONQ, ad eandem partem, eodem or-
              <lb/>
            dine ſumptæ, ſunt vt ipſæ, AC, OQ, quæ dictis tangentibus inci-
              <lb/>
              <note position="left" xlink:label="note-0090-03" xlink:href="note-0090-03a" xml:space="preserve">Defin. 10.</note>
            dunt ad eundem angulum ex eadem parte, quęideò ſunt earum inci-
              <lb/>
            dentes, ergo ſemicirculi, ABC, ONQ, ſunt figuræ planæ fimiles
              <lb/>
            ſuxta meam definitionem, quarum & </s>
            <s xml:id="echoid-s1796" xml:space="preserve">oppoſitarum tangentium, quę
              <lb/>
            ab extremitate diametrorum ducuntur, incidentes ſunt ipſi diame-
              <lb/>
            tri; </s>
            <s xml:id="echoid-s1797" xml:space="preserve">ſic etiam patebit ſemicirculos, ADC, OZQ, necnon circu-
              <lb/>
            los, AC, OQ, eſſe ſimiles, iuxta eandem definitionem; </s>
            <s xml:id="echoid-s1798" xml:space="preserve">quod oſten-
              <lb/>
            dendum erat.</s>
            <s xml:id="echoid-s1799" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div179" type="section" level="1" n="117">
          <head xml:id="echoid-head128" xml:space="preserve">THEOREMA XXVIII. PROPOS. XXXI.</head>
          <p>
            <s xml:id="echoid-s1800" xml:space="preserve">POſitis infraſcriptis definitionibus ſimilium cylindro-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s1801" xml:space="preserve">conorum, ſequitur definitio generalis, quam
              <lb/>
            de ſimilibus ſolidis ipſe attuli.</s>
            <s xml:id="echoid-s1802" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum