Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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          <p>
            <s xml:id="echoid-s6800" xml:space="preserve">
              <pb o="62" file="0246" n="246" rhead=""/>
            E P K, minor S P Y, & </s>
            <s xml:id="echoid-s6801" xml:space="preserve">in quauis figura ad E verticem màioris axis interio-
              <lb/>
            rem ſectionem contingat recta A E C, quæ ad vtranque partem exterioris
              <lb/>
            pertinget, ac bifariam ſecabitur in E. </s>
            <s xml:id="echoid-s6802" xml:space="preserve">Dico ipſam A E C eſſe
              <note symbol="a" position="left" xlink:label="note-0246-01" xlink:href="note-0246-01a" xml:space="preserve">Coroll.
                <lb/>
              45. huius.</note>
            exteriori ſectioni applicatarum, atque interiorem contingentium. </s>
            <s xml:id="echoid-s6803" xml:space="preserve">Et in El-
              <lb/>
            lipſibus contingentem R S T ad verticem minoris axis eſſe _MAXIMAM_.</s>
            <s xml:id="echoid-s6804" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6805" xml:space="preserve">Sit quæcunque alia contingens L D M ad punctum D, quæ item exte-
              <lb/>
            riori ſectioui occurret in L, M, & </s>
            <s xml:id="echoid-s6806" xml:space="preserve">bifariam ſecabitur in D, & </s>
            <s xml:id="echoid-s6807" xml:space="preserve">per D
              <note symbol="b" position="left" xlink:label="note-0246-02" xlink:href="note-0246-02a" xml:space="preserve">ibidem.</note>
            tur H D I ipſi A E C æquidiſtans, exteriori occurrens in H, I. </s>
            <s xml:id="echoid-s6808" xml:space="preserve">Et cum in
              <lb/>
            ſectione A B C per punctum D intra ipſam ſumptum, ſint duæ H D I, L D
              <lb/>
            M, quarum prima maiori axi B G eſt perpendicularis, altera verò inclina-
              <lb/>
            ta, erit rectangulum H D I minus rectangulo L D M, (cum ipſum H D I ſit
              <lb/>
            _MINIMVM_ ) ſed H D I æquatur quadrato A E, ergo quadratum A
              <note symbol="c" position="left" xlink:label="note-0246-03" xlink:href="note-0246-03a" xml:space="preserve">33. 34. h.</note>
              <note symbol="d" position="left" xlink:label="note-0246-04" xlink:href="note-0246-04a" xml:space="preserve">46. h.</note>
              <figure xlink:label="fig-0246-01" xlink:href="fig-0246-01a" number="202">
                <image file="0246-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0246-01"/>
              </figure>
            minus erit rectangulo L D M, ſiue quadrato L D, & </s>
            <s xml:id="echoid-s6809" xml:space="preserve">quadruplum quadru-
              <lb/>
            plo minus, hoc eſt quadratum A C minus quadrato L M, ſiue contingens
              <lb/>
            linea A C minor contingente A M, & </s>
            <s xml:id="echoid-s6810" xml:space="preserve">hoc ſemper, vbicunque contingat
              <lb/>
            obliqua A M: </s>
            <s xml:id="echoid-s6811" xml:space="preserve">quare A E C erit _MINIMA_ interiorem ſectionem contin-
              <lb/>
            gentium. </s>
            <s xml:id="echoid-s6812" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s6813" xml:space="preserve">c.</s>
            <s xml:id="echoid-s6814" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6815" xml:space="preserve">Iam, ducta ſit per D, recta V D X æquidiſtans contingenti R S T. </s>
            <s xml:id="echoid-s6816" xml:space="preserve">Et cum
              <lb/>
            in Ellipſi A B C ſit per punctum D recta V D X minori axi O Q perpendi-
              <lb/>
            cularis, ſitq; </s>
            <s xml:id="echoid-s6817" xml:space="preserve">alia obliqua L D M; </s>
            <s xml:id="echoid-s6818" xml:space="preserve">erit rectangulum V D X maius rectangulo
              <lb/>
            L D M (cum V D X ſit _MAXIMVM_) ſed V D X æquatur quadrato R
              <note symbol="e" position="left" xlink:label="note-0246-05" xlink:href="note-0246-05a" xml:space="preserve">34. h.</note>
              <note symbol="f" position="left" xlink:label="note-0246-06" xlink:href="note-0246-06a" xml:space="preserve">46. h.</note>
            quare quadratum R S maius erit rectangulo L D M, ſiue quadrato L D, & </s>
            <s xml:id="echoid-s6819" xml:space="preserve">
              <lb/>
            quadruplum quadruplo maius, hoc eſt quadratum R T maius quadrato L
              <lb/>
            M, hoc eſt linea R T maior linea R M, & </s>
            <s xml:id="echoid-s6820" xml:space="preserve">hoc ſemper de qualibet contin-
              <lb/>
            gente inter S, & </s>
            <s xml:id="echoid-s6821" xml:space="preserve">E, quare ipſa R T erit _MAXIMA_ interiorem Ellipſim
              <lb/>
            contingentium. </s>
            <s xml:id="echoid-s6822" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s6823" xml:space="preserve"/>
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