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

Page concordance

< >
Scan Original
171 151
172 152
173 153
174 154
175 155
176 156
177 157
178 158
179 159
180 160
181 161
182 162
183 163
184 164
185 165
186 166
187 167
188 168
189 169
190 170
191 171
192 172
193 173
194 174
195 175
196 176
197 177
198 178
199 179
200 180
< >
page |< < (156) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div388" type="section" level="1" n="234">
          <p>
            <s xml:id="echoid-s3687" xml:space="preserve">
              <pb o="156" file="0176" n="176" rhead="GEOMETRIÆ"/>
            quoties, BD, ſecta eſſe ſupponitur, exceptis tamen extremis, vt ex.
              <lb/>
            </s>
            <s xml:id="echoid-s3688" xml:space="preserve">gr. </s>
            <s xml:id="echoid-s3689" xml:space="preserve">ipſa, CI, in qua parte, CI, quæin recta, CI, feparari debuiſ-
              <lb/>
            ſent per lineas, AEC, AFI, in puncta, C, I, partibus, BE, FD,
              <lb/>
            reſpondentia degenerauerunt. </s>
            <s xml:id="echoid-s3690" xml:space="preserve">Dico quæcunque demonſtrantur in
              <lb/>
            linea, BD, circa quadrata, vel rectangula, illi, vel illius partibus ap-
              <lb/>
            plicata, verificari de omnibus quadratis totius figurę, BADC, ſiue
              <lb/>
            partium eiuſdem figuræ per dictas lineas conſtitutarum, ſiue de re-
              <lb/>
            ctangulis ſub eiuſdem partibus. </s>
            <s xml:id="echoid-s3691" xml:space="preserve">Vtex gr. </s>
            <s xml:id="echoid-s3692" xml:space="preserve">quia in 3. </s>
            <s xml:id="echoid-s3693" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3694" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s3695" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3696" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0176-01" xlink:href="note-0176-01a" xml:space="preserve">Vide D.
                <lb/>
              Defin. 8.
                <lb/>
              huius.</note>
            Elem. </s>
            <s xml:id="echoid-s3697" xml:space="preserve">oſtenditur rectangulum ſub, BD, DF, æquari rectangulo
              <lb/>
            ſub, BFD, cum quadrato, FD, ſic dico verum eſſe rectangula ſub
              <lb/>
              <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a" number="101">
                <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0176-01"/>
              </figure>
            figura, ABCD, & </s>
            <s xml:id="echoid-s3698" xml:space="preserve">figura, ADI, æquari re-
              <lb/>
            ctangulis ſub figuris, ABIF, ADIF, cum om-
              <lb/>
            nibus quadratis figuræ, ADIF, ſi enim aliam
              <lb/>
            vtcunque duxerimus regulæ, BD, parallelam,
              <lb/>
            vt, HO, ſecantem lineas, AC, in, M, &</s>
            <s xml:id="echoid-s3699" xml:space="preserve">, A
              <lb/>
            I, in, N, verum eſſe comperiemus rectangulum,
              <lb/>
            HON, æquari rectangulo, HNO, cum qua-
              <lb/>
            drato, NO, & </s>
            <s xml:id="echoid-s3700" xml:space="preserve">idem in cęteris regulę, BD, pa-
              <lb/>
            rallelis in figura, ABCD, ductis reperiemus,
              <lb/>
            ergo verum erit rectangula illa ſimul collecta, ideſt rectangula ſub fi-
              <lb/>
              <note position="left" xlink:label="note-0176-02" xlink:href="note-0176-02a" xml:space="preserve">Coroll. 4.
                <lb/>
              huius.</note>
            gura, ABID, & </s>
            <s xml:id="echoid-s3701" xml:space="preserve">figura, ADI, æquari rectangulis ſub figuris, AB
              <lb/>
            I, ADI, cum omnibus quadratis, ADI, quod 3. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">Propoſit. </s>
            <s xml:id="echoid-s3703" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3704" xml:space="preserve">lib.
              <lb/>
            </s>
            <s xml:id="echoid-s3705" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s3706" xml:space="preserve">reſpondet.</s>
            <s xml:id="echoid-s3707" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3708" xml:space="preserve">Similiter ſi ſupponamus, BF, bifariam ſecari in, E, cui adiunga-
              <lb/>
            tur, FD, ſuppoſuerimus etiam lineam, AC, bifariam ſecare quam-
              <lb/>
            libet omnium linearum figuræ, ABI, regula, BD, ſupradictarum,
              <lb/>
            quarum ſingulis aditur, quę in directum manetin figura, ADI, ve-
              <lb/>
            luti Propoſ. </s>
            <s xml:id="echoid-s3709" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">oſtenditur rectangulum, BDF, cum quadrato, FE,
              <lb/>
            æquari quadrato, ED, ita hic ad modum ſuperioris oſtendemus re-
              <lb/>
            ctangula ſub figura, ABID, &</s>
            <s xml:id="echoid-s3711" xml:space="preserve">, ADI, cum omnibus quadratis fi-
              <lb/>
            guræ, ACI, æquari omnibus quadratis figuræ, ACD, quod re-
              <lb/>
            ſpondet Prop. </s>
            <s xml:id="echoid-s3712" xml:space="preserve">6. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">eiuſdem lib. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">Conſimiliter reliqua demonſtrabimus,
              <lb/>
            vnde iuxta I. </s>
            <s xml:id="echoid-s3715" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">Secundi Elem. </s>
            <s xml:id="echoid-s3717" xml:space="preserve">colligemus.</s>
            <s xml:id="echoid-s3718" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div391" type="section" level="1" n="235">
          <head xml:id="echoid-head250" xml:space="preserve">A. COROLLARII SECTIO I.</head>
          <p style="it">
            <s xml:id="echoid-s3719" xml:space="preserve">_R_Ectangula ſub figura indiuiſa, ABID, & </s>
            <s xml:id="echoid-s3720" xml:space="preserve">ſub diuiſa, ACD, per
              <lb/>
            lineam, AI, æquari rectangulis ſub indiuiſa, ABID, & </s>
            <s xml:id="echoid-s3721" xml:space="preserve">ſub
              <lb/>
            partibus diuiſæ, quæ ſunt, ACI, AID.</s>
            <s xml:id="echoid-s3722" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum