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

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          <p>
            <s xml:id="echoid-s5846" xml:space="preserve">
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            intra Hyperbolen, inter axem, & </s>
            <s xml:id="echoid-s5847" xml:space="preserve">peripheriam, vt in ſexta, & </s>
            <s xml:id="echoid-s5848" xml:space="preserve">ſeptima
              <lb/>
            (nam ſi eſſet in ipſa peripheria, vt in A, tunc _MINIMA_ abiret in pun-
              <lb/>
            ctum.) </s>
            <s xml:id="echoid-s5849" xml:space="preserve">Iungatur H, centrum Hyperbolæ, cum dato puncto F recta linea
              <lb/>
            H F, quæ ita ſecetur in I, vt H I ad I F ſit vt tranſuerſum latus G B ad
              <lb/>
            rectum B E, ſumaturque H L æqualis F I, & </s>
            <s xml:id="echoid-s5850" xml:space="preserve">per L agatur L M axi B D
              <lb/>
            æquidiſtans, ac per I axi ordinata N I O, & </s>
            <s xml:id="echoid-s5851" xml:space="preserve">in angulo N O M per datum
              <lb/>
            in eo punctum A deſcribatur Hyperbole F A, quæ in vno tantùm
              <note symbol="a" position="left" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">4. ſecun-
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              di conic.</note>
            ctum A cum ſectione A B C conueniet. </s>
            <s xml:id="echoid-s5852" xml:space="preserve">Dico iunctam F A eſſe
              <note symbol="b" position="left" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">12. h.</note>
            _MAM_ quæſitam.</s>
            <s xml:id="echoid-s5853" xml:space="preserve"/>
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          <figure number="173">
            <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0210-01"/>
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          <p>
            <s xml:id="echoid-s5854" xml:space="preserve">Ducatur A P axi ordinata, & </s>
            <s xml:id="echoid-s5855" xml:space="preserve">A Q Hyperbolen contingens in A,
              <note symbol="c" position="left" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">2. pr. h.</note>
            ſecabit axim in Q. </s>
            <s xml:id="echoid-s5856" xml:space="preserve">Et quoniam in Hyperbola A F ſumpta ſunt duo
              <note symbol="d" position="left" xlink:label="note-0210-04" xlink:href="note-0210-04a" xml:space="preserve">24. pri-
                <lb/>
              mi conic.</note>
            cta A, F, è quorum altero A ducta eſt A P alteri aſymptoto N O æqui-
              <lb/>
            diſtans, ex altero verò F, recta F I L H vtranque aſymptoton ſecans in
              <lb/>
            I, L; </s>
            <s xml:id="echoid-s5857" xml:space="preserve">eſtque L H in directum, & </s>
            <s xml:id="echoid-s5858" xml:space="preserve">æqualis poſita ipſi I F, & </s>
            <s xml:id="echoid-s5859" xml:space="preserve">ex H recta
              <lb/>
            H B P alteri aſymptoto O M æquidiſtans, cum alia A P conueniens in P,
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            erit iuncta I P parallela ad F A; </s>
            <s xml:id="echoid-s5860" xml:space="preserve">ſed H P ſecat I P alteram
              <note symbol="e" position="left" xlink:label="note-0210-05" xlink:href="note-0210-05a" xml:space="preserve">14. h.</note>
            quare producta ſecabit quoque reliquam H F: </s>
            <s xml:id="echoid-s5861" xml:space="preserve">ſecet igitur in R. </s>
            <s xml:id="echoid-s5862" xml:space="preserve">Erit er-
              <lb/>
            go in triangulo H F R (ob parallelas) H P ad P R, vt H I ad I F, vel </s>
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