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

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          <p>
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              <pb o="149" file="0173" n="173" rhead=""/>
            punctis G, H, in Ellipſis peripheria vbi-
              <lb/>
              <figure xlink:label="fig-0173-01" xlink:href="fig-0173-01a" number="139">
                <image file="0173-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0173-01"/>
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            cunque inter ſemi-axes aſſumptis, ſint
              <lb/>
            contingentibus perpẽdiculares GI, HL.
              <lb/>
            </s>
            <s xml:id="echoid-s4953" xml:space="preserve">Conſtat, ſi cum centris E, L, I, F, inter-
              <lb/>
            uallis verò EA, LH, IG, FB, circuli de-
              <lb/>
            ſcribantur, ipſos Ellipſi ABCD inſcri-
              <lb/>
            ptos eſſe, ac _MAXIMOS_ ad
              <note symbol="a" position="right" xlink:label="note-0173-01" xlink:href="note-0173-01a" xml:space="preserve">26. 92. h.
                <lb/>
              1. Coroll.
                <lb/>
              20. h.</note>
            A, H, G, B inſcriptibilium. </s>
            <s xml:id="echoid-s4954" xml:space="preserve">Dico iam
              <lb/>
            inter hos _MAXIMOS, MAXIMV M_
              <lb/>
            eſſe qui ad A, _MINIMVM_ verò, qui
              <lb/>
            ad B inſcribitur. </s>
            <s xml:id="echoid-s4955" xml:space="preserve">Aliorum autem inſcri-
              <lb/>
            ptum ad punctum H, quod à vertice
              <lb/>
            B maioris axis magis remouetur, maio-
              <lb/>
            rem eſſe inſcripto ad punctum G, quod
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            ipſi vertici propius eſt.</s>
            <s xml:id="echoid-s4956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4957" xml:space="preserve">Etenim quelibet perpendicularis LH,
              <lb/>
            IG inter ſemi-axes, minor eſt ſemi- axe maiori EA, ſed maior ſemper
              <note symbol="b" position="right" xlink:label="note-0173-02" xlink:href="note-0173-02a" xml:space="preserve">91. h.</note>
            mi- recto F B: </s>
            <s xml:id="echoid-s4958" xml:space="preserve">vnde circulus ex E A erit _MAXIMVS_, & </s>
            <s xml:id="echoid-s4959" xml:space="preserve">ex F B _MINI-_
              <lb/>
            _MVS_ inſcriptibilium: </s>
            <s xml:id="echoid-s4960" xml:space="preserve">ſed L H maior eſt I G: </s>
            <s xml:id="echoid-s4961" xml:space="preserve">quapropter circulus
              <note symbol="c" position="right" xlink:label="note-0173-03" xlink:href="note-0173-03a" xml:space="preserve">94. h.</note>
            L A, erit maior circulo ex I G, Quod probandum erat.</s>
            <s xml:id="echoid-s4962" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div501" type="section" level="1" n="203">
          <head xml:id="echoid-head208" xml:space="preserve">THEOR. LI. PROP. C.</head>
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            <s xml:id="echoid-s4963" xml:space="preserve">MINIMORVM circulorum ad puncta Ellipticæ periphe-
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            riæ circumſcriptorum, MINIMVS eſt, qui ad verticem maio-
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            ris axis circumſcribitur. </s>
            <s xml:id="echoid-s4964" xml:space="preserve">MAXIMVS verò qui ad verticem
              <lb/>
            minoris. </s>
            <s xml:id="echoid-s4965" xml:space="preserve">Aliorum autem is, cuius contactus à vertice minoris
              <lb/>
            axis magis diſtat, minor eſt.</s>
            <s xml:id="echoid-s4966" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4967" xml:space="preserve">ESto Ellipſis ABCD, cuius axis maior A C, minor B D, centrum E,
              <lb/>
            & </s>
            <s xml:id="echoid-s4968" xml:space="preserve">ſumpta ſit BF æqualis dimidio recti, cuius tranſuerſum latus eſt
              <lb/>
            BD, & </s>
            <s xml:id="echoid-s4969" xml:space="preserve">ex punctis G, H, vbi-
              <lb/>
            cunque in Ellipſis peripheria
              <lb/>
              <figure xlink:label="fig-0173-02" xlink:href="fig-0173-02a" number="140">
                <image file="0173-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0173-02"/>
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            inter ſemi- axes aſſumptis, ſint
              <lb/>
            contingentibus perpendicula-
              <lb/>
            res GI, H L. </s>
            <s xml:id="echoid-s4970" xml:space="preserve">Conſtat iam, ſi
              <lb/>
            ex centris E, L, I, F, cum in-
              <lb/>
            teruallis EA, LH, I G, F B de-
              <lb/>
            ſcribantur circuli, ipſos Ellipſi
              <lb/>
            ABCD circumſcriptos eſſe, & </s>
            <s xml:id="echoid-s4971" xml:space="preserve">
              <lb/>
            _MINIMOS_ ad puncta A,
              <note symbol="d" position="right" xlink:label="note-0173-04" xlink:href="note-0173-04a" xml:space="preserve">26. 92. h.
                <lb/>
              1. Coroll.
                <lb/>
              20. h.</note>
            G, B, circumſcriptibilium. </s>
            <s xml:id="echoid-s4972" xml:space="preserve">Di-
              <lb/>
            co tamen inter hos _MINI-_
              <lb/>
            _MOS, MINIMVM_ eſſe, qui
              <lb/>
            ad A; </s>
            <s xml:id="echoid-s4973" xml:space="preserve">_MAXIMVM_, quiad </s>
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