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

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            ſecat Elli pſim datam GBL, _a_ cum & </s>
            <s xml:id="echoid-s1749" xml:space="preserve">iuncta regula EN ſecet regulam FD.
              <lb/>
            </s>
            <s xml:id="echoid-s1750" xml:space="preserve">Quare Ellipſis ABC, erit _MINIMA_ quæſita circumſcripta, cum dato recto
              <lb/>
            BE. </s>
            <s xml:id="echoid-s1751" xml:space="preserve">Quod vltimò, &</s>
            <s xml:id="echoid-s1752" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1753" xml:space="preserve"/>
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        <div xml:id="echoid-div157" type="section" level="1" n="84">
          <head xml:id="echoid-head89" xml:space="preserve">PROBL. XI. PROP. XXVI.</head>
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            <s xml:id="echoid-s1754" xml:space="preserve">Datæ Ellipſi circa minorem axim, per eius verticem MAXI-
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            MVM circulum inſcribere. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">Item.</s>
            <s xml:id="echoid-s1756" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1757" xml:space="preserve">Datæ Ellipſi circa maiorem axim, per eius verticem MINI-
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            MVM circulum circumſcribere.</s>
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            <s xml:id="echoid-s1759" xml:space="preserve">SIt in 1. </s>
            <s xml:id="echoid-s1760" xml:space="preserve">fig. </s>
            <s xml:id="echoid-s1761" xml:space="preserve">data Ellipſis ABC, circa minorem axim BD, cuius rectũ ſit BE,
              <lb/>
            regula DE, & </s>
            <s xml:id="echoid-s1762" xml:space="preserve">oporteat per verticem B _MAXIMVM_ circulum inſcribere.</s>
            <s xml:id="echoid-s1763" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1764" xml:space="preserve">Deſcribatur circulus GBHD, cuius dimetiens ſit BD, quem dico eſſe _MA_-
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            _XIMVM_ quæſitum.</s>
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          <figure number="45">
            <image file="0075-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0075-01"/>
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            <s xml:id="echoid-s1766" xml:space="preserve">Sumpta enim BF æquali BD, erit ipſa rectum latus deſcripti circuli: </s>
            <s xml:id="echoid-s1767" xml:space="preserve">iun-
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            ctaque DF eius regula cum ſit axis minor BD, minor recto latere BE, erit
              <lb/>
            etiam BF minor BE, vnde regula DF cadet intra regulam DE, ideoque cir-
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            culus GBH inſcriptus erit Ellipſi ABC, eritque _MAXIMVS_: </s>
            <s xml:id="echoid-s1768" xml:space="preserve">nam
              <note symbol="a" position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve">1. Co-
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              roll. prop.
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              19. huius.</note>
            alius per B adſcriptus, cuius diameter, minor ſit ipſa BD, minor eſt circulo GBH, & </s>
            <s xml:id="echoid-s1769" xml:space="preserve">cuius diameter BI ſit maior BD eſt quidem maior circulo
              <note symbol="b" position="right" xlink:label="note-0075-02" xlink:href="note-0075-02a" xml:space="preserve">5. Co-
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              rol. prop.
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              19. huius.</note>
            ſed vel ſecat, vel cadit extra Ellipſim ABC, cum punctum I quoque cadat
              <lb/>
            extra. </s>
            <s xml:id="echoid-s1770" xml:space="preserve">Erit ergo GBH _MAXIMVS_ circulus per verticem B minoris axis da-
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              <note symbol="c" position="right" xlink:label="note-0075-03" xlink:href="note-0075-03a" xml:space="preserve">ibidem.</note>
            tæ Ellipſi ABC inſcriptus. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">Quod primò erat, &</s>
            <s xml:id="echoid-s1772" xml:space="preserve">c.</s>
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            <s xml:id="echoid-s1774" xml:space="preserve">Sit verò in 2. </s>
            <s xml:id="echoid-s1775" xml:space="preserve">figura, data Ellipſis ABCD, cuius maior axis BD, rectum BE,
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            regula DE. </s>
            <s xml:id="echoid-s1776" xml:space="preserve">Oportet per verticem B _MINIMVM_ circulum circumſcribere.</s>
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            <s xml:id="echoid-s1778" xml:space="preserve">Deſcribatur circulus GBHD, cuius diameter ſit axis maior BD. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">Dico
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            hunc eſſe _MINIMVM_ quæſitum.</s>
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          <p>
            <s xml:id="echoid-s1781" xml:space="preserve">Cum ſit enim axis BD maior recto latere BE, ſumpta BF æquali BD, ipſa
              <lb/>
            erit latus rectum circuli GBH, & </s>
            <s xml:id="echoid-s1782" xml:space="preserve">maior BE: </s>
            <s xml:id="echoid-s1783" xml:space="preserve">vnde circuli regula DF cadet
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              <note symbol="d" position="right" xlink:label="note-0075-04" xlink:href="note-0075-04a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            tota extra Ellipſis regulam DE, ac ideò circulus erit Ellipſi circumſcriptus, eritque _MINIMVS_; </s>
            <s xml:id="echoid-s1784" xml:space="preserve">quoniam quilibet alius circulus GBH per B adſcriptus,
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              <note symbol="e" position="right" xlink:label="note-0075-05" xlink:href="note-0075-05a" xml:space="preserve">5. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            cuius diameter ſit maior BD, eſt maior ipſo GBH, & </s>
            <s xml:id="echoid-s1785" xml:space="preserve">quicunque alius, cuius diameter ſit minor ipſa BD, qualis eſt BI, minor eſt quidem circulo GBH,</s>
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