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

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            <s xml:id="echoid-s650" xml:space="preserve">
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            tranſeunte, & </s>
            <s xml:id="echoid-s651" xml:space="preserve">horum communis ſe-
              <lb/>
              <figure xlink:label="fig-0036-01" xlink:href="fig-0036-01a" number="12">
                <image file="0036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0036-01"/>
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            ctio ſitrecta E F, cui in plano GEH
              <lb/>
            perpendicularis ducatur recta G B H
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            ad vtramque partem plani A E F pro-
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            ducta, in qua ſumpto quocunq; </s>
            <s xml:id="echoid-s652" xml:space="preserve">pun-
              <lb/>
            cto G, fiat, vt G B ad B E, ita B E ad
              <lb/>
            BH; </s>
            <s xml:id="echoid-s653" xml:space="preserve">(& </s>
            <s xml:id="echoid-s654" xml:space="preserve">erit rectangulum BGH æqua-
              <lb/>
            le quadrato BE, vel BF) iungaturque
              <lb/>
            BA, & </s>
            <s xml:id="echoid-s655" xml:space="preserve">per H in plano per HG, & </s>
            <s xml:id="echoid-s656" xml:space="preserve">GA
              <lb/>
            ducto agatur recta HI ipſi BA paral-
              <lb/>
            lela.</s>
            <s xml:id="echoid-s657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s658" xml:space="preserve">Itaque cum GH, EF in vno ſint pla-
              <lb/>
            no, ac inter ſe perpendiculares, ſitque
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            rectangulum GBH æquale quadrato
              <lb/>
            vtriuſque EB, BF, ſi circa G H, tan-
              <lb/>
            quam diametrum deſcribatur circulus
              <lb/>
            GEHF, ipſe tranſibit per E, & </s>
            <s xml:id="echoid-s659" xml:space="preserve">F. </s>
            <s xml:id="echoid-s660" xml:space="preserve">Si
              <lb/>
            ergo intelligatur recta IAG circa pe-
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            ripheriam circuli GE, H F conuerti,
              <lb/>
            manente eius extremo puncto I, deſcribetur conus IGH cuius vertex I, ba-
              <lb/>
            ſis circulus GH, & </s>
            <s xml:id="echoid-s661" xml:space="preserve">communis ſectio conicæ ſuperficiei cum ſubiecto plano
              <lb/>
            erit linea EMANF, quam dico eſſe Parabolen quæſitam.</s>
            <s xml:id="echoid-s662" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s663" xml:space="preserve">Conus enim IGH, cuius vertex I, & </s>
            <s xml:id="echoid-s664" xml:space="preserve">baſis diameter GH ſecatur plano per
              <lb/>
            axem deſcribens triãgulum GIH; </s>
            <s xml:id="echoid-s665" xml:space="preserve">ſecatur autem, & </s>
            <s xml:id="echoid-s666" xml:space="preserve">altero plano EAF (quod
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            eſt datum ſubiectum planum) baſi coni non æquidiſtante, cum eam ſecet,
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            ſecante baſim coniſecundum rectam lineam EF, quæ ad GH baſim triangu-
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            li per axem eſt perpendicularis, atque eſt AB diameter ſectionis EAF vni
              <lb/>
            laterum H I trianguli per axem æquidiſtans, talis ſectio E A F per primam
              <lb/>
            huius erit Parabolæ, cuius diameter A B, vertex A, & </s>
            <s xml:id="echoid-s667" xml:space="preserve">ordinatim ducta EF,
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            quæ ipſi diametro ad angulum ABF, dato angulo D æqualem, ap-
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            plicata eſt, ex ipſa conſtructione. </s>
            <s xml:id="echoid-s668" xml:space="preserve">Et cum factum ſit vt AB,
              <lb/>
            ad BE, ita BE ad A C, erit quadratum AB ad qua-
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            dratum BE, vel ad rectangulum GBH, vt
              <lb/>
            AB ad AC. </s>
            <s xml:id="echoid-s669" xml:space="preserve">Quare AC erit rectum
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            latus Parabolæ EMANF,
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            deſcriptæ vti quære-
              <lb/>
            batur: </s>
            <s xml:id="echoid-s670" xml:space="preserve">Quod erat
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            faciendum.</s>
            <s xml:id="echoid-s671" xml:space="preserve"/>
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          <figure number="13">
            <image file="0036-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0036-02"/>
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