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

List of thumbnails

< >
541
541 (521) 		542
542 (522)
543
543 (523) 		544
544 (524)
545
545 (525) 		546
546 (526)
547
547 (527) 		548
548 (528)
549
549 (529) 		550
550 (530)
< >
page |< < (530) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div1224" type="section" level="1" n="737">
          <p>
            <s xml:id="echoid-s13701" xml:space="preserve">
              <pb o="530" file="0550" n="550" rhead="GEOMETRIÆ"/>
            illæ non aliam mutationem, quam prædictam in ſuis demonſtra-
              <lb/>
            tionibus, popoſcere videbuntur. </s>
            <s xml:id="echoid-s13702" xml:space="preserve">Quoad regulas autem, iuxta
              <lb/>
            quas dicimus ſolida rectangula contineri, poterimus etiam vice
              <lb/>
            duarum vnam tantum retinere, pro vt in methodo indiuiſibilium
              <lb/>
            effectum eſt, vt ex. </s>
            <s xml:id="echoid-s13703" xml:space="preserve">g. </s>
            <s xml:id="echoid-s13704" xml:space="preserve">in fig. </s>
            <s xml:id="echoid-s13705" xml:space="preserve">huius prop. </s>
            <s xml:id="echoid-s13706" xml:space="preserve">poterat ſufficere ipſa, DF,
              <lb/>
            altera enim regula non alio fungitur offitio, quam determinandi
              <lb/>
            cum priori regula vnum planum, cui plana ſolida rectangula ſecã-
              <lb/>
            tia, ac in illis rectangula plana producentia, æquidiſtant, & </s>
            <s xml:id="echoid-s13707" xml:space="preserve">hoc in
              <lb/>
            antecedentibus effectum eſt, vt clarior ſolidorum rectangulorum
              <lb/>
            deſcripcio haberetur, in poſterum tamen vnam tantum regulam
              <lb/>
            innuemus, alteram tacitè ſubintelligentes, dum præfata vni cuidã
              <lb/>
            eſſe parallela ſemper ſupponere debeamus, erunt autem eædem
              <lb/>
            regulæ, quæ in propoſitionibus infra citandis adhibitæ fuerunt, niſi
              <lb/>
            alias regulas innuendi quandoq; </s>
            <s xml:id="echoid-s13708" xml:space="preserve">neceſſitatem habuerimus.</s>
            <s xml:id="echoid-s13709" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1225" type="section" level="1" n="738">
          <head xml:id="echoid-head771" xml:space="preserve">THEOREMA XVII. PROPOS. XVII.</head>
          <p>
            <s xml:id="echoid-s13710" xml:space="preserve">IN eodem Prop. </s>
            <s xml:id="echoid-s13711" xml:space="preserve">30. </s>
            <s xml:id="echoid-s13712" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s13713" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13714" xml:space="preserve">ſchemate, regula eadem ibi
              <lb/>
            aſſumpta, rectangulum ſolidum ſub, AF, FB, ad rectan-
              <lb/>
            gulum ſolidum ſub trapezio, ADEC, & </s>
            <s xml:id="echoid-s13715" xml:space="preserve">triangulo, BEC,
              <lb/>
            erit vt, DF, ad compoſitam ex, {1/2}. </s>
            <s xml:id="echoid-s13716" xml:space="preserve">DE, & </s>
            <s xml:id="echoid-s13717" xml:space="preserve">{1/3}. </s>
            <s xml:id="echoid-s13718" xml:space="preserve">EF.</s>
            <s xml:id="echoid-s13719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13720" xml:space="preserve">Hæc oſtendetur vtibi, prædicta tantum nominum mutatione
              <lb/>
            facta, vt meditanti innoteſcet.</s>
            <s xml:id="echoid-s13721" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1226" type="section" level="1" n="739">
          <head xml:id="echoid-head772" xml:space="preserve">THEOREMA XVIII PROPOS. XVIII.</head>
          <p>
            <s xml:id="echoid-s13722" xml:space="preserve">IN ſchemate Prop. </s>
            <s xml:id="echoid-s13723" xml:space="preserve">3 I. </s>
            <s xml:id="echoid-s13724" xml:space="preserve">eiuſdem Lib. </s>
            <s xml:id="echoid-s13725" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13726" xml:space="preserve">regula eadem,
              <lb/>
            rectangulum ſolidum ſub, AO, OB, ad rectangulum ſo-
              <lb/>
            lidum ſub trapezijs, HACN, MBCN, eſt vt rectangulum,
              <lb/>
            HOM, ad rectangulum ſub, HO, MN, cum rectangulo ſub
              <lb/>
            compoſito ex {1/2}. </s>
            <s xml:id="echoid-s13727" xml:space="preserve">HM, & </s>
            <s xml:id="echoid-s13728" xml:space="preserve">@. </s>
            <s xml:id="echoid-s13729" xml:space="preserve">NO, & </s>
            <s xml:id="echoid-s13730" xml:space="preserve">ſub, NO.</s>
            <s xml:id="echoid-s13731" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13732" xml:space="preserve">Hæc ſimiliter vt antecedens expedietur.</s>
            <s xml:id="echoid-s13733" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1227" type="section" level="1" n="740">
          <head xml:id="echoid-head773" xml:space="preserve">THEOREMA XIX. PROPOS. XIX.</head>
          <p>
            <s xml:id="echoid-s13734" xml:space="preserve">IN ſchemate Prop. </s>
            <s xml:id="echoid-s13735" xml:space="preserve">32. </s>
            <s xml:id="echoid-s13736" xml:space="preserve">Lib. </s>
            <s xml:id="echoid-s13737" xml:space="preserve">2. </s>
            <s xml:id="echoid-s13738" xml:space="preserve">ſimiliter regula eadem
              <lb/>
            retenta, rectangulum ſolidum ſub, AE, ER, ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum