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

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        <div xml:id="echoid-div737" type="section" level="1" n="294">
          <p>
            <s xml:id="echoid-s7049" xml:space="preserve">
              <pb o="70" file="0254" n="254" rhead=""/>
            plano baſis Coni, vel Cylindri A C efficiens communem ſectionem G A D.
              <lb/>
            </s>
            <s xml:id="echoid-s7050" xml:space="preserve">Dico ipſum planum G D K H, licet in infinitum extendatur, in vnico tantùm
              <lb/>
            latere B A ſuperficiem Conicam, vel Cylindricam contingere, ac propterea
              <lb/>
            hanc totam cadere infra planum contingens.</s>
            <s xml:id="echoid-s7051" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7052" xml:space="preserve">Quoniam cum axis Coni, vel Cylindrirecti ſit perpendicularis plano baſis,
              <lb/>
            erit planum per axem B A C rectum baſi A C, ſiue planum baſis A C rectum
              <lb/>
            plano per axem A B C, cui rectum quoque poſitum fuit planum per B A, A D
              <lb/>
            ductum, quare G A D communis planorum ſectio eidem plano per axem erit
              <lb/>
            perpendicularis, vnde angulus D A C rectus erit, ſed eſt C A diameter
              <note symbol="a" position="left" xlink:label="note-0254-01" xlink:href="note-0254-01a" xml:space="preserve">19. vnd.
                <lb/>
              Elem.</note>
            culi A C, quare G A D circuli peripheriam continget, ac tota cadet extra co-
              <lb/>
            nicam, vel cylindricam ſuperſiciem.</s>
            <s xml:id="echoid-s7053" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s7054" xml:space="preserve">Iam per B axis verticem concipiatur ductum pla-
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                <image file="0254-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0254-01"/>
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            num S T baſi A C ęquidiſtans, quod communem
              <lb/>
            ſectionem faciet cum plano G K rectam Q B R ipſi
              <lb/>
            G A D parallelam, abſcindetque de plano G
              <note symbol="b" position="left" xlink:label="note-0254-02" xlink:href="note-0254-02a" xml:space="preserve">16. ibid.</note>
            vtrinque in infinitum extenſo, partem Q R K H,
              <lb/>
            quæ tota cadet ſupra planum S T ad oppoſitas par-
              <lb/>
            tes conicæ, vel cylindricæ ſuperficiei B A C (cum
              <lb/>
            hæc tota cadat inter æquidiſtantia plana S T, A C,
              <lb/>
            vt ſatis conſtat,) & </s>
            <s xml:id="echoid-s7055" xml:space="preserve">partem Q R D G, quæ tota
              <lb/>
            erit ad partes eiuſdem ſuperſiciei. </s>
            <s xml:id="echoid-s7056" xml:space="preserve">Sumatur ergo in
              <lb/>
            plano Q R D G extra lineam B A, inter æquidiſtã-
              <lb/>
            tes Q R, G D quodlibet punctum E, & </s>
            <s xml:id="echoid-s7057" xml:space="preserve">iuncta B E
              <lb/>
            producatur: </s>
            <s xml:id="echoid-s7058" xml:space="preserve">patet ipſam cum A D conuenire: </s>
            <s xml:id="echoid-s7059" xml:space="preserve">(cumrecta B E ſit in eodem
              <lb/>
            plano in quo ſunt B A, & </s>
            <s xml:id="echoid-s7060" xml:space="preserve">A D, & </s>
            <s xml:id="echoid-s7061" xml:space="preserve">alteram parallelarum ſecet in B) conueniat
              <lb/>
            in F, & </s>
            <s xml:id="echoid-s7062" xml:space="preserve">cum punctum F ſit extra ſolidi ſuperſiciem, ipſa quoque B F cadet to-
              <lb/>
            ta extra eandem, quare punctum E erit extra ipſam ſuperficiem, & </s>
            <s xml:id="echoid-s7063" xml:space="preserve">ſic
              <note symbol="c" position="left" xlink:label="note-0254-03" xlink:href="note-0254-03a" xml:space="preserve">Coroll.
                <lb/>
              primę pri-
                <lb/>
              mi Conic.</note>
            quolibet alio puncto plani G R, quod ſit extra latus B A, quapropter planum
              <lb/>
            G R ſuperficiem dati ſolidi contingit per rectam B A, ac ideo ipſa ſuperficies
              <lb/>
            cadit tota ad alteram partem plani G R. </s>
            <s xml:id="echoid-s7064" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s7065" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7066" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div740" type="section" level="1" n="295">
          <head xml:id="echoid-head304" xml:space="preserve">ALITER.</head>
          <p>
            <s xml:id="echoid-s7067" xml:space="preserve">SI per quodcunque aliud punctum N lateris B A concipiatur duci planum
              <lb/>
            ſecans Conum, vel Cylindrum, quod ſit baſi A C parallelum, ipſum in
              <lb/>
            ſolidi ſuperficie circuli peripheriam deſcribet, & </s>
            <s xml:id="echoid-s7068" xml:space="preserve">in plano per axem
              <note symbol="d" position="left" xlink:label="note-0254-04" xlink:href="note-0254-04a" xml:space="preserve">4. primi
                <lb/>
              Conic.</note>
            ſeu diametrum N P, quæ ipſi A C æ quidiſtabit, in plano verò Q D
              <note symbol="e" position="left" xlink:label="note-0254-05" xlink:href="note-0254-05a" xml:space="preserve">16. vnd.
                <lb/>
              Elem.</note>
            M N O, quæ item rectæ G A D erit parallela (cum ſint communes ſectiones
              <lb/>
            æquidiſtantium planorum cum altero plano) eritque angulus O N P
              <note symbol="f" position="left" xlink:label="note-0254-06" xlink:href="note-0254-06a" xml:space="preserve">10. ibid.</note>
            angulo D A C, ſiue rectus, (cum ſuperiùs demonſtratum ſit ipſum D A C
              <lb/>
            rectum eſſe) hoc eſt recta M N O peripheriam N P continget in N, & </s>
            <s xml:id="echoid-s7069" xml:space="preserve">ex vtra-
              <lb/>
            que parte cadet extra ſolidi ſuperficiem, & </s>
            <s xml:id="echoid-s7070" xml:space="preserve">hoc ſemper de qualibet alia ducta
              <lb/>
            in plano B D ipſi G D æquidiſtante: </s>
            <s xml:id="echoid-s7071" xml:space="preserve">quare totum planum G R, quod per la-
              <lb/>
            tus B A ductum fuit rectum ad planum A B C per axem ductum, ſolidi ſuper-
              <lb/>
            ficiem contingit tantùm per latus B A: </s>
            <s xml:id="echoid-s7072" xml:space="preserve">vnde ipſa ſuperficies cadit tota ad alte-
              <lb/>
            ram partem plani G R. </s>
            <s xml:id="echoid-s7073" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s7074" xml:space="preserve">c.</s>
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