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

Table of contents

< >
[391.] COROLLARIVM XXIII.
[392.] COROLLARIVM XXIV.
[393.] COROLLARIVM XXV.
[394.] COROLLARIVM XXVI.
[395.] COROLLARIVM XXVII.
[396.] COROLLARIVM XXVIII. SECTIO PRIOR.
[397.] SECTIO POSTERIOR.
[398.] COROLL. XXIX. SECTIO PRIMA.
[399.] SECTIO II.
[400.] SECTIO III.
[401.] SECTIO IV.
[402.] SCHOLIVM.
[403.] Finis Tertij Libri.
[404.] CAVALER II LIBER QVARTVS. In quo de Parabola, & ſolidis ab eadem genitis enucleatur doctrina.
[405.] THEOREMAI. PROPOS. I.
[406.] COROLLARIVM.
[407.] THEOREMA II. PROPOS. II.
[408.] THEOREMA III. PROPOS. III.
[409.] THEOREMA IV. PROPOS. IV.
[410.] COROLLARIVM.
[411.] THEOREMA V. PROPOS. V.
[412.] COROLLARIV M.
[413.] THEOREMA VI. PROPOS. VI.
[414.] COROLLARIV M.
[415.] THEOREMA VII. PROPOS. VII.
[416.] THEOREMA VIII. PROPOS. VIII.
[417.] SCHOLIV M.
[418.] PROBLEMA I. PROPOS. IX.
[419.] THEOREMAIX. PROPOS. X.
[420.] COROLLARIV M.
< >
page |< < (373) of 569 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div900" type="section" level="1" n="538">
          <p>
            <s xml:id="echoid-s9596" xml:space="preserve">
              <pb o="373" file="0393" n="393" rhead="LIBER V."/>
            dempto quadrato, ME, quia verò tripla, BE, eſt compoſita ex, E
              <lb/>
            X, & </s>
            <s xml:id="echoid-s9597" xml:space="preserve">dupla, EN, ſi a rectangulo ſub compoſita ex, EX, & </s>
            <s xml:id="echoid-s9598" xml:space="preserve">dupla,
              <lb/>
            EN, & </s>
            <s xml:id="echoid-s9599" xml:space="preserve">ſub, EM, abſtuleris quadratum, ME, .</s>
            <s xml:id="echoid-s9600" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9601" xml:space="preserve">rectangulum ſub,
              <lb/>
            MF, &</s>
            <s xml:id="echoid-s9602" xml:space="preserve">, ME, remanebit rectangulum ſub compoſita ex ipſa, XE,
              <lb/>
            EN, NM, & </s>
            <s xml:id="echoid-s9603" xml:space="preserve">ſub, EM, illas ergo tres componentes rationes in has
              <lb/>
            duas reſolutas habemus, ſcilicet in eam, quam habet rectangulũ
              <lb/>
            ſub, XEN, integra, & </s>
            <s xml:id="echoid-s9604" xml:space="preserve">ſub, EN, ad rectangulum ſub integra, XE,
              <lb/>
            EN, NM, & </s>
            <s xml:id="echoid-s9605" xml:space="preserve">ſub, ME, & </s>
            <s xml:id="echoid-s9606" xml:space="preserve">in eam, quam habet, NE, ad, EM, quæ
              <lb/>
            duæ rationes componunt rationem parallelepipedi ſub, NE, & </s>
            <s xml:id="echoid-s9607" xml:space="preserve">
              <lb/>
            ſub rectangulo integræ, XEN, ductæ in, EN, ideſt parallelepipe-
              <lb/>
              <note position="right" xlink:label="note-0393-01" xlink:href="note-0393-01a" xml:space="preserve">3.6. .1.</note>
            di ſub integra, XEN, & </s>
            <s xml:id="echoid-s9608" xml:space="preserve">quadrato, NE, ad parallelepipedum ſub,
              <lb/>
            ME, & </s>
            <s xml:id="echoid-s9609" xml:space="preserve">rectangulo integræ, XE, EN, NM, ductæ in, ME, .</s>
            <s xml:id="echoid-s9610" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9611" xml:space="preserve">ad
              <lb/>
            parallelepipedum ſub integra, XE, EN, NM, & </s>
            <s xml:id="echoid-s9612" xml:space="preserve">quadrato, ME,
              <lb/>
            ergo omnia quadrata, AF, demptis omnibus quadratis hyperbo-
              <lb/>
            læ, DNF, ad omnia quadrata, SF, demptis omnibus quadratis
              <lb/>
            fruſti, HDFG, erunt vt parallelepipedum ſub integra, XEN, & </s>
            <s xml:id="echoid-s9613" xml:space="preserve">
              <lb/>
            quadrato, NE, ad parallelepipedum ſub integra, XE, EN, NM,
              <lb/>
            & </s>
            <s xml:id="echoid-s9614" xml:space="preserve">quadrato, ME, quod erat oſtendendum.</s>
            <s xml:id="echoid-s9615" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div902" type="section" level="1" n="539">
          <head xml:id="echoid-head563" xml:space="preserve">PROBLEMA I. PROPOS. VI.</head>
          <p>
            <s xml:id="echoid-s9616" xml:space="preserve">A Data hyperbola portionem abſcindere per lineam
              <lb/>
            ad eiuſdem axim, vel diametrum ordinatim appli-
              <lb/>
            catam, cuius omnia quadrata, regula propoſitæ hyperbo-
              <lb/>
            læ baſi, ad omnia quadrata trianguli in eadem baſi, & </s>
            <s xml:id="echoid-s9617" xml:space="preserve">cir-
              <lb/>
            ca eundem axim, vel diametrum cum portione, ſiue hyper-
              <lb/>
            bola abſciſſa, exiſtentis, habeant datam rationem, quam
              <lb/>
            oportet eſſe quidem maioris inæqualitatis, ſed tamen mi-
              <lb/>
            norem ſexquialtera.</s>
            <s xml:id="echoid-s9618" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9619" xml:space="preserve">Sit ergo data hyperbola, FEG, cuius axis, vel diameter, E M & </s>
            <s xml:id="echoid-s9620" xml:space="preserve">
              <lb/>
            larus tranſuerſum, CE, cuius ſit, AE, ſexquialtera, baſis, & </s>
            <s xml:id="echoid-s9621" xml:space="preserve">regu-
              <lb/>
            la, FG, data ratio, quam habet, HR, ad, RL, maioris inæquali-
              <lb/>
            tatis, ſed minor ſexquialtera, oportet ergo ab hyperbola, FEG,
              <lb/>
            per lineam ad, EM, ordinatim applicatam .</s>
            <s xml:id="echoid-s9622" xml:space="preserve">i. </s>
            <s xml:id="echoid-s9623" xml:space="preserve">baſi, fiue regulæ,
              <lb/>
            FG, parallelam, portionem, ſiue hyperbolam abſcindele, cuius
              <lb/>
            omnia quadrata ad omnia quadrata trianguli in eadem baſi, & </s>
            <s xml:id="echoid-s9624" xml:space="preserve">
              <lb/>
            circa eundem axim, vel diametrum cum ipſa habeant rationem,
              <lb/>
            quam habet, HR, ad, RL; </s>
            <s xml:id="echoid-s9625" xml:space="preserve">quia ergo ratio, HR, ad, RL, eſt mi-
              <lb/>
            nor ſexquialtera, erit minor ea, quam habet, AE, ad, EC, & </s>
            <s xml:id="echoid-s9626" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>