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

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        <div xml:id="echoid-div937" type="section" level="1" n="374">
          <head xml:id="echoid-head383" xml:space="preserve">COROLL. I.</head>
          <p>
            <s xml:id="echoid-s9023" xml:space="preserve">EX hac igitur conſtat in Cono ſcaleno, tum _MAXIMVM_, tum _MINI-_
              <lb/>
            _MVM_ latus perpendiculare eſſe ad rectas ex eorum extremis terminis
              <lb/>
            baſis peripheriam contingentes.</s>
            <s xml:id="echoid-s9024" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9025" xml:space="preserve">Nam ſuperiùs primo loco demonſtrauimus rectam B A, quæ eſt _MAXI-_
              <lb/>
            _MVM_ Coni latus, rectum angulum efficere cum contingente A F, & </s>
            <s xml:id="echoid-s9026" xml:space="preserve">rectam
              <lb/>
            B C, quæ eſt latus _MINIMVM_, cum contingente C H rectum pariter an-
              <lb/>
            gulum conſtituere.</s>
            <s xml:id="echoid-s9027" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div938" type="section" level="1" n="375">
          <head xml:id="echoid-head384" xml:space="preserve">COROLL. II.</head>
          <p>
            <s xml:id="echoid-s9028" xml:space="preserve">PAtet quoque in eodem Cono ſcaleno, perpendicularem ex vertice du-
              <lb/>
            ctam ſuper aliam contingentem ad extrema baſis cuiuſcunque trian-
              <lb/>
            guli per axem non recti ad baſim Coni, eam eſſe, quæ iungit eundem verti-
              <lb/>
            cem cum interſectione ipſius tangentis cum ea recta linea, quæ à veſtigio
              <lb/>
            verticis ipſi baſi prædictitrianguli per axem æquidiſtans ducitur.</s>
            <s xml:id="echoid-s9029" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9030" xml:space="preserve">In triangulo enim I B L per axem ducto, ſed ſuper baſim A I C L obli-
              <lb/>
            quo, ibi demonſtratum fuit rectas B M, & </s>
            <s xml:id="echoid-s9031" xml:space="preserve">B N perpendiculares eſſe
              <lb/>
            ſuper contingentes I M, & </s>
            <s xml:id="echoid-s9032" xml:space="preserve">L N, ductas ex terminis I, & </s>
            <s xml:id="echoid-s9033" xml:space="preserve">L baſis I L eiuſ-
              <lb/>
            dem trianguli, atque iam puncta M, & </s>
            <s xml:id="echoid-s9034" xml:space="preserve">N ſunt interſectiones ipſarum tan-
              <lb/>
            gentium cum recta M E N, quæ per verticis veſtigium E æquidiſtans duci-
              <lb/>
            tur ad I L baſim trianguli.</s>
            <s xml:id="echoid-s9035" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div939" type="section" level="1" n="376">
          <head xml:id="echoid-head385" xml:space="preserve">THEOR. LXIV. PROP. IC.</head>
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            <s xml:id="echoid-s9036" xml:space="preserve">In quocunque Cono ſcaleno, Parabolæ portiones iuxta quæli-
              <lb/>
            bet Coni latera genitæ, & </s>
            <s xml:id="echoid-s9037" xml:space="preserve">quarum diametri, in earum triangulis
              <lb/>
            per axem ab ijſdem lateribus proportionaliter diſtent, vel qua rum
              <lb/>
            baſes ſint æquales, habent altitudines proportionales perpendicu-
              <lb/>
            laribus, quę ducuntur à Coni vertice ſuper rectas baſis peripheriam
              <lb/>
            contingentes ad puncta, quibus eadem latera occurrunt.</s>
            <s xml:id="echoid-s9038" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9039" xml:space="preserve">ESto Conus ſcalenus A B C, cuius vertex B, baſis circulus A C, cen-
              <lb/>
            trum D, & </s>
            <s xml:id="echoid-s9040" xml:space="preserve">Coni altitudo ſit B E, per quam, & </s>
            <s xml:id="echoid-s9041" xml:space="preserve">per axim ductum ſit
              <lb/>
            planum ad baſim erectum, efficiens in Cono triangulum A B C: </s>
            <s xml:id="echoid-s9042" xml:space="preserve">& </s>
            <s xml:id="echoid-s9043" xml:space="preserve">iterum
              <lb/>
            ſectus ſit Conus quocunque alio plano per axem efficiente triangulum ſuper
              <lb/>
            baſim obliquum G B H, atque iuxta vtriuſque horum triangulorum latera
              <lb/>
            B A, B G tanquam regulas, cõcipiantur duci - plana, parabolicas portiones
              <lb/>
            efficientia, ita vt communis ſectio Parabolæ genitæ iuxta latus B A cum
              <lb/>
            triangulo A B C ſit recta P I, (quæ in triangulo A B C æquidiſtabit lateri
              <lb/>
            B A eritque Parabolæ diameter) & </s>
            <s xml:id="echoid-s9044" xml:space="preserve">cum baſi A C ſit recta L I M
              <note symbol="a" position="left" xlink:label="note-0324-01" xlink:href="note-0324-01a" xml:space="preserve">1. primi
                <lb/>
              buius.</note>
            rectæ A D C erit perpendicularis, atque eiuſdem Parabolæ baſis) commu-
              <lb/>
            nis autem ſectio Parabolæ genitæ iuxta latus B G cum triangulo G B H, ſit
              <lb/>
            recta Q S, (quæ parallela erit ipſi B G, ac item erit diameter
              <note symbol="b" position="left" xlink:label="note-0324-02" xlink:href="note-0324-02a" xml:space="preserve">ibidem.</note>
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