Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
page |< < (246) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div593" type="section" level="1" n="346">
          <p>
            <s xml:id="echoid-s6093" xml:space="preserve">
              <pb o="246" file="0266" n="266" rhead="GEOMETRIÆ"/>
            V. </s>
            <s xml:id="echoid-s6094" xml:space="preserve">regula, FM, .</s>
            <s xml:id="echoid-s6095" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6096" xml:space="preserve">ex ea, quam habet reſiduum rectangulum Theor.
              <lb/>
            </s>
            <s xml:id="echoid-s6097" xml:space="preserve">antecedentis ad quadratum, FM, & </s>
            <s xml:id="echoid-s6098" xml:space="preserve">ex ratione omnium quadrato-
              <lb/>
              <note position="left" xlink:label="note-0266-01" xlink:href="note-0266-01a" xml:space="preserve">Ex antec.</note>
            rum, Δ V, regula, FM, ad omnia quadrata eiuſdem, Δ V, regula,
              <lb/>
            R V, .</s>
            <s xml:id="echoid-s6099" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6100" xml:space="preserve">ex ea, quam habet, Δ R, ad, RV, vel, ſumpta, Δ R, com-
              <lb/>
              <note position="left" xlink:label="note-0266-02" xlink:href="note-0266-02a" xml:space="preserve">29. l. 2.</note>
            muni altitudine ex ea, quam habet quadratum, Δ R, vel quadra-
              <lb/>
              <figure xlink:label="fig-0266-01" xlink:href="fig-0266-01a" number="164">
                <image file="0266-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0266-01"/>
              </figure>
            tum, FM, ad rectangulum ſub, FM,
              <lb/>
            R V; </s>
            <s xml:id="echoid-s6101" xml:space="preserve">& </s>
            <s xml:id="echoid-s6102" xml:space="preserve">tandem ex ea, quam habent
              <lb/>
              <note position="left" xlink:label="note-0266-03" xlink:href="note-0266-03a" xml:space="preserve">1. huius.</note>
            omnia quadrata, Δ V, ad omnia qua-
              <lb/>
            drata portionis, RFV, .</s>
            <s xml:id="echoid-s6103" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6104" xml:space="preserve">ex ea, quam
              <lb/>
            habet, MH, ad compoſitam ex, {1/2}, M
              <lb/>
            H, &</s>
            <s xml:id="echoid-s6105" xml:space="preserve">, {1/6}, FM. </s>
            <s xml:id="echoid-s6106" xml:space="preserve">Rationes autem re-
              <lb/>
            ctanguli reſidui Theor.</s>
            <s xml:id="echoid-s6107" xml:space="preserve">antecedentis ad
              <lb/>
              <note position="left" xlink:label="note-0266-04" xlink:href="note-0266-04a" xml:space="preserve">Defin. 12.
                <lb/>
              l. 1.</note>
            quadratum, FM, & </s>
            <s xml:id="echoid-s6108" xml:space="preserve">quadrati, FM,
              <lb/>
            ad rectangulum ſub, FM, RV, re-
              <lb/>
            ſoluuntur in rationem rectanguli reſi-
              <lb/>
            dui Theor. </s>
            <s xml:id="echoid-s6109" xml:space="preserve">antecedentis ad rectangu-
              <lb/>
            lum ſub, FM, RV, quę iuncta rationi
              <lb/>
            ipſius, MH, ad compoſitam ex, {1/2}, M
              <lb/>
              <note position="left" xlink:label="note-0266-05" xlink:href="note-0266-05a" xml:space="preserve">G. Cor. 4.
                <lb/>
              gen. 34.
                <lb/>
              l. 2.</note>
            H, &</s>
            <s xml:id="echoid-s6110" xml:space="preserve">, {1/6}, FM, cõponit rationem paral-
              <lb/>
            lelepipedi ſub baſi reſiduo rectangulo
              <lb/>
            Theor. </s>
            <s xml:id="echoid-s6111" xml:space="preserve">antecedentis, altitudine, MH,
              <lb/>
            ad parallelepipedum ſub baſi rectan-
              <lb/>
            gulo ſub, FM, RV, & </s>
            <s xml:id="echoid-s6112" xml:space="preserve">ſub compoſita
              <lb/>
            ex, {1/2}, MH, &</s>
            <s xml:id="echoid-s6113" xml:space="preserve">, {1/6}, FM: </s>
            <s xml:id="echoid-s6114" xml:space="preserve">Triplicentur
              <lb/>
            horum parallelepipedoru altitudines,
              <lb/>
            ſiet pro an ecedentis altitudine tripla,
              <lb/>
            M H, & </s>
            <s xml:id="echoid-s6115" xml:space="preserve">pro altitudine parallelepipedi conſequentis tripla dimidiæ,
              <lb/>
            M H,.</s>
            <s xml:id="echoid-s6116" xml:space="preserve">. ſexquialtera ipſius, MH, . </s>
            <s xml:id="echoid-s6117" xml:space="preserve">. </s>
            <s xml:id="echoid-s6118" xml:space="preserve">ſexquialtera, MI, & </s>
            <s xml:id="echoid-s6119" xml:space="preserve">ſexquial
              <lb/>
            tera, IH, cum, {1/2}, FM, porro ſi ſexquialterę, MI, iunxeris ſexqui-
              <lb/>
            alteram, IH, cum dimidia, FM, .</s>
            <s xml:id="echoid-s6120" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6121" xml:space="preserve">duplam, IH, quoniam ſex-
              <lb/>
            quialtera, IH, eſt, MI, IN, ſi inquam illi iunxeris bis, IH, com-
              <lb/>
            ponetur altitudo conſequentis parailelepipedi, quę erit, MH, HN;
              <lb/>
            </s>
            <s xml:id="echoid-s6122" xml:space="preserve">omnia ergo quadrata portionis, RFV, regula, FM, ad omnia qua-
              <lb/>
            drata eiuſdem, regula, RV, erunt vt parallelepipedum ſub bafi re-
              <lb/>
            ſiduo rectangulo Theor. </s>
            <s xml:id="echoid-s6123" xml:space="preserve">antecedentis, altitudine tripla, MH, ad
              <lb/>
            parallelepipedum ſub baſi rectangulo, ſub, FM, RV, altitudine li-
              <lb/>
            nea compoſita ex, MH, HN, tum in circuli, tum ellipſis figura,
              <lb/>
            quod oſtendere oportebat.</s>
            <s xml:id="echoid-s6124" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum