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

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          <pb o="5" file="0025" n="25" rhead=""/>
          <p>
            <s xml:id="echoid-s404" xml:space="preserve">Ducatur enim per N linea RNS parallela ad BC, eſt autem & </s>
            <s xml:id="echoid-s405" xml:space="preserve">MN ipſi DE
              <lb/>
            æquidiſtans, quare angulus RNM æqualis erit angulo BGD, nempe
              <note symbol="a" position="right" xlink:label="note-0025-01" xlink:href="note-0025-01a" xml:space="preserve">10. Vn-
                <lb/>
              dec Elem.</note>
            & </s>
            <s xml:id="echoid-s406" xml:space="preserve">planum tranſiens per MN, RS æquidiſtabit plano per BCDE, hoc
              <note symbol="b" position="right" xlink:label="note-0025-02" xlink:href="note-0025-02a" xml:space="preserve">15. Vn-
                <lb/>
              dec. Elem.</note>
            baſi coni; </s>
            <s xml:id="echoid-s407" xml:space="preserve">ſi igitur planum per MNRS producatur ſectio circulus erit,
              <note symbol="c" position="right" xlink:label="note-0025-03" xlink:href="note-0025-03a" xml:space="preserve">4. primi
                <lb/>
              conic.</note>
            diameter RNS, atque eſt ad ipſam perpendicularis MN, ergo rectangulum
              <lb/>
            RNS æquale eſt quadrato MN, vti rectangulum BGC æquale eſt quadra-
              <lb/>
            to DG.</s>
            <s xml:id="echoid-s408" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s409" xml:space="preserve">Iam cum ſit NX parallela ad GV, & </s>
            <s xml:id="echoid-s410" xml:space="preserve">NS ad GC, erit in prima figura GV
              <lb/>
            ad NX, vt GC ad NS, ob æqualitatem; </s>
            <s xml:id="echoid-s411" xml:space="preserve">in reliquis verò erit GV ad NX, vt
              <lb/>
            GH ad HN, vel GC ad NS, ob triangulorum ſimilitudinem; </s>
            <s xml:id="echoid-s412" xml:space="preserve">quare permu-
              <lb/>
            tando in omnibus, GV ad GC, erit vt NX ad NS.</s>
            <s xml:id="echoid-s413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s414" xml:space="preserve">Amplius cum in prima figura factum ſit vt quadratum FG ad rectãgulum
              <lb/>
            BGC, ſiue ad quadratum GD, ita recta HF ad FL, vel ad GV ei æqualis, ob
              <lb/>
            parallelogrammum FV, erit FG ad GV, vt GV ad GD; </s>
            <s xml:id="echoid-s415" xml:space="preserve">quare rectangulum
              <lb/>
            FGV æquatur quadrato DG, ſiue rectangulo BGC. </s>
            <s xml:id="echoid-s416" xml:space="preserve">Item in reliquis figuris,
              <lb/>
            cum factum ſit vt rectangulum HGF, ad rectangulum BGC, ita recta HF ad
              <lb/>
            FL, vel HG ad GV, & </s>
            <s xml:id="echoid-s417" xml:space="preserve">idem rectangulum HGF ad rectangulum FGV ſit vt
              <lb/>
            eadem HG ad GV, erit rectangulum BGC æquale rectangulo FGV: </s>
            <s xml:id="echoid-s418" xml:space="preserve">cum
              <lb/>
            ergo in ſingulis figuris rectangulum BGC æquale ſit rectangulo FGV, erit
              <lb/>
            BG ad GF, ſiue RN ad NF, vt VG ad GC, ſiue vt XN ad NS: </s>
            <s xml:id="echoid-s419" xml:space="preserve">rectangulum
              <lb/>
            ergo RNS, ſiue quadratum MN æquatur rectangulo XNF. </s>
            <s xml:id="echoid-s420" xml:space="preserve">Linea igitur MN
              <lb/>
            poteſt rectangulum ſub O
              <unsure/>
            N, & </s>
            <s xml:id="echoid-s421" xml:space="preserve">NF, quod adiacet lineæ FL, latitudinem
              <lb/>
            habens FN, in prima figura, ſed in ſecunda ipſum rectangulum excedit, & </s>
            <s xml:id="echoid-s422" xml:space="preserve">
              <lb/>
            in tertia & </s>
            <s xml:id="echoid-s423" xml:space="preserve">quarta ab eodem deficit, rectangulo ſub LO, & </s>
            <s xml:id="echoid-s424" xml:space="preserve">OX, ſimili ei,
              <lb/>
            quod ſub HF, & </s>
            <s xml:id="echoid-s425" xml:space="preserve">FL continetur. </s>
            <s xml:id="echoid-s426" xml:space="preserve">Quod erat demonſtrandum.</s>
            <s xml:id="echoid-s427" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div16" type="section" level="1" n="12">
          <head xml:id="echoid-head16" xml:space="preserve">Definitiones Primæ.</head>
          <head xml:id="echoid-head17" xml:space="preserve">I.</head>
          <p>
            <s xml:id="echoid-s428" xml:space="preserve">Sectio DFE, cuius diameter FG in prima figura æquidiſtat AC vni laterum
              <lb/>
            trianguli per axem, vocatur PARABOLE.</s>
            <s xml:id="echoid-s429" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div17" type="section" level="1" n="13">
          <head xml:id="echoid-head18" xml:space="preserve">II.</head>
          <p>
            <s xml:id="echoid-s430" xml:space="preserve">Et cuius diameter in ſecunda figura occrrrit vtrique lateri trianguli per axẽ,
              <lb/>
            dicitur HYPERBOLE.</s>
            <s xml:id="echoid-s431" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div18" type="section" level="1" n="14">
          <head xml:id="echoid-head19" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s432" xml:space="preserve">Et cuius diameter, in tertia, & </s>
            <s xml:id="echoid-s433" xml:space="preserve">quarta conuenit cum vtroque latere infra
              <lb/>
            verticem trianguli per axem, ELLIPSIS nuncupatur.</s>
            <s xml:id="echoid-s434" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div19" type="section" level="1" n="15">
          <head xml:id="echoid-head20" xml:space="preserve">IV.</head>
          <p>
            <s xml:id="echoid-s435" xml:space="preserve">Segmentum verò HF diametri ſectionis inter latera trianguli per axem in-
              <lb/>
            terceptum, in ſecunda, tertia, & </s>
            <s xml:id="echoid-s436" xml:space="preserve">quarta, dicitur LATVS TRANSVER-
              <lb/>
            SVM Hyperbolæ, vel Ellipſis, quod in ſequentibus intelligatur ſemper
              <lb/>
            extra Hyperbolen ex ipſius vertice in directum poſitum cum diametro,
              <lb/>
            licet in conſtructionibus expreſsè non dicatur.</s>
            <s xml:id="echoid-s437" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div20" type="section" level="1" n="16">
          <head xml:id="echoid-head21" xml:space="preserve">V.</head>
          <p>
            <s xml:id="echoid-s438" xml:space="preserve">In omnibus autem figuris linea FL, quarto loco inuenta, dicitur LATVS
              <lb/>
            RECTVM ſectionis, quod deinceps concipiatur ſemper contingenter
              <lb/>
            applicari ex ſectionis vertice, ſiue ordinatim ductis æquidiſtans.</s>
            <s xml:id="echoid-s439" xml:space="preserve"/>
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