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

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          <p>
            <s xml:id="echoid-s5884" xml:space="preserve">
              <pb o="30" file="0212" n="212" rhead=""/>
            P A, & </s>
            <s xml:id="echoid-s5885" xml:space="preserve">rectangulum R P Q inter ſe ſunt æqualia, ſed eſt A P ipſi Q R
              <lb/>
            perpendicularis, ergo angulus Q A R rectus erit, pariterque is qui ei
              <note symbol="a" position="left" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">203. Se-
                <lb/>
              pt. Pappi.</note>
            inceps Q A F. </s>
            <s xml:id="echoid-s5886" xml:space="preserve">Quare perpendicularis F A erit _MINIMA_ quæſita. </s>
            <s xml:id="echoid-s5887" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">10. h.</note>
            faciendum erat.</s>
            <s xml:id="echoid-s5888" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div610" type="section" level="1" n="244">
          <head xml:id="echoid-head252" xml:space="preserve">PROBL. III. PROP. XXIII.</head>
          <p>
            <s xml:id="echoid-s5889" xml:space="preserve">A dato puncto, ad datæ Ellipſis peripheriam, MAXIMAM,
              <lb/>
            & </s>
            <s xml:id="echoid-s5890" xml:space="preserve">MINIMAM rectam lineam ducere.</s>
            <s xml:id="echoid-s5891" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5892" xml:space="preserve">SIt data Ellipſis A B C D, cuius centrum E, axis minor A C, maior B
              <lb/>
            D, rectum latus B F, & </s>
            <s xml:id="echoid-s5893" xml:space="preserve">datum punctum ſit G. </s>
            <s xml:id="echoid-s5894" xml:space="preserve">Oportet ex G, ad
              <lb/>
            peripheriam A B C, _MAXIMAM_, & </s>
            <s xml:id="echoid-s5895" xml:space="preserve">_MINIMAM_ rectam lineam ducere.</s>
            <s xml:id="echoid-s5896" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5897" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5898" xml:space="preserve">Si primò datum punctum congruit cum centro E: </s>
            <s xml:id="echoid-s5899" xml:space="preserve">duo maiores ſemi-
              <lb/>
            -axes E B, E D, erunt _MAXIMAE_, duo verò ſemi- axes minores E A,
              <lb/>
              <note symbol="c" position="left" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">86. primi
                <lb/>
              huius.</note>
            E C erunt _MINIMAE_.</s>
            <s xml:id="echoid-s5900" xml:space="preserve"/>
          </p>
          <figure number="175">
            <image file="0212-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0212-01"/>
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            <s xml:id="echoid-s5901" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5902" xml:space="preserve">Si datum punctum fuerit in vertice B maioris axis; </s>
            <s xml:id="echoid-s5903" xml:space="preserve">ipſæ maior axis
              <lb/>
            B D erit _MAXIMA_ ducibilium ex B, &</s>
            <s xml:id="echoid-s5904" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5905" xml:space="preserve">Nam ſi concipiatur deſcriptus
              <lb/>
            circulus B H D I ex radio E B, hoc eſt circa diametrum B D, eius peri-
              <lb/>
            pheria cadet tota extra peripheriam Ellipſis A B C D; </s>
            <s xml:id="echoid-s5906" xml:space="preserve">& </s>
            <s xml:id="echoid-s5907" xml:space="preserve">cum B D
              <note symbol="d" position="left" xlink:label="note-0212-04" xlink:href="note-0212-04a" xml:space="preserve">ex 26.
                <lb/>
              pr. huius.</note>
            _MAXIMA_ ad peripheriam circuli, eò ampliùs erit _MAXIMA_ ad inſcri-
              <lb/>
            ptam Ellipſis peripheriam. </s>
            <s xml:id="echoid-s5908" xml:space="preserve">Verùm non dabitur _MINIMA_ ex B, cum ipſa
              <lb/>
            in punctum abeat.</s>
            <s xml:id="echoid-s5909" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5910" xml:space="preserve">3. </s>
            <s xml:id="echoid-s5911" xml:space="preserve">Si autem datum punctum G in eadem prima figura fuerit in axe maio-
              <lb/>
            ri, extra tamen Ellipſim: </s>
            <s xml:id="echoid-s5912" xml:space="preserve">tota G D erit _MAXIMA_: </s>
            <s xml:id="echoid-s5913" xml:space="preserve">eſt enim _MAXIMA_
              <lb/>
            ad peripheriam circuli B H D I, cum in ea ſit centrum, ergo ad periphe-
              <lb/>
            riam inſcriptæ Ellipſis omnino _MAXIMA_ erit. </s>
            <s xml:id="echoid-s5914" xml:space="preserve">G B verò erit
              <note symbol="e" position="left" xlink:label="note-0212-05" xlink:href="note-0212-05a" xml:space="preserve">10. h.</note>
            cum ipſa G B ſit extra Ellipſim perpendicularis ad rectum B F, quod ad
              <lb/>
            B contingit Ellipſim.</s>
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