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

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            <s xml:id="echoid-s3659" xml:space="preserve">
              <pb o="109" file="0133" n="133" rhead=""/>
            Cipſius latera BA, BC eum contingant; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">& </s>
            <s xml:id="echoid-s3661" xml:space="preserve">erit _MAXIMVS_: </s>
            <s xml:id="echoid-s3662" xml:space="preserve">Nam licet fa-
              <lb/>
            cta ſupra EF eadem penitùs, conſtructione nempe ſumpta FG æquali ad FE,
              <lb/>
            & </s>
            <s xml:id="echoid-s3663" xml:space="preserve">ducta GH perpendiculari ad GA, oſtendetur pariter H eſſe centrum alte-
              <lb/>
            rius circuli dato angulo inſcripti, ſed is erit minor circulo ex DE, cum ob
              <lb/>
            parallelas GH, AD, ſit AB ad BG, vt DA ad HG, ſed eſt AB maior BG, vn-
              <lb/>
            de radius DA erit maior radio HG, ſiue circulus AEC maior circulo ex HE.
              <lb/>
            </s>
            <s xml:id="echoid-s3664" xml:space="preserve">Iam quilibet alius circulus per E, dato angulo adſcriptus, cuius diameter
              <lb/>
            minor ſit EI, minor eſt ipſo AEC, & </s>
            <s xml:id="echoid-s3665" xml:space="preserve">quilibet alius, cuius diameter ſit maior
              <lb/>
            ipſa EI, eſt quidem maior AEC, ſed omnino ſecat dati anguli latera, cum
              <lb/>
            hæc circulum contingant: </s>
            <s xml:id="echoid-s3666" xml:space="preserve">ex quo circulus ex DE erit _MAXIMVS_ inſcriptus
              <lb/>
            quæſitus. </s>
            <s xml:id="echoid-s3667" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s3668" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3670" xml:space="preserve">SIverò ad datum punctum B extra circulum AEC, cuius ſit centrum D, ſit
              <lb/>
            ei circumſcribendus _MINIMVS_ angulus rectilineus; </s>
            <s xml:id="echoid-s3671" xml:space="preserve">iam per ſe patet
              <lb/>
            angulum ABC, à ductis contingentibus ex B, eſſe _MINIMVM_ quæſitum.
              <lb/>
            </s>
            <s xml:id="echoid-s3672" xml:space="preserve">Quod vltimò faciendum, ac demonſtrandum erat.</s>
            <s xml:id="echoid-s3673" xml:space="preserve"/>
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        <div xml:id="echoid-div352" type="section" level="1" n="151">
          <head xml:id="echoid-head156" xml:space="preserve">LEMMA VII. PROP. LXVI.</head>
          <p>
            <s xml:id="echoid-s3674" xml:space="preserve">In dato angulo, à recta linea per verticem vtcunque ſecto, lineas
              <lb/>
            applicare, quæ à prædicta diuidantur in data ratione.</s>
            <s xml:id="echoid-s3675" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3676" xml:space="preserve">SIt datus angulus ABC, vtcunque ſectus à re-
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              <figure xlink:label="fig-0133-01" xlink:href="fig-0133-01a" number="99">
                <image file="0133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0133-01"/>
              </figure>
            cta BD, punctum in eo ſit D, ex quo opor-
              <lb/>
            tet rectam, qualis eſt ADC, applicare ita vt ip-
              <lb/>
            ſius partes AD, DC ſint in data ratione, veluti
              <lb/>
            E ad F.</s>
            <s xml:id="echoid-s3677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3678" xml:space="preserve">Ducatur DG parallela ad alteram linearum,
              <lb/>
            angulum continentium, vt ad AB; </s>
            <s xml:id="echoid-s3679" xml:space="preserve">& </s>
            <s xml:id="echoid-s3680" xml:space="preserve">fiat vt E ad
              <lb/>
            F, ita BG ad GC, iungaturque CD, quæ cum
              <lb/>
            BA conueniat in A. </s>
            <s xml:id="echoid-s3681" xml:space="preserve">Dico factum eſſe, quod
              <lb/>
            proponebatur.</s>
            <s xml:id="echoid-s3682" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s3683" xml:space="preserve">Et enim, ob parallelas, vt AD ad DC, ita BG
              <lb/>
            ad GC, vel E ad F. </s>
            <s xml:id="echoid-s3684" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s3685" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3686" xml:space="preserve"/>
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        <div xml:id="echoid-div354" type="section" level="1" n="152">
          <head xml:id="echoid-head157" xml:space="preserve">SCHOLIVM.</head>
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            <s xml:id="echoid-s3687" xml:space="preserve">SI data ratio E ad F, fuerit ratio æqualitatis, tunc BD, licet præter morem,
              <lb/>
            vocetur dati anguli diameter, & </s>
            <s xml:id="echoid-s3688" xml:space="preserve">ſi bifariam, & </s>
            <s xml:id="echoid-s3689" xml:space="preserve">ad rectos angulos ipſas
              <lb/>
            applicatas ſecuerit, dicatur axis.</s>
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