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

Table of figures

< >
[Figure 201]
Page: 307
[Figure 202]
Page: 308
[Figure 203]
Page: 309
[Figure 204]
Page: 310
[Figure 205]
Page: 311
[Figure 206]
Page: 312
[Figure 207]
Page: 313
[Figure 208]
Page: 314
[Figure 209]
Page: 315
[Figure 210]
Page: 316
[Figure 211]
Page: 317
[Figure 212]
Page: 319
[Figure 213]
Page: 320
[Figure 214]
Page: 320
[Figure 215]
Page: 321
[Figure 216]
Page: 322
[Figure 217]
Page: 324
[Figure 218]
Page: 326
[Figure 219]
Page: 327
[Figure 220]
Page: 328
[Figure 221]
Page: 330
[Figure 222]
Page: 331
[Figure 223]
Page: 332
[Figure 224]
Page: 333
[Figure 225]
Page: 335
[Figure 226]
Page: 336
[Figure 227]
Page: 337
[Figure 228]
Page: 338
[Figure 229]
Page: 340
[Figure 230]
Page: 343
< >
page |< < (190) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div476" type="section" level="1" n="287">
          <pb o="190" file="0210" n="210" rhead="GEOMETRI Æ"/>
        </div>
        <div xml:id="echoid-div479" type="section" level="1" n="288">
          <head xml:id="echoid-head304" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4676" xml:space="preserve">_H_Inc patet cubùm totius, AC, æquari parallelepipedis ſub ſingulis
              <lb/>
            partibus i pſius, AC, & </s>
            <s xml:id="echoid-s4677" xml:space="preserve">ſingulis partibus quadrati, AC, quod
              <lb/>
            etiam patet ex Theoremate 35.</s>
            <s xml:id="echoid-s4678" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div480" type="section" level="1" n="289">
          <head xml:id="echoid-head305" xml:space="preserve">THEOREMA XXXVIII. PROPOS. XXXVIII.</head>
          <p>
            <s xml:id="echoid-s4679" xml:space="preserve">SI recta linea in vno puncto ſecta ſit vtcumq; </s>
            <s xml:id="echoid-s4680" xml:space="preserve">cubus totius
              <lb/>
            æquatur cubis partium, vna cum parallel@ pipedis rer
              <lb/>
            ſub qualibet partium, & </s>
            <s xml:id="echoid-s4681" xml:space="preserve">quadrato reliquæ. </s>
            <s xml:id="echoid-s4682" xml:space="preserve">Vel æquatur
              <lb/>
            cubis partium vna cum tribus parallelepipedis, ſub tota, & </s>
            <s xml:id="echoid-s4683" xml:space="preserve">
              <lb/>
            eiuſdem partibus contentis.</s>
            <s xml:id="echoid-s4684" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4685" xml:space="preserve">Sit recta linea, AC, vtcumque ſecta in puncto, B. </s>
            <s xml:id="echoid-s4686" xml:space="preserve">Dico cubum,
              <lb/>
            AC, æquari cubis, AB, BC, & </s>
            <s xml:id="echoid-s4687" xml:space="preserve">parallelepipedis ter ſub, AB, & </s>
            <s xml:id="echoid-s4688" xml:space="preserve">
              <lb/>
            quadrato, BC, & </s>
            <s xml:id="echoid-s4689" xml:space="preserve">ter ſub, BC, & </s>
            <s xml:id="echoid-s4690" xml:space="preserve">quadrato, AB. </s>
            <s xml:id="echoid-s4691" xml:space="preserve">Nam parallele-
              <lb/>
            pipedum ſub, AC, & </s>
            <s xml:id="echoid-s4692" xml:space="preserve">quadrato, AC, (qui eſt cubus, AC,) æqua-
              <lb/>
              <note position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">ExCorol.
                <lb/>
              ant. vel ex
                <lb/>
              35. huius.</note>
            tur parallelepipedis ſub ſingulis partibus ipſius, AC, & </s>
            <s xml:id="echoid-s4693" xml:space="preserve">ſub ſingulis
              <lb/>
            partibus quadrati, AC, ab hac diuiſione prouenientibus, ideſt pa-
              <lb/>
            rallelepipedo ſub, AB, & </s>
            <s xml:id="echoid-s4694" xml:space="preserve">quadrato, AB, qui eſt cubus, AB, item
              <lb/>
            ſub, AB, & </s>
            <s xml:id="echoid-s4695" xml:space="preserve">quadrato, BC, item ſub, AB, & </s>
            <s xml:id="echoid-s4696" xml:space="preserve">rectangulo, ABC, bis,
              <lb/>
              <note position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">36. huius.
                <lb/>
              Pars I.</note>
            ideſt ſub, CB, & </s>
            <s xml:id="echoid-s4697" xml:space="preserve">quadrato, BA, bis ſumpto, habemus ergo vnum
              <lb/>
              <figure xlink:label="fig-0210-01" xlink:href="fig-0210-01a" number="126">
                <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0210-01"/>
              </figure>
            cubum, AB, vnum parallelepipedum ſub,
              <lb/>
            AB, & </s>
            <s xml:id="echoid-s4698" xml:space="preserve">quadrato, BC, & </s>
            <s xml:id="echoid-s4699" xml:space="preserve">duo ſub, BC, & </s>
            <s xml:id="echoid-s4700" xml:space="preserve">
              <lb/>
            quadrato, BA; </s>
            <s xml:id="echoid-s4701" xml:space="preserve">tranſeamus nunc ad aliam
              <lb/>
            partem, BC, remanent ergo parallelepipe.
              <lb/>
            </s>
            <s xml:id="echoid-s4702" xml:space="preserve">da ſub, BC, & </s>
            <s xml:id="echoid-s4703" xml:space="preserve">quadrato, BC, ideſt vnus cubus, BC, item ſub, C
              <lb/>
            B, & </s>
            <s xml:id="echoid-s4704" xml:space="preserve">quadrato, AB, & </s>
            <s xml:id="echoid-s4705" xml:space="preserve">tandem ſub, CB, & </s>
            <s xml:id="echoid-s4706" xml:space="preserve">rectangulo, CBA, bis,
              <lb/>
            ideſt ſub, AB, & </s>
            <s xml:id="echoid-s4707" xml:space="preserve">quadrato, BC, bis, ſi igitur hæc poſteriora pa-
              <lb/>
              <note position="left" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">30. huius.
                <lb/>
              Pars I.</note>
            rallelepipeda prioribus iunxeris habebis cubum, AB, cubum, BC,
              <lb/>
            parallelepipedum ter ſub, AB, & </s>
            <s xml:id="echoid-s4708" xml:space="preserve">quadrato, BC, & </s>
            <s xml:id="echoid-s4709" xml:space="preserve">ter ſub, BC, & </s>
            <s xml:id="echoid-s4710" xml:space="preserve">
              <lb/>
            quadrato, BA, quibus æquale erit parallelepipedum ſub, CA, & </s>
            <s xml:id="echoid-s4711" xml:space="preserve">
              <lb/>
            quadrato, CA, ideſt cubus, CA. </s>
            <s xml:id="echoid-s4712" xml:space="preserve">Quia verò parallelepipedum ſub,
              <lb/>
            CB, & </s>
            <s xml:id="echoid-s4713" xml:space="preserve">quadrato, BA, ideſt ſub, AB, & </s>
            <s xml:id="echoid-s4714" xml:space="preserve">rectangulo, ABC, cum
              <lb/>
            parallelepipedo ſub, AB, & </s>
            <s xml:id="echoid-s4715" xml:space="preserve">quadrato, BC, ideſt ſub, CB, & </s>
            <s xml:id="echoid-s4716" xml:space="preserve">re-
              <lb/>
            ctangulo, ABC, æquatur, ex 35. </s>
            <s xml:id="echoid-s4717" xml:space="preserve">huius, parallelepipedo ſub tota,
              <lb/>
            AC, & </s>
            <s xml:id="echoid-s4718" xml:space="preserve">rectangulo ſub partibus, AB, BC, ideò dicta ſex parallelepi-
              <lb/>
            peda tribus ſub tota, AC, & </s>
            <s xml:id="echoid-s4719" xml:space="preserve">partibus eiuidem, AB, BC, æqualia
              <lb/>
            c
              <unsure/>
            runt, quod demonſtrare propoſitum fuit.</s>
            <s xml:id="echoid-s4720" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum