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

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            <s xml:id="echoid-s5706" xml:space="preserve">
              <pb o="23" file="0205" n="205" rhead=""/>
            ſed E H, G F ſunt etiam parallelæ, ergo, & </s>
            <s xml:id="echoid-s5707" xml:space="preserve">E G æquidiſtat H F, ſed A
              <lb/>
            B quoque ipſi H F æquidiſtat, vt modò oſtendimus: </s>
            <s xml:id="echoid-s5708" xml:space="preserve">quare A B, & </s>
            <s xml:id="echoid-s5709" xml:space="preserve">E G
              <lb/>
            ſunt inter ſe parallelæ. </s>
            <s xml:id="echoid-s5710" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s5711" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5712" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div591" type="section" level="1" n="240">
          <head xml:id="echoid-head248" xml:space="preserve">PROBL. I. PROP. XX.</head>
          <p>
            <s xml:id="echoid-s5713" xml:space="preserve">A dato puncto, ad datæ Parabolę peripheriam, MINIMAM
              <lb/>
            rectam lineam ducere.</s>
            <s xml:id="echoid-s5714" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5715" xml:space="preserve">SIt data Parabole A B C, cuius axis B D, vertex B, rectum latus B E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5716" xml:space="preserve">datum vbicunque punctum ſit F. </s>
            <s xml:id="echoid-s5717" xml:space="preserve">Oportet ex F ad peripheriam
              <lb/>
            A B C, _MINIMAM_ rectam lineam ducere.</s>
            <s xml:id="echoid-s5718" xml:space="preserve"/>
          </p>
          <figure number="165">
            <image file="0205-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0205-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s5719" xml:space="preserve">Eſto primùm datum punctum F extra
              <lb/>
            Parabolen in axe producto, vt in prima
              <lb/>
            figura. </s>
            <s xml:id="echoid-s5720" xml:space="preserve">Dico ipſam F B eſſe _MINIMAM_.</s>
            <s xml:id="echoid-s5721" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5722" xml:space="preserve">Nam cum B D ſit axis Parabolæ, ſi ex
              <lb/>
            B ducatur B G ordinatis æquidiſtans, ipſa
              <lb/>
            cum F D rectos angulos efficiet, ac Para-
              <lb/>
              <note symbol="a" position="right" xlink:label="note-0205-01" xlink:href="note-0205-01a" xml:space="preserve">32. pri-
                <lb/>
              mi conic.</note>
            bolen continget. </s>
            <s xml:id="echoid-s5723" xml:space="preserve">Cum ergo B F perpen- dicularis ſit contingenti B G, erit F B _MI_-
              <lb/>
            _MIMA_ omnium, quæ ex F ad
              <note symbol="b" position="right" xlink:label="note-0205-02" xlink:href="note-0205-02a" xml:space="preserve">10. h.</note>
            riam A B C educi poſſunt. </s>
            <s xml:id="echoid-s5724" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s5725" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5726" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5727" xml:space="preserve">Si verò datum punctum F, in ſecunda
              <lb/>
            figura, fuerit in ipſo axe B D intra Para-
              <lb/>
            bolen A B C, quod diſtet à vertice B, per
              <lb/>
            interuallum non maius dimidio recti B E, idem axis ſegmentum F B erit
              <lb/>
            _MINIMA_ recta quæſita.</s>
            <s xml:id="echoid-s5728" xml:space="preserve"/>
          </p>
          <note symbol="c" position="right" xml:space="preserve">9. hulus
            <lb/>
          ad nu. h.</note>
          <p>
            <s xml:id="echoid-s5729" xml:space="preserve">Si autem datum punctum F in eadem fi-
              <lb/>
              <figure xlink:label="fig-0205-02" xlink:href="fig-0205-02a" number="166">
                <image file="0205-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0205-02"/>
              </figure>
            gura ſit in axe B D, ſed interuallum F B
              <lb/>
            maius ſit dimidio recti B E. </s>
            <s xml:id="echoid-s5730" xml:space="preserve">Secetur F G
              <lb/>
            æqualis eidem dimidio, & </s>
            <s xml:id="echoid-s5731" xml:space="preserve">applicetut G A
              <lb/>
            peripheriæ occurrens in A. </s>
            <s xml:id="echoid-s5732" xml:space="preserve">Dico iunctam
              <lb/>
            F A eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s5733" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5734" xml:space="preserve">Ducta enim ex A contingente A
              <note symbol="d" position="right" xlink:label="note-0205-04" xlink:href="note-0205-04a" xml:space="preserve">2. pr. h.</note>
            ipſa cum axe producta conueniet in H;</s>
            <s xml:id="echoid-s5735" xml:space="preserve">
              <note symbol="e" position="right" xlink:label="note-0205-05" xlink:href="note-0205-05a" xml:space="preserve">24. pri-
                <lb/>
              mi conic.</note>
            eritque H B ęqualis B G, ſiue H G
              <note symbol="f" position="right" xlink:label="note-0205-06" xlink:href="note-0205-06a" xml:space="preserve">35. ibid.</note>
            G B, eſtque E B dupla G F, ex conſtructio-
              <lb/>
            ne, ergo H G ad G B eſt vt E B ad G F; </s>
            <s xml:id="echoid-s5736" xml:space="preserve">ex
              <lb/>
            quo rectangulum H G F æquabitur rectan-
              <lb/>
            gulo E B G, ſiue quadrato G A; </s>
            <s xml:id="echoid-s5737" xml:space="preserve">
              <note symbol="g" position="right" xlink:label="note-0205-07" xlink:href="note-0205-07a" xml:space="preserve">Coroll.
                <lb/>
              pr. 1. h.</note>
            angulus F A H rectus erit. </s>
            <s xml:id="echoid-s5738" xml:space="preserve">Cumque A F ſit ex contactu A Contingenti A H perpendicularis, & </s>
            <s xml:id="echoid-s5739" xml:space="preserve">punctum F ſit in axe, erit F A _MINIMA_
              <note symbol="h" position="right" xlink:label="note-0205-08" xlink:href="note-0205-08a" xml:space="preserve">203. Se-
                <lb/>
              pt. Pappi.</note>
            @ibilium ad Parabolæ peripheriam A B C. </s>
            <s xml:id="echoid-s5740" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s5741" xml:space="preserve">c.</s>
            <s xml:id="echoid-s5742" xml:space="preserve"/>
          </p>
          <note symbol="i" position="right" xml:space="preserve">11. h. ad
            <lb/>
          num. 1.</note>
          <p>
            <s xml:id="echoid-s5743" xml:space="preserve">Si denique datum punctum F ſit extra Parabolen A B C, vt in tertia
              <lb/>
            figura, vel extra, vt in quarta, inter axem B D, & </s>
            <s xml:id="echoid-s5744" xml:space="preserve">peripheriam B A;
              <lb/>
            </s>
            <s xml:id="echoid-s5745" xml:space="preserve">Applicetur ex recta F F G axi occurrens in G, dematurque de axe </s>
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