Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Page concordance

< >
Scan Original
121 84
122 85
123 86
124 87
125 88
126 89
127 90
128 91
129 92
130 93
131 94
132 95
133 96
134 97
135 98
136 99
137 100
138 101
139 102
140 103
141 104
142 105
143 106
144 107
145 108
146 109
147 110
148 111
149 112
150 113
< >
page |< < (86) of 525 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div228" type="section" level="1" n="77">
          <p>
            <s xml:id="echoid-s4266" xml:space="preserve">
              <pb o="86" file="122" n="123" rhead="Comment. in I. Cap. Sphæræ"/>
            turq́ue ab acu to angulo A, ad latus oppoſitum B C, recta A D, utcunque. </s>
            <s xml:id="echoid-s4267" xml:space="preserve">Di-
              <lb/>
            co maiore m eſſe proportionem rectæ B C, ad rectam C D, quàm anguli B A C,
              <lb/>
              <figure xlink:label="fig-122-01" xlink:href="fig-122-01a" number="23">
                <image file="122-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/122-01"/>
              </figure>
            ad angulum C A D. </s>
            <s xml:id="echoid-s4268" xml:space="preserve">Quoniam enim recta A D,
              <lb/>
            maior quidem eſt, quàm A C, minor uero, quã
              <lb/>
            A B, ſi centro A, interuallo autem A D, circu-
              <lb/>
            lus deſcribatur; </s>
            <s xml:id="echoid-s4269" xml:space="preserve">ſecabit is rectam A C, protractã
              <lb/>
              <note position="left" xlink:label="note-122-01" xlink:href="note-122-01a" xml:space="preserve">19. primi.</note>
            infra punctum C, ut in E, at uero rectam A B, ſu
              <lb/>
            pra punctum B, ut in F. </s>
            <s xml:id="echoid-s4270" xml:space="preserve">Et quia maior eſt pro-
              <lb/>
            portio trianguli B A D, ad ſectorem F A D, quã
              <lb/>
            trianguli D A C, ad ſectorem D A E, (propterea
              <lb/>
            quòd ibi eſt proportio maioris inæqualitatis, hic
              <lb/>
            autem minoris inæqualitatis) erit quoque permu
              <unsure/>
              <lb/>
            tando maior proportio trianguli B A D, ad triã-
              <lb/>
              <note position="left" xlink:label="note-122-02" xlink:href="note-122-02a" xml:space="preserve">27. quinti.</note>
            gulum D A C, quàm ſectoris F A D, ad ſectorem
              <lb/>
            D A E. </s>
            <s xml:id="echoid-s4271" xml:space="preserve">Com ponendo igitur maior quoque erit proportio trianguli B A C, ad
              <lb/>
              <note position="left" xlink:label="note-122-03" xlink:href="note-122-03a" xml:space="preserve">28. quinti.</note>
            triangulum D A C, hoc eſt, rectæ B C, ad rectam C D, (habent enim trian-
              <lb/>
            gula B A C, D A C, eandem proportionem, quàm baſes B C, C D.) </s>
            <s xml:id="echoid-s4272" xml:space="preserve">quàm
              <lb/>
              <note position="left" xlink:label="note-122-04" xlink:href="note-122-04a" xml:space="preserve">2. ſexti.</note>
            ſectoris F A E, ad ſectorem D A E, hoc eſt, quàm anguli B A C, ad angulum
              <lb/>
            C A D; </s>
            <s xml:id="echoid-s4273" xml:space="preserve">quòd ex coroll. </s>
            <s xml:id="echoid-s4274" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4275" xml:space="preserve">propoſ. </s>
            <s xml:id="echoid-s4276" xml:space="preserve">33. </s>
            <s xml:id="echoid-s4277" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s4278" xml:space="preserve">6. </s>
            <s xml:id="echoid-s4279" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s4280" xml:space="preserve">eandem habeant proportio-
              <lb/>
            n em ſectores, quàm anguli. </s>
            <s xml:id="echoid-s4281" xml:space="preserve">Quocirca in omni triangulo rectangulo, &</s>
            <s xml:id="echoid-s4282" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4283" xml:space="preserve">quod
              <lb/>
            demonſtrandum erat.</s>
            <s xml:id="echoid-s4284" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div230" type="section" level="1" n="78">
          <head xml:id="echoid-head82" style="it" xml:space="preserve">THEOR. 6. PROPOS. 6.</head>
          <note position="left" xml:space="preserve">Inter figu-
            <lb/>
          ras Iſoperi-
            <lb/>
          metras, quę
            <lb/>
          plures an-
            <lb/>
          gulos, ſeu
            <lb/>
          latera con-
            <lb/>
          @inet, illa
            <lb/>
          @aior eſt.</note>
          <p style="it">
            <s xml:id="echoid-s4285" xml:space="preserve">
              <emph style="sc">Isoperimetrarvm</emph>
            figurarum regularium maior eſt il-
              <lb/>
            la, quæ plures continet angulos, plur areue latera.</s>
            <s xml:id="echoid-s4286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4287" xml:space="preserve">
              <emph style="sc">Sint</emph>
            duæ figuræ regulares iſoperimetræ A B C, D E F, habeatq́; </s>
            <s xml:id="echoid-s4288" xml:space="preserve">plura
              <lb/>
            latera, ſiue angulos figura A B C, quàm D E F. </s>
            <s xml:id="echoid-s4289" xml:space="preserve">Dico A B C, maiorem eſſe,
              <lb/>
              <figure xlink:label="fig-122-02" xlink:href="fig-122-02a" number="24">
                <image file="122-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/122-02"/>
              </figure>
            quàm D E F. </s>
            <s xml:id="echoid-s4290" xml:space="preserve">Deſcribantur enim circa figuras circuli, à quorum centris G, H,
              <lb/>
            ducantur ad B C, E F, perpendiculares G I, H K, quæ diuident rectas B C,
              <lb/>
              <note position="left" xlink:label="note-122-06" xlink:href="note-122-06a" xml:space="preserve">@. tertij.</note>
            E F, bifariam. </s>
            <s xml:id="echoid-s4291" xml:space="preserve">Quo niam igitur figura A B C, plura habet latera, quàm D E F.
              <lb/>
            </s>
            <s xml:id="echoid-s4292" xml:space="preserve">f
              <unsure/>
            bi iſoperimetra, efficitur, ut latus B C, ſæpius repetitum metiatur </s>
          </p>
        </div>
      </text>
    </echo>
Impressum