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

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          <p>
            <s xml:id="echoid-s3625" xml:space="preserve">
              <pb o="108" file="0132" n="132" rhead=""/>
            Dico Ellipſim ETF vertici B propiorem, minorem eſſe Ellipſi DVE ab ipſo
              <lb/>
            vertice remotiori.</s>
            <s xml:id="echoid-s3626" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3627" xml:space="preserve">Applicata enim ADC; </s>
            <s xml:id="echoid-s3628" xml:space="preserve">eſt DH
              <lb/>
              <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a" number="97">
                <image file="0132-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0132-01"/>
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              <note symbol="a" position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">32. vel
                <lb/>
              63. huius.</note>
            ad HE, vt AD, ad EG, ſed eſt AD maior EG, quare & </s>
            <s xml:id="echoid-s3629" xml:space="preserve">DH erit
              <lb/>
            maior HE, eademq; </s>
            <s xml:id="echoid-s3630" xml:space="preserve">ratione EM
              <lb/>
            maior MF, vnde harum Ellipſiũ
              <lb/>
            centra cadent infra H, & </s>
            <s xml:id="echoid-s3631" xml:space="preserve">M, vt
              <lb/>
            in O, & </s>
            <s xml:id="echoid-s3632" xml:space="preserve">O, ex quibus applicatis
              <lb/>
            OP, QR Ellipſium ſemi-diame-
              <lb/>
            tris coniugatis, productaque QR
              <lb/>
            vſque ad ſectionem in S, cum in
              <lb/>
            Ellipſi DVE ſit OP maior
              <note symbol="b" position="left" xlink:label="note-0132-02" xlink:href="note-0132-02a" xml:space="preserve">63. h.</note>
            & </s>
            <s xml:id="echoid-s3633" xml:space="preserve">in angulo, vel ſectione ABC
              <lb/>
            ſit HV maior QS, & </s>
            <s xml:id="echoid-s3634" xml:space="preserve">QS
              <note symbol="c" position="left" xlink:label="note-0132-03" xlink:href="note-0132-03a" xml:space="preserve">32. h.</note>
            QR, eò magis OP erit maior QR, & </s>
            <s xml:id="echoid-s3635" xml:space="preserve">duplum duplo maios, hoc eſt Ellipſis
              <lb/>
            DVE coniugata diameter, maior coniugata diametro Ellipſis ETF, ſed trãſ-
              <lb/>
            uerſa latera ED, EF ſunt æqualia, vnde & </s>
            <s xml:id="echoid-s3636" xml:space="preserve">latus rectum Ellipſis DVE maios
              <lb/>
            recto ETF, ſuntque huiuſmodi Ellipſes æqualiter inclinatæ cum eidem ſe-
              <lb/>
            ctioni ſint ſimul adſcriptæ: </s>
            <s xml:id="echoid-s3637" xml:space="preserve">quare Ellipſis DVE, maius habens rectum latus,
              <lb/>
            maior erit ETF minoris recti lateris, quę dati anguli, vel ſectionis
              <note symbol="d" position="left" xlink:label="note-0132-04" xlink:href="note-0132-04a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            propior eſt. </s>
            <s xml:id="echoid-s3638" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s3639" xml:space="preserve"/>
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        <div xml:id="echoid-div350" type="section" level="1" n="150">
          <head xml:id="echoid-head155" xml:space="preserve">PROBL. XXIV. PROP. LXV.</head>
          <p>
            <s xml:id="echoid-s3640" xml:space="preserve">Per datum punctum in axe dati anguli rectilinei MAXIMVM
              <lb/>
            circulum inſcribere & </s>
            <s xml:id="echoid-s3641" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s3642" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3643" xml:space="preserve">SIt datus angulus rectilineus ABC, cuius axis, ſiue linea ipſum bifariam
              <lb/>
            ſecans ſit BD, in quo datum ſit punctum E, per quod oporteat _MAXI_-
              <lb/>
            _MVM_ circulum inſcribere.</s>
            <s xml:id="echoid-s3644" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3645" xml:space="preserve">Ducatur ex E ſuper axim BD perpendicularis
              <lb/>
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                <image file="0132-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0132-02"/>
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            EF, cui infra F ſumatur FA æqualis, & </s>
            <s xml:id="echoid-s3646" xml:space="preserve">ex A eri-
              <lb/>
            gatur AD perpendicularis ad BA, quæ axi oc-
              <lb/>
            curret in D (cum angulus ABD ſit omnino acu-
              <lb/>
            tus, & </s>
            <s xml:id="echoid-s3647" xml:space="preserve">BAD rectus, hoc eſt ſimul ſumpti minores
              <lb/>
            duobus rectis). </s>
            <s xml:id="echoid-s3648" xml:space="preserve">Dico punctum D eſſe centrum
              <lb/>
            quæſiti circuli. </s>
            <s xml:id="echoid-s3649" xml:space="preserve">Nam iuncta AE; </s>
            <s xml:id="echoid-s3650" xml:space="preserve">cum ſint FA,
              <lb/>
            FE inter ſe æquales, erunt anguli ad baſim AE æ-
              <lb/>
            quales, ſed toti FED, FAD æquales ſunt, cum
              <lb/>
            ſint recti, vnde reliqui DEA, DAE æquales erũt,
              <lb/>
            ſiue latus DE ipſi DA æqualle. </s>
            <s xml:id="echoid-s3651" xml:space="preserve">Ductaque DC
              <lb/>
            perpendiculari ad BC; </s>
            <s xml:id="echoid-s3652" xml:space="preserve">in triangulis DBA, DBC
              <lb/>
            ſunt anguli ad B, & </s>
            <s xml:id="echoid-s3653" xml:space="preserve">ad A, & </s>
            <s xml:id="echoid-s3654" xml:space="preserve">C æquales inter ſe,
              <lb/>
            & </s>
            <s xml:id="echoid-s3655" xml:space="preserve">latus BD commune, ergo, & </s>
            <s xml:id="echoid-s3656" xml:space="preserve">DC ipſi DA, ſiue DE, ęqualis erit: </s>
            <s xml:id="echoid-s3657" xml:space="preserve">quapro-
              <lb/>
            pter ſi cum centro D, interuallo DA circulus deſcribatur, ipſæ per puncta E,
              <lb/>
            & </s>
            <s xml:id="echoid-s3658" xml:space="preserve">C tranſibit, eritque angulo ABC inſcrintus. </s>
            <s xml:id="echoid-s3659" xml:space="preserve">cum obrectos angulos ad </s>
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