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

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          <p>
            <s xml:id="echoid-s5205" xml:space="preserve">
              <pb o="3" file="0185" n="185" rhead=""/>
            B D maior D H) erit rectangulum ſub recto C B in ſegmentum B H
              <lb/>
            ſiue quadrarum G H, maius rectangulo ſub aggregato B D cum D H,
              <note symbol="a" position="right" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">Coroll.
                <lb/>
              primę pri.
                <lb/>
              mi huius.</note>
            idem ſegmentum B H, quibus addito communi quadrato D H, erit qua-
              <lb/>
            dratum G H cum H D quadrato, ſiue vnicum quadratum G D, maius re-
              <lb/>
            ctangulo ſub aggregato B D cum D H in B H. </s>
            <s xml:id="echoid-s5206" xml:space="preserve">vnà cum quadrato D H,
              <lb/>
            ſiue maius vnico quadrato B D, hoc eſt linea D G maior erit D B. </s>
            <s xml:id="echoid-s5207" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-0185-02" xlink:href="note-0185-02a" xml:space="preserve">1. h.</note>
            ergo D B _MINIMA_ ducibilium ad Parabolæ peripheriam ex axis puncto
              <lb/>
            D, quod abeſt à vertice per interuallum non maius dimidio recti lateris
              <lb/>
            B C. </s>
            <s xml:id="echoid-s5208" xml:space="preserve">Quod primò demonſtrandum erat.</s>
            <s xml:id="echoid-s5209" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5210" xml:space="preserve">Præterea ſit quæpiam alia D M maiorem eſſiciens angulum cum _MI-_
              <lb/>
            _NIMA_ D B, quàm D G, & </s>
            <s xml:id="echoid-s5211" xml:space="preserve">ex M applicetur M N. </s>
            <s xml:id="echoid-s5212" xml:space="preserve">Iam quadratum M N
              <lb/>
            ſuperat quadratum G H eo exceſſu, quo rectangulum C B N ſuperat re-
              <lb/>
            ctangulum C B H, (ob æqualitatem) hoc eſt rectangulo ſub recto C
              <note symbol="c" position="right" xlink:label="note-0185-03" xlink:href="note-0185-03a" xml:space="preserve">Coroll.
                <lb/>
              primę pri
                <lb/>
              mi huius.</note>
            in H N, ſed quadratum D H ſuperat quadratum D N rectangulo ſub ea- dem H N, & </s>
            <s xml:id="echoid-s5213" xml:space="preserve">ſub aggregato H D cum D N, quod aggregatum, ex hypo-
              <lb/>
              <note symbol="d" position="right" xlink:label="note-0185-04" xlink:href="note-0185-04a" xml:space="preserve">1. h.</note>
            teſi, minus eſt ipſo recto B C, ergo exceſſus quadrati M N ſupra quadra-
              <lb/>
            tum G H, maior eſt exceſſu quadrati H D ſupra D N, vnde aggregatum
              <lb/>
            extremorum quadratorum M N, N D, ſiue vnicum quadratum MD, ma-
              <lb/>
            ius erit aggregato quadratorum mediorum G H, H D, ſiue vnico
              <note symbol="e" position="right" xlink:label="note-0185-05" xlink:href="note-0185-05a" xml:space="preserve">2. h.</note>
            drato G D, hoc eſt linea D M maior D G.</s>
            <s xml:id="echoid-s5214" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5215" xml:space="preserve">Vlteriùs, quadratum A D ſuperat quadratum M N rectangulo ſub D N,
              <lb/>
            & </s>
            <s xml:id="echoid-s5216" xml:space="preserve">recto B C, & </s>
            <s xml:id="echoid-s5217" xml:space="preserve">quadratum D M, ſuperat idem quadratum M N quadra-
              <lb/>
            to D N, quod eſt minus prædicto rectangulo ſub D N, & </s>
            <s xml:id="echoid-s5218" xml:space="preserve">recto C B, qua-
              <lb/>
            re exceſſus quadrati A D ſupra M N, maior eſt exceſſu quadrati D M,
              <lb/>
            ſupra idem quadratum M N; </s>
            <s xml:id="echoid-s5219" xml:space="preserve">quapropter A D quadratum maius eſt qua-
              <lb/>
            drato D M, ſiue linea A D maior ipſa D M.</s>
            <s xml:id="echoid-s5220" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5221" xml:space="preserve">Tandem ducta quacunque D O infra D E, agatur ex E recta E L ęqui-
              <lb/>
            diſtans ad B D. </s>
            <s xml:id="echoid-s5222" xml:space="preserve">Cum angulus B D E ſit obtuſus, erit quoque parallela-
              <lb/>
            rum alternus D E L obtuſus, ideoque in triangulo D E L angulus D L E
              <lb/>
            acutus, ſiue minor angulo D E L: </s>
            <s xml:id="echoid-s5223" xml:space="preserve">quare latus D E minus latere D L, & </s>
            <s xml:id="echoid-s5224" xml:space="preserve">
              <lb/>
            eò minus educta D O. </s>
            <s xml:id="echoid-s5225" xml:space="preserve">Vnde quæ minorem cum _MINIMA_ conſtituit an-
              <lb/>
            gulum minor eſt, &</s>
            <s xml:id="echoid-s5226" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5227" xml:space="preserve">Quod omnino oſtendere propoſitum fuit.</s>
            <s xml:id="echoid-s5228" xml:space="preserve"/>
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        <div xml:id="echoid-div534" type="section" level="1" n="222">
          <head xml:id="echoid-head230" xml:space="preserve">LEMMA III. PROP. IV.</head>
          <p>
            <s xml:id="echoid-s5229" xml:space="preserve">Si inter latera parallela AD, BC, menſalis ABCD rectangulę ad
              <lb/>
            B, ducta fuerit quædam linea EH ipſis lateribus æquidiſtans, ſitq;
              <lb/>
            </s>
            <s xml:id="echoid-s5230" xml:space="preserve">AD minor BC. </s>
            <s xml:id="echoid-s5231" xml:space="preserve">Dico rectangulum ABC, ſuperare rectangulum
              <lb/>
            AEH maiori exceſſu, quàm ſit rectangulum EBC.</s>
            <s xml:id="echoid-s5232" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5233" xml:space="preserve">COmpletis enim rectãgulis EG, BF, EC;
              <lb/>
            </s>
            <s xml:id="echoid-s5234" xml:space="preserve">
              <figure xlink:label="fig-0185-01" xlink:href="fig-0185-01a" number="146">
                <image file="0185-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0185-01"/>
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            patet rectangulum ABC ſuperare re-
              <lb/>
            ctangulum AEH gnomone ECG, ſed gno-
              <lb/>
            mon ECG maios eſt rectangulo EBC, vnde
              <lb/>
            rectangulum ABC, ſuperat rectangulum A
              <lb/>
            EH maiori quantitate quàm ſit rectãgulum
              <lb/>
            EBC. </s>
            <s xml:id="echoid-s5235" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s5236" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5237" xml:space="preserve"/>
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