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

Page concordance

< >
Scan Original
461 441
462 442
463 443
464 444
465 445
466 446
467 447
468 448
469 449
470 450
471 451
472 452
473 453
474 454
475 455
476 456
477 457
478 458
479 459
480 460
481 461
482 462
483 463
484 464
485 467
486 468
487 469
488 470
489 471
490 472
< >
page |< < (458) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1073" type="section" level="1" n="643">
          <pb o="458" file="0478" n="478" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s11713" xml:space="preserve">Huius demoſtratio non erit alia à demoſtratione 13. </s>
            <s xml:id="echoid-s11714" xml:space="preserve">huius,
              <lb/>
            propterea ibi recolatur.</s>
            <s xml:id="echoid-s11715" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1074" type="section" level="1" n="644">
          <head xml:id="echoid-head674" xml:space="preserve">THEOREMA XIX. PROPOS. XIX.</head>
          <p>
            <s xml:id="echoid-s11716" xml:space="preserve">PRimi circuli ſpatium helicum ad ſpatium helicum ſe-
              <lb/>
            cundi circuli erit, vt tertia pars quadrati radij primi
              <lb/>
            circuli ad rectangulum ſub rad io primi, & </s>
            <s xml:id="echoid-s11717" xml:space="preserve">ſecundi circuli,
              <lb/>
            vna cum tertia parte quadrati exceſſus radij ſecundi circu-
              <lb/>
            li ſuper radium primi. </s>
            <s xml:id="echoid-s11718" xml:space="preserve">Spatium verò ſecundi circuli ad
              <lb/>
            ſpatium tertij erit, vt rectangulum ſub radio eiuſdem, & </s>
            <s xml:id="echoid-s11719" xml:space="preserve">
              <lb/>
            ſub radio circuli vnitate minoris, ideſt primi, vna cum ter-
              <lb/>
            tia parte quadrati differentiæ horum radiorũ, ad rectangu-
              <lb/>
            lum ſub radio eiuſdem, & </s>
            <s xml:id="echoid-s11720" xml:space="preserve">ſub radio circuli vnitate maio-
              <lb/>
            ris, ideſt tertij, vna cum tertia parte quadrati differentiæ
              <lb/>
            iſtorum radiorum, & </s>
            <s xml:id="echoid-s11721" xml:space="preserve">ſic deinceps in reliquis.</s>
            <s xml:id="echoid-s11722" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11723" xml:space="preserve">Exponantur ſuper eodem centro, A, circuli, primus, HRVO,
              <lb/>
            ſecundus, kLNM, tertius autem, CDFB, cum ſpatijs ſub ſpirali-
              <lb/>
            bus eiuſdem numeri cum circulis, primo, AGHA, ſecundo, HPK
              <lb/>
            MH, tertio autem, MZSBM. </s>
            <s xml:id="echoid-s11724" xml:space="preserve">Dico ſpatium primum ad ſecundũ
              <lb/>
            eſſe vt {1/3}. </s>
            <s xml:id="echoid-s11725" xml:space="preserve">quadrati HA, ad rectangulum ſub, HA, AM, vna cum {1/3}.
              <lb/>
            </s>
            <s xml:id="echoid-s11726" xml:space="preserve">quadrati, HM, ſecundum verò ad tertium eſſe vt rectangulum ſub,
              <lb/>
            HA, AM, cum {1/3}. </s>
            <s xml:id="echoid-s11727" xml:space="preserve">quadrati, HM, ad rectangulum ſub, MA, AB,
              <lb/>
            vna cum {1/5}. </s>
            <s xml:id="echoid-s11728" xml:space="preserve">quadrati, MB. </s>
            <s xml:id="echoid-s11729" xml:space="preserve">Nam ſpatium, AGH, ad ſpatium, HP
              <lb/>
            kM, habet rationem compoſita ex ratione ſpatij, AGH, ad cir-
              <lb/>
            culum, OVRH, ideſt ex ratione {1/3}. </s>
            <s xml:id="echoid-s11730" xml:space="preserve">quadrati, HA, ad quadratum,
              <lb/>
              <note position="left" xlink:label="note-0478-01" xlink:href="note-0478-01a" xml:space="preserve">9. huius.</note>
            HA, & </s>
            <s xml:id="echoid-s11731" xml:space="preserve">ex ratione circuli, OVRH, ad circulum, MkLN, ideſt ex
              <lb/>
            ratione quadrati, HA, ad quadratum, AM, & </s>
            <s xml:id="echoid-s11732" xml:space="preserve">ex ratione circuli, C
              <lb/>
              <note position="left" xlink:label="note-0478-02" xlink:href="note-0478-02a" xml:space="preserve">Coroll. 2.
                <lb/>
              11. l. 3.
                <lb/>
              15. huius.
                <lb/>
              Defin. 12.
                <lb/>
              l. 1.</note>
            DFB, ad ſpatium, HPMH, ideſt ex ratione quadrati, MA, ad re-
              <lb/>
            ctangulum, MAH, vna cum {1/3}. </s>
            <s xml:id="echoid-s11733" xml:space="preserve">quadrati, MH, quæ rationes com-
              <lb/>
            ponunt rationem {1/3}. </s>
            <s xml:id="echoid-s11734" xml:space="preserve">quadrati, AH, ad rectangulum, MAH, cum
              <lb/>
            {1/3}. </s>
            <s xml:id="echoid-s11735" xml:space="preserve">quadrati, HM. </s>
            <s xml:id="echoid-s11736" xml:space="preserve">Item ſpatium, HPMH, ad ſpatium, MZSBM,
              <lb/>
            habet rationem compoſitam ex ratione ſpatij, HPMH, ad circu-
              <lb/>
            lum, kLNM, ideſt ex ratione rectanguli, HAM, cum {1/3}. </s>
            <s xml:id="echoid-s11737" xml:space="preserve">quadrati,
              <lb/>
              <note position="left" xlink:label="note-0478-03" xlink:href="note-0478-03a" xml:space="preserve">15. huiu.</note>
            HM, ad quadratum, AM, & </s>
            <s xml:id="echoid-s11738" xml:space="preserve">ex ratione circuli, kLNM, ad circu-
              <lb/>
            lum, CDFB, ideſt quadrati, MA, ad quadratum, AB, & </s>
            <s xml:id="echoid-s11739" xml:space="preserve">tandem
              <lb/>
              <note position="left" xlink:label="note-0478-04" xlink:href="note-0478-04a" xml:space="preserve">Coroll. 2.
                <lb/>
              11. l. 3.
                <lb/>
              15. huius.</note>
            ex ratione circuli, CDFB, ad ſpatium, MZSBM, ideſt ex ratione
              <lb/>
            quadrati, BA, ad rectangulum, BAM, cum {1/3}. </s>
            <s xml:id="echoid-s11740" xml:space="preserve">quadrati, MB, </s>
          </p>
        </div>
      </text>
    </echo>
Impressum