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

Page concordance

< >
Scan Original
241 221
242 222
243 223
244 224
245 225
246 226
247 227
248 228
249 229
250 230
251 231
252 232
253 233
254 234
255 235
256 236
257 237
258 238
259 239
260 240
261 241
262 242
263 243
264 244
265 245
266 246
267 247
268 248
269 249
270 250
< >
page |< < (225) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div555" type="section" level="1" n="330">
          <p>
            <s xml:id="echoid-s5489" xml:space="preserve">
              <pb o="225" file="0245" n="245" rhead="LIBER III."/>
            M,B, E, G. </s>
            <s xml:id="echoid-s5490" xml:space="preserve">Dico igitur omnia quadrata parallelogrammi, HF,
              <lb/>
            ſimul cum rectangulis bis ſub, HF, & </s>
            <s xml:id="echoid-s5491" xml:space="preserve">parallelogrammo, FC, ad
              <lb/>
            omnia quadrata circuli, vel ellipſis, MBEG, ſimul cum rectangu-
              <lb/>
            lis bis ſub eodem circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5492" xml:space="preserve">ſub quadrilineo, M
              <lb/>
            GEOC, eſſe vt parallelogrammum, HF, ad circulum, vel ellipſim,
              <lb/>
            MBEG : </s>
            <s xml:id="echoid-s5493" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s5494" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5495" xml:space="preserve">quadrata parallelogrammi, HO, ad omnia
              <lb/>
              <note position="right" xlink:label="note-0245-01" xlink:href="note-0245-01a" xml:space="preserve">9. Lib. 2.</note>
            quadrata parallelogrammi, MO, ſunt vt quadratum, DO, ad qua-
              <lb/>
            dratum, OE, omnia item quadrata parallelogrammi, MO, ad re-
              <lb/>
              <note position="right" xlink:label="note-0245-02" xlink:href="note-0245-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26.lib.2.</note>
            ctangula ſub parallelogrammo, MO, & </s>
            <s xml:id="echoid-s5496" xml:space="preserve">portione, MGE, ſunt vt,
              <lb/>
            MO, ad portionem, MGE, fiat vt, MF, ad portionem, MGE,
              <lb/>
            ita, FE, ad, EI, erit ergo vt, MO, ad portionem, MGE, ita, O
              <lb/>
            E, ad, EI, ergo omnia quadrata, MO, ad rectangula ſub, MO, & </s>
            <s xml:id="echoid-s5497" xml:space="preserve">
              <lb/>
            portione, MGE, erunt vt, OE, ad, EI, .</s>
            <s xml:id="echoid-s5498" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5499" xml:space="preserve">vt quadratum, OE,
              <lb/>
              <note position="right" xlink:label="note-0245-03" xlink:href="note-0245-03a" xml:space="preserve">5.Lib.2.</note>
            ad rectangulum ſub, OE, EI, erant autem omnia quadrata, HO,
              <lb/>
            ad omnia quadrata, OM, vt quadratum, DO, ad quadratum, O
              <lb/>
            E, ergo ex æquali omnia quadrata, HO, ad rectangula ſub, MO,
              <lb/>
            & </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ſub portione, MGE, erunt vt quadratum, DO, ad rectangu-
              <lb/>
            lum ſub, OE, EI, ad eadem verò quater ſumpta, vt quadratum, D
              <lb/>
            O, ad rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s5501" xml:space="preserve">quadrupla, EI; </s>
            <s xml:id="echoid-s5502" xml:space="preserve">rectangula autem
              <lb/>
              <figure xlink:label="fig-0245-01" xlink:href="fig-0245-01a" number="152">
                <image file="0245-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0245-01"/>
              </figure>
            ſub, MO, & </s>
            <s xml:id="echoid-s5503" xml:space="preserve">por-
              <lb/>
              <note position="right" xlink:label="note-0245-04" xlink:href="note-0245-04a" xml:space="preserve">Per C, 23.
                <lb/>
              lib.2.</note>
            tione, MGE, æ-
              <lb/>
            quantur rectangulis
              <lb/>
            ſub quadrilineo, M
              <lb/>
            GEOC, & </s>
            <s xml:id="echoid-s5504" xml:space="preserve">por
              <lb/>
            tione, MGE, vna
              <lb/>
            cum omnibus qua
              <lb/>
            dratis portionis, M
              <lb/>
            GE, ilia ig tur qua-
              <lb/>
            ter ſumpta reddunt
              <lb/>
            quater rectangula ſub portione, MGE, & </s>
            <s xml:id="echoid-s5505" xml:space="preserve">quadrilineo, MGEO
              <lb/>
            C, vna cum omnibus quadratis portionis, MGE, quater ſumptis,
              <lb/>
            quia verò omnia quadrata circuli, vel ellipſis, MBEG, æquantur
              <lb/>
              <note position="right" xlink:label="note-0245-05" xlink:href="note-0245-05a" xml:space="preserve">Per D.23.
                <lb/>
              lib,2.</note>
            omnibus quadratis portionis, MBE, & </s>
            <s xml:id="echoid-s5506" xml:space="preserve">portionis, MGE, vna cum
              <lb/>
            rectangulis bis ſub vtriſq; </s>
            <s xml:id="echoid-s5507" xml:space="preserve">portionibus .</s>
            <s xml:id="echoid-s5508" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5509" xml:space="preserve">vna cum omnibus quadratis
              <lb/>
            portionis, MGE, bis ſumptis, & </s>
            <s xml:id="echoid-s5510" xml:space="preserve">omnia quadrata portionis, MBE,
              <lb/>
            æquantur omnibus quadratis portionis, MGE, ideò omnia quadra-
              <lb/>
            ta portionis, MGE, quater ſumpta æquantur omnib. </s>
            <s xml:id="echoid-s5511" xml:space="preserve">quadratis cir-
              <lb/>
            culi, vel ellipſis, MBEG, item rectangula ſub portione, MGE, & </s>
            <s xml:id="echoid-s5512" xml:space="preserve">
              <lb/>
            quadrilineo, MGEOC, quater æquantur rectangulis ſub toto circu-
              <lb/>
            lo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5513" xml:space="preserve">ſub quadrilineo, MGEOC, bis ſumptis, itaut
              <lb/>
            hucuſq; </s>
            <s xml:id="echoid-s5514" xml:space="preserve">probauerimus rectangula ſub portione, MGE, & </s>
            <s xml:id="echoid-s5515" xml:space="preserve">paralle-
              <lb/>
            logrammo, MO, quater ſumpta æquari omnibus quadratis </s>
          </p>
        </div>
      </text>
    </echo>
Impressum