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

Page concordance

< >
Scan Original
221 201
222 202
223 203
224 204
225 205
226 206
227 207
228 208
229 209
230 210
231 211
232 212
233 213
234 214
235 215
236 216
237 217
238 218
239 219
240 220
241 221
242 222
243 223
244 224
245 225
246 226
247 227
248 228
249 229
250 230
< >
page |< < (172) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div425" type="section" level="1" n="258">
          <p>
            <s xml:id="echoid-s4206" xml:space="preserve">
              <pb o="172" file="0192" n="192" rhead="GEOMETRIÆ"/>
            BEC, CEF, .</s>
            <s xml:id="echoid-s4207" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4208" xml:space="preserve">ſunt ad illa, vt, EF, ad, {1/6}, eiuſdem, EF, ergo ex
              <lb/>
              <note position="left" xlink:label="note-0192-01" xlink:href="note-0192-01a" xml:space="preserve">Elicitur
                <lb/>
              ex.</note>
            æquali, rectingula ſub, AE, EC, ad rectangula ſub triangulis, BE
              <lb/>
              <note position="left" xlink:label="note-0192-02" xlink:href="note-0192-02a" xml:space="preserve">24. huius.</note>
            C, CEF, erunt vt, DE, ad, {1/6}, EF, eadem verò ad rectangula ſub,
              <lb/>
            AE, & </s>
            <s xml:id="echoid-s4209" xml:space="preserve">triangulo, BEC, ſiue, CEF, oſtenſa ſunt eſſe, vt, DE,
              <lb/>
            ad, {1/2}, DE, ergo, colligendo, rectangula ſub, AE, EC, ad rectan-
              <lb/>
            gula ſub, AE, & </s>
            <s xml:id="echoid-s4210" xml:space="preserve">triangulo, CEF, & </s>
            <s xml:id="echoid-s4211" xml:space="preserve">ſub triangulo, BEC, & </s>
            <s xml:id="echoid-s4212" xml:space="preserve">eo-
              <lb/>
            dem, CEF, .</s>
            <s xml:id="echoid-s4213" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4214" xml:space="preserve">ad rectangula ſub trapezio, ADEC, & </s>
            <s xml:id="echoid-s4215" xml:space="preserve">triangulo,
              <lb/>
              <note position="left" xlink:label="note-0192-03" xlink:href="note-0192-03a" xml:space="preserve">Per A. Co
                <lb/>
              roll. 23.
                <lb/>
              huius.</note>
            CEF, erunt vt, DE, ad compoſitam ex, {1/2}, DE, &</s>
            <s xml:id="echoid-s4216" xml:space="preserve">, {1/6}, EF, quę
              <lb/>
            eſt Theorematis prima pars.</s>
            <s xml:id="echoid-s4217" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4218" xml:space="preserve">Dico vlterius rectangula ſub, AF, FB, ad rectangula ſub trape-
              <lb/>
            zio, ADEC, & </s>
            <s xml:id="echoid-s4219" xml:space="preserve">triangulo, BEC, eſſe vt, DF, ad compoſitam ex,
              <lb/>
            {1/6}, DE, &</s>
            <s xml:id="echoid-s4220" xml:space="preserve">, {1/3}, EF; </s>
            <s xml:id="echoid-s4221" xml:space="preserve">rectangula .</s>
            <s xml:id="echoid-s4222" xml:space="preserve">n. </s>
            <s xml:id="echoid-s4223" xml:space="preserve">ſub, AF, FB, ad rectangula ſub,
              <lb/>
            AE, EC, ſunt vt rectangulum, DFE, ad rectangulum, DEF, .</s>
            <s xml:id="echoid-s4224" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s4225" xml:space="preserve">
              <note position="left" xlink:label="note-0192-04" xlink:href="note-0192-04a" xml:space="preserve">14. huius.</note>
            vt, FD, ad, DE, rectangula vero ſub, AE, EC, ad rectangula ſub,
              <lb/>
              <note position="left" xlink:label="note-0192-05" xlink:href="note-0192-05a" xml:space="preserve">3. huius.</note>
              <figure xlink:label="fig-0192-01" xlink:href="fig-0192-01a" number="112">
                <image file="0192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0192-01"/>
              </figure>
            AE, & </s>
            <s xml:id="echoid-s4226" xml:space="preserve">triangulo, BEC, ſunt vt, B
              <lb/>
              <note position="left" xlink:label="note-0192-06" xlink:href="note-0192-06a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. huius.</note>
            F, ad triangulum, BEC, .</s>
            <s xml:id="echoid-s4227" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4228" xml:space="preserve">dupla .</s>
            <s xml:id="echoid-s4229" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s4230" xml:space="preserve">vt, DE, ad, {1/2}, ipſius, DE, ergo, ex
              <lb/>
            æquali rectangula ſub, AF, FB, ad
              <lb/>
            rectangula ſub, AE, & </s>
            <s xml:id="echoid-s4231" xml:space="preserve">triangulo, B
              <lb/>
            EC, erunt vt, FD, ad, {1/2}, DE, quod
              <lb/>
            ſerua. </s>
            <s xml:id="echoid-s4232" xml:space="preserve">Item rectangula ſub, AF, FB,
              <lb/>
              <note position="left" xlink:label="note-0192-07" xlink:href="note-0192-07a" xml:space="preserve">14. huius.
                <lb/>
              3. huius.
                <lb/>
              24. huius.</note>
            ad omnia quadrata, BF, ſunt vt re-
              <lb/>
            ctangulum, DFE, ad quadratum, F
              <lb/>
            E, .</s>
            <s xml:id="echoid-s4233" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4234" xml:space="preserve">vt, DF, ad, FE: </s>
            <s xml:id="echoid-s4235" xml:space="preserve">Omnia verò
              <lb/>
            quadrata, BF, ſunt tripla omnium
              <lb/>
            quadratorum trianguli, BEC, .</s>
            <s xml:id="echoid-s4236" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4237" xml:space="preserve">ſunt vt, FE, ad, {1/3}, FE, ergo ex
              <lb/>
            æquali rectangula ſub, AF, FB, ad omnia quadrata trianguli, BE
              <lb/>
            C, ſunt vt, DF, ad, {1/3}, FE, erant autem eadem ad rectangula ſub,
              <lb/>
            AE, & </s>
            <s xml:id="echoid-s4238" xml:space="preserve">triangulo, BEC, vt, DF, ad, {1/2}, DE, ergo, colligendo,
              <lb/>
            rectangula ſub, AF, FB, ad rectangula ſub, AE, & </s>
            <s xml:id="echoid-s4239" xml:space="preserve">triangulo, BE
              <lb/>
            C, vna cum omnibus quadratis trianguli, BEC, .</s>
            <s xml:id="echoid-s4240" xml:space="preserve">i. </s>
            <s xml:id="echoid-s4241" xml:space="preserve">ad rectangula
              <lb/>
            ſub trapezio, ADEC, & </s>
            <s xml:id="echoid-s4242" xml:space="preserve">triangulo, BEC, erunt vt, DF, ad com-
              <lb/>
              <note position="left" xlink:label="note-0192-08" xlink:href="note-0192-08a" xml:space="preserve">Per C.
                <lb/>
              Coroll.
                <lb/>
              23. huius.</note>
            poſitam ex, {1/2}, DE, &</s>
            <s xml:id="echoid-s4243" xml:space="preserve">, {1/3}, EF, quę eſt Theorematis ſecunda pars;
              <lb/>
            </s>
            <s xml:id="echoid-s4244" xml:space="preserve">hæc autem erant demonſtranda.</s>
            <s xml:id="echoid-s4245" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div429" type="section" level="1" n="259">
          <head xml:id="echoid-head274" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4246" xml:space="preserve">_C_Olligimus autem ex hoc Theoremate rectangula ſub maximis ab-
              <lb/>
            ſciſſarum propoſitæ lineæ, adiunctis eiſdem tot vni cuidam æquali-
              <lb/>
            bus, ad rectangula ſub omnibus abſciſſis eiuſdem adiunctaiam dicta li-
              <lb/>
            nea, & </s>
            <s xml:id="echoid-s4247" xml:space="preserve">ſub reſiduis abſciſſarum eiuſdem, eſſe vt adiuncta ad compoſitam
              <lb/>
            ex, {1/2}, adiunctæ, & </s>
            <s xml:id="echoid-s4248" xml:space="preserve">{1/2}, propoſitæ lineæ, & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">hoc ex prima parte </s>
          </p>
        </div>
      </text>
    </echo>
Impressum