Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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            cularem AE, vt in H, patet iunctam HA, cum recta BAI inæquales angu-
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            los efficere, ac ideò peripheriam circuli ad partem acuti anguli cadere extra
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            datum angulum, & </s>
            <s xml:id="echoid-s4838" xml:space="preserve">ad partem obtuſi cadere intra, ſicque latus dati anguli
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            ſecare. </s>
            <s xml:id="echoid-s4839" xml:space="preserve">Quapropter circulus ACD erit _MAXIMVS_ inſcriptus ad datum
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            punctum A. </s>
            <s xml:id="echoid-s4840" xml:space="preserve">Quod erat faciendum.</s>
            <s xml:id="echoid-s4841" xml:space="preserve"/>
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        <div xml:id="echoid-div487" type="section" level="1" n="197">
          <head xml:id="echoid-head202" xml:space="preserve">PROBL. XXXV. PROP. XCV.</head>
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            <s xml:id="echoid-s4842" xml:space="preserve">Datæ Parabolæ, vel Hyperbolæ, ſiue Ellipſi circa maiorem
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            axim, ad datum punctum in eius peripheria, præter axis verticem,
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            MAXIMVM circulum inſcribere.</s>
            <s xml:id="echoid-s4843" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4844" xml:space="preserve">SIt ABC data Parabole, vel Hyperbole, in prima figura, vel Ellipſis circa
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            maiorem axim BO, in ſecunda, quarum vertex ſit B, & </s>
            <s xml:id="echoid-s4845" xml:space="preserve">punctum in ea
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            ſumptum præter B ſit E. </s>
            <s xml:id="echoid-s4846" xml:space="preserve">Oportet ad punctum E _MAXIMVM_ datæ ſectioni
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            circulum inſcribere.</s>
            <s xml:id="echoid-s4847" xml:space="preserve"/>
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            <s xml:id="echoid-s4848" xml:space="preserve">Ducatur ex E ſectionem con-
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              <figure xlink:label="fig-0169-01" xlink:href="fig-0169-01a" number="135">
                <image file="0169-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0169-01"/>
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            tingens EF, cui erigatur perpen-
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            dicularis ED axi occurrens
              <note symbol="a" position="right" xlink:label="note-0169-01" xlink:href="note-0169-01a" xml:space="preserve">88. h.</note>
            D. </s>
            <s xml:id="echoid-s4849" xml:space="preserve">Dico ſi cum centro D, inter-
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            uallo DE, circulus EGHI deſcri-
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            batur ipſum eſſe quæſitum: </s>
            <s xml:id="echoid-s4850" xml:space="preserve">nam
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            eſſe inſcriptum patet ex prima
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            parte 92. </s>
            <s xml:id="echoid-s4851" xml:space="preserve">huius; </s>
            <s xml:id="echoid-s4852" xml:space="preserve">quod autem ſit
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            _MAXIMVS_ conſtabit ſic: </s>
            <s xml:id="echoid-s4853" xml:space="preserve">appli-
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            cata enim ELH, & </s>
            <s xml:id="echoid-s4854" xml:space="preserve">producta EF
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            axi occurrens in F, iunctaque
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            FH, hæc pariter ſectionem
              <note symbol="b" position="right" xlink:label="note-0169-02" xlink:href="note-0169-02a" xml:space="preserve">59. h.</note>
            tinget, & </s>
            <s xml:id="echoid-s4855" xml:space="preserve">fiet angulus E F H, & </s>
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            quilibet alius circulus, vel cadet intra AGHI, vel ſecabit latera anguli EFH,
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            vt in præcedenti oſtenſum fuit, ac ideò ſecabit priùs ſectionem. </s>
            <s xml:id="echoid-s4857" xml:space="preserve">Quare cir-
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            culus EGHI erit _MAXIMVS_ ſectioni inſcriptus ad punctum AE. </s>
            <s xml:id="echoid-s4858" xml:space="preserve">Quod erat
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            faciendum.</s>
            <s xml:id="echoid-s4859" xml:space="preserve"/>
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        <div xml:id="echoid-div489" type="section" level="1" n="198">
          <head xml:id="echoid-head203" xml:space="preserve">PROBL. XXXVI. PROP. XCVI.</head>
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            <s xml:id="echoid-s4860" xml:space="preserve">Datæ Ellipſi circa minorem axim, ad datum punctum in
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            eius peripheria, præter axis verticem, MINIMVM circulum
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            circumſcribere.</s>
            <s xml:id="echoid-s4861" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s4862" xml:space="preserve">SIt data Ellipſis ABC, circa minorem axim BO, cuius vertex B, & </s>
            <s xml:id="echoid-s4863" xml:space="preserve">in pe-
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            pheria datum punctum, præter B, ſit E, per quod oporteat _MINIMVM_
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            circulum circumſcribere.</s>
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