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

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          <head xml:id="echoid-head235" xml:space="preserve">THEOR. V. PROP. IX.</head>
          <p>
            <s xml:id="echoid-s5419" xml:space="preserve">MINIMA linearum, ad peripheriam cuiulibet coni - ſectio-
              <lb/>
            nis ducibilium à puncto axis (quod
              <unsure/>
            in Ellipſi ſit axis maior) di-
              <lb/>
            ſtante
              <unsure/>
            à vertice per interuallum non maius dimidio recti lateris,
              <lb/>
            eſt idem axis ſegmentum inter aſſignatum punctum, & </s>
            <s xml:id="echoid-s5420" xml:space="preserve">verticem
              <lb/>
            interceptum. </s>
            <s xml:id="echoid-s5421" xml:space="preserve">At in Ellipſi tantùm, MAXIMA eſt reliquum ma-
              <lb/>
            ioris axis ſegmentum, in quo centrum reperitur.</s>
            <s xml:id="echoid-s5422" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5423" xml:space="preserve">In Ellipſi verò circa minorem axim; </s>
            <s xml:id="echoid-s5424" xml:space="preserve">MAXIMA ducibilium
              <lb/>
            à puncto eiuſdem axis, quod diſtet à vertice per interuallum non
              <lb/>
            minus dimidio recti, eſt ipſum axis ſegmentum, inter aſſumptum
              <lb/>
            punctum, & </s>
            <s xml:id="echoid-s5425" xml:space="preserve">verticem interceptum. </s>
            <s xml:id="echoid-s5426" xml:space="preserve">MINIMA verò eſt reliquum
              <lb/>
            minoris axis ſegmentum, in quo centrum non reperitur.</s>
            <s xml:id="echoid-s5427" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5428" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5429" xml:space="preserve">ESto A B C quæcunque coni-ſectio, vel Parabole, vel Hyperbole, vt
              <lb/>
            in prima figura, vel Ellipſis, vt in ſecunda, circa maiorem axim
              <lb/>
            B D, in quo ſumptum ſit pun-
              <lb/>
              <figure xlink:label="fig-0193-01" xlink:href="fig-0193-01a" number="153">
                <image file="0193-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0193-01"/>
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            ctum E, quod primò diſtet à
              <lb/>
            vertice B per interuallum ęqua-
              <lb/>
            le dimidio recti lateris axis BD,
              <lb/>
            quodq; </s>
            <s xml:id="echoid-s5430" xml:space="preserve">in Ellipſi omnino minus
              <lb/>
            erit ſemi - axe B H (eſt enim ſe-
              <lb/>
            mi - axis maior ad ſemi - axim
              <lb/>
            minorem, vt ſemi - axis minor
              <lb/>
            ad ſemi-rectum.) </s>
            <s xml:id="echoid-s5431" xml:space="preserve">Dico ſegmen-
              <lb/>
            tum axis E B eſſe _MINIMAM_
              <lb/>
            linearum ex E ducibilium ad
              <lb/>
            ſectionis peripheriam ABC, & </s>
            <s xml:id="echoid-s5432" xml:space="preserve">
              <lb/>
            reliquam B D, in qua eſt cen-
              <lb/>
            trum, eſſe _MAXIMAM._</s>
            <s xml:id="echoid-s5433" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5434" xml:space="preserve">Deſcripto enim cum centro
              <lb/>
            E, interuallo E B circulo B F,
              <lb/>
            ipſe cadet totus intra
              <note symbol="a" position="right" xlink:label="note-0193-01" xlink:href="note-0193-01a" xml:space="preserve">1. Co-
                <lb/>
              roll. 20. 1.
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              huius.</note>
            A B C: </s>
            <s xml:id="echoid-s5435" xml:space="preserve">quare, quę ex centro E
              <lb/>
            ad ſectionis peripheriam ducẽ-
              <lb/>
            tur, præter ad B, omnino maio-
              <lb/>
            res erunt, quàm ductæ ex eo-
              <lb/>
            dem centro ad circuli periphe-
              <lb/>
            riam, quibus æqualis eſt E B.
              <lb/>
            </s>
            <s xml:id="echoid-s5436" xml:space="preserve">Ergo ipſa E B erit _MINIMA_.</s>
            <s xml:id="echoid-s5437" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5438" xml:space="preserve">Si verò, diſtantia à vertice B fuerit minor eodem recti dimidio qualis
              <lb/>
            eſt G B: </s>
            <s xml:id="echoid-s5439" xml:space="preserve">cum ad peripheriam circuli B F ipſa G B ſit _MINIMA_, eò magis
              <lb/>
            _MINIMA_ erit ad Ellipſis circumſcriptam peripheriam A B C D.</s>
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