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

Page concordance

< >
Scan Original
361 341
362 342
363 343
364 344
365 345
366 346
367 347
368 348
369 349
370 350
371 351
372 352
373 353
374 354
375 355
376 356
377 357
378 358
379 359
380 360
381 361
382 362
383 363
384 364
385 365
386 366
387 367
388 368
389 369
390 370
< >
page |< < (369) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div895" type="section" level="1" n="536">
          <p>
            <s xml:id="echoid-s9368" xml:space="preserve">
              <pb o="369" file="0389" n="389" rhead="LIBER V."/>
            NX, & </s>
            <s xml:id="echoid-s9369" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9370" xml:space="preserve">{2/3}- NE, regula eadem, DF, retenta; </s>
            <s xml:id="echoid-s9371" xml:space="preserve">oſten-
              <lb/>
            demus?</s>
            <s xml:id="echoid-s9372" xml:space="preserve">? omnia quadrata parallelogrammi, SF, ad om-
              <lb/>
            nia quadrata fruſti hyperbolæ, HDFG, eſſe vt rectangu-
              <lb/>
            lum, OEN, ad rectangulum ſub, OE, &</s>
            <s xml:id="echoid-s9373" xml:space="preserve">, NM, vna cum re-
              <lb/>
            ctangulo ſub compoſita ex. </s>
            <s xml:id="echoid-s9374" xml:space="preserve">No, &</s>
            <s xml:id="echoid-s9375" xml:space="preserve">. ME, & </s>
            <s xml:id="echoid-s9376" xml:space="preserve">ſub, ME;
              <lb/>
            </s>
            <s xml:id="echoid-s9377" xml:space="preserve">Omnia verò quadrata trianguli, DMF, ad omnia quadra-
              <lb/>
            ta eiuſdem fruſti, HDFG, eſſe vt rectangulum, OEN, ad
              <lb/>
            rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s9378" xml:space="preserve">tripla, NM, vna cum rectangulo
              <lb/>
            ſub compoſita ex, NX, & </s>
            <s xml:id="echoid-s9379" xml:space="preserve">ME, ſub, ME.</s>
            <s xml:id="echoid-s9380" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9381" xml:space="preserve">Sumatur in, ME, vtcunq; </s>
            <s xml:id="echoid-s9382" xml:space="preserve">punctum, L, & </s>
            <s xml:id="echoid-s9383" xml:space="preserve">per ipſum regulæ,
              <lb/>
            DF, parallela ducatur, LK, curuam hyp rbolicam in, I, ſecans;
              <lb/>
            </s>
            <s xml:id="echoid-s9384" xml:space="preserve">
              <figure xlink:label="fig-0389-01" xlink:href="fig-0389-01a" number="266">
                <image file="0389-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0389-01"/>
              </figure>
            Eſt ergo quadratum, EF, vel quadratum,
              <lb/>
            LK, ad quadratum, LI, vt rectangulum,
              <lb/>
            OEN, adrectangulum, OLN; </s>
            <s xml:id="echoid-s9385" xml:space="preserve">eſt autem
              <lb/>
            parallelogrammum, MF, in eadem baſi, & </s>
            <s xml:id="echoid-s9386" xml:space="preserve">
              <lb/>
            altitudine cum figura, MGFE, punctum,
              <lb/>
            L, ſumptum eſt vt cunque, perq; </s>
            <s xml:id="echoid-s9387" xml:space="preserve">ipſum re-
              <lb/>
            gulæ, DF, ducta parallela, LK, repertum
              <lb/>
            eſt, vt quadratum, KL, ad quadratum, LI,
              <lb/>
            ita eſſe rectangulum, OEN, ad rectangulũ,
              <lb/>
            OLN; </s>
            <s xml:id="echoid-s9388" xml:space="preserve">quatuor ergo ordinum magnitudi-
              <lb/>
            nes conſtructæ iuxta has quatuor inuentas
              <lb/>
            magnitudines proportionales, erunt quoq;
              <lb/>
            </s>
            <s xml:id="echoid-s9389" xml:space="preserve">proportionales .</s>
            <s xml:id="echoid-s9390" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9391" xml:space="preserve">omnia quadrata: </s>
            <s xml:id="echoid-s9392" xml:space="preserve">MF, ad
              <lb/>
            omnia quadrata figuræ, MGFE, quæ ſunt
              <lb/>
            magnitudines primi, & </s>
            <s xml:id="echoid-s9393" xml:space="preserve">ſecundi ordinis conſtructæ iuxta primã, & </s>
            <s xml:id="echoid-s9394" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0389-01" xlink:href="note-0389-01a" xml:space="preserve">Coroll. 3.
                <lb/>
              26. l. 2.</note>
            ſecundam .</s>
            <s xml:id="echoid-s9395" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9396" xml:space="preserve">iuxta quadratum, KL, & </s>
            <s xml:id="echoid-s9397" xml:space="preserve">quadratum, LI, erunt, vt
              <lb/>
            rectangula ſub maximis abſciſſarum, EM, adiuncta, MO, & </s>
            <s xml:id="echoid-s9398" xml:space="preserve">ſub
              <lb/>
            maximis abſciſſarum, EM, adiuncta, MN, ad rectangula ſub om-
              <lb/>
            nibus abſciſsis, EM, adiuncta, MO, & </s>
            <s xml:id="echoid-s9399" xml:space="preserve">ſub omnibus abſciſsis, EM,
              <lb/>
            adiuncta, MN, quæ ſunt magnitudines tertij, & </s>
            <s xml:id="echoid-s9400" xml:space="preserve">quarti ordinis
              <lb/>
            collectæ iuxta tertiam, & </s>
            <s xml:id="echoid-s9401" xml:space="preserve">quartam .</s>
            <s xml:id="echoid-s9402" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s9403" xml:space="preserve">iuxta rectangulum, OEN,
              <lb/>
            OLN; </s>
            <s xml:id="echoid-s9404" xml:space="preserve">verum rectangula ſub maximis abſciſlarum, EM, adiuncta,
              <lb/>
            MO, & </s>
            <s xml:id="echoid-s9405" xml:space="preserve">ſub eiſdem adiuncta, MN, ad rectangula ſub omnibus ab-
              <lb/>
            ſciſsis, EM, adiuncta, MO, & </s>
            <s xml:id="echoid-s9406" xml:space="preserve">ſub ijſdem adiuncta, MN, omnibus
              <lb/>
              <note position="right" xlink:label="note-0389-02" xlink:href="note-0389-02a" xml:space="preserve">Corol. 21.
                <lb/>
              l. 2.</note>
            recti vel eiuſdem obliqui tranſitus ſumptis, ſunt, vt rectangulum,
              <lb/>
            OEN, ad rectangulum ſub, OE, &</s>
            <s xml:id="echoid-s9407" xml:space="preserve">, NM, vna cum rectangulo ſub
              <lb/>
            compoſita ex {1/2}. </s>
            <s xml:id="echoid-s9408" xml:space="preserve">ON, & </s>
            <s xml:id="echoid-s9409" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s9410" xml:space="preserve">ME, & </s>
            <s xml:id="echoid-s9411" xml:space="preserve">ſub, ME, ergo omnia quadra-
              <lb/>
            ta, MF, ad omnia quadrata figuræ, GMEF, vel horum quadru-
              <lb/>
            pla .</s>
            <s xml:id="echoid-s9412" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9413" xml:space="preserve">omnia quadrata, SF, ad omnia quadrata fruſti, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum