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

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          <p>
            <s xml:id="echoid-s7280" xml:space="preserve">
              <pb o="79" file="0265" n="265" rhead=""/>
            ctione D A E ſit _MINIMA_, (ſed quæ in angulo, primæ figuræ, erit perpen-
              <lb/>
            dicularis ad A D) ipſa H D erit quoque _MINIMA_ in ſolido.</s>
            <s xml:id="echoid-s7281" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7282" xml:space="preserve">Nam ſi H D eſt _MINIMA_
              <lb/>
            ad peripheriam D A E patet
              <lb/>
              <figure xlink:label="fig-0265-01" xlink:href="fig-0265-01a" number="221">
                <image file="0265-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0265-01"/>
              </figure>
            ex 20. </s>
            <s xml:id="echoid-s7283" xml:space="preserve">22. </s>
            <s xml:id="echoid-s7284" xml:space="preserve">ac 23. </s>
            <s xml:id="echoid-s7285" xml:space="preserve">huius, ipſam
              <lb/>
            H D perpendicularem eſſe
              <lb/>
            rectæ F D G, quæ ad pun-
              <lb/>
            ctum D ſectionem contingat.
              <lb/>
            </s>
            <s xml:id="echoid-s7286" xml:space="preserve">Si ergo centro H, interuallo
              <lb/>
            H D circulus deſcribatur
              <note symbol="a" position="right" xlink:label="note-0265-01" xlink:href="note-0265-01a" xml:space="preserve">92. pri-
                <lb/>
              mihuius.</note>
            E B, ipſe cadet totus intra ſe-
              <lb/>
            ctionem, eam contingens tan-
              <lb/>
            tùm in duobus punctis D E:
              <lb/>
            </s>
            <s xml:id="echoid-s7287" xml:space="preserve">quare in reuolutione ſectio-
              <lb/>
            nis D A E circa axim A B
              <lb/>
            deſcribetur datum ſolidum, & </s>
            <s xml:id="echoid-s7288" xml:space="preserve">à circulo ſphæra, quæ tota cadet intra ſoli-
              <lb/>
            dum, eius concauam ſuperficiem contingens tantùm per peripheriam D
              <note symbol="b" position="right" xlink:label="note-0265-02" xlink:href="note-0265-02a" xml:space="preserve">56. h.</note>
            E eius circuli, qui in reuolutione deſcribitur à puncto D; </s>
            <s xml:id="echoid-s7289" xml:space="preserve">& </s>
            <s xml:id="echoid-s7290" xml:space="preserve">ipſa H D, vna
              <lb/>
            cum qualibet alia eductarum ab H ad prædictam peripheriam D I E, erit
              <lb/>
            _MINIMA_ in ſolido quæſita; </s>
            <s xml:id="echoid-s7291" xml:space="preserve">cum hæ omnes ſint æquales inter ſe, eò quod
              <lb/>
            ſint latera Conirecti, cuius baſis eſt circulus D I E, vertex H; </s>
            <s xml:id="echoid-s7292" xml:space="preserve">cumque om-
              <lb/>
            nes alię eductæ ab H ad ſolidi ſuperficiem, occurrant priùs ſphęricæ ſuper-
              <lb/>
            ficiei (quæ cadit tota intra ſolidi ſuperficiem) quàm ſuperficiei conicæ, aut
              <lb/>
            dati ſolidi conoidalis.</s>
            <s xml:id="echoid-s7293" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7294" xml:space="preserve">Siverò datum punctum ſit C inter axem, & </s>
            <s xml:id="echoid-s7295" xml:space="preserve">ſectionem: </s>
            <s xml:id="echoid-s7296" xml:space="preserve">ducta item C D,
              <lb/>
            quæ in ſectione ſit _MINIMA_. </s>
            <s xml:id="echoid-s7297" xml:space="preserve">Dico ipſam quoque eſſe _MINIMAM_ in
              <note symbol="c" position="right" xlink:label="note-0265-03" xlink:href="note-0265-03a" xml:space="preserve">20. 22.
                <lb/>
              23. h.</note>
            lido.</s>
            <s xml:id="echoid-s7298" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7299" xml:space="preserve">Cum enim C D ſit _MINIMA_ ad ſectionis peripheriam D A E, ipſa C D
              <lb/>
            erit contingenti F D G perpendicularis, quare, & </s>
            <s xml:id="echoid-s7300" xml:space="preserve">producta axi
              <note symbol="d" position="right" xlink:label="note-0265-04" xlink:href="note-0265-04a" xml:space="preserve">88. pr. h.</note>
            vt in H: </s>
            <s xml:id="echoid-s7301" xml:space="preserve">quo facto centro, ac interuallo H D deſcripto circulo D E B, & </s>
            <s xml:id="echoid-s7302" xml:space="preserve">
              <lb/>
            facta reuolutione circa axim A B, procreabitur denuo datum ſolidum, & </s>
            <s xml:id="echoid-s7303" xml:space="preserve">
              <lb/>
            ſphæra, cuius ſuperficies cadet tota intra ſolidi ſuperficiem, ſed recta C
              <note symbol="e" position="right" xlink:label="note-0265-05" xlink:href="note-0265-05a" xml:space="preserve">56. h.</note>
            eſt _MINIMA_ à puncto C ad ſphæræ ſuperficiem eductarú quare ipſa
              <note symbol="f" position="right" xlink:label="note-0265-06" xlink:href="note-0265-06a" xml:space="preserve">ex 60. h.</note>
            D eſt omnino _MINIMA_ ex C ducibilium ad concauam, & </s>
            <s xml:id="echoid-s7304" xml:space="preserve">exteriorem ſo-
              <lb/>
            lidi ſuperficiem. </s>
            <s xml:id="echoid-s7305" xml:space="preserve">Quod facere oportebat.</s>
            <s xml:id="echoid-s7306" xml:space="preserve"/>
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        <div xml:id="echoid-div770" type="section" level="1" n="304">
          <head xml:id="echoid-head313" xml:space="preserve">PROBL. XIII. PROP. LXII.</head>
          <p>
            <s xml:id="echoid-s7307" xml:space="preserve">A puncto vbicunque dato, ad Sphæroidis ſuperficiem, MAXI-
              <lb/>
              <note position="right" xlink:label="note-0265-07" xlink:href="note-0265-07a" xml:space="preserve">Schema-
                <lb/>
              tiſmus 4.</note>
            MAM, & </s>
            <s xml:id="echoid-s7308" xml:space="preserve">MINIMAM rectam lineam ducere.</s>
            <s xml:id="echoid-s7309" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7310" xml:space="preserve">ESto datum Sphæroides A B C D, cuius axis reuolutionis ſit B D, cen-
              <lb/>
            trum E, & </s>
            <s xml:id="echoid-s7311" xml:space="preserve">punctum datum ſit F. </s>
            <s xml:id="echoid-s7312" xml:space="preserve">Oportet primò ex F ad Sphæroidis
              <lb/>
            fuperficiem _MAXIMAM_ rectam lineam ducere.</s>
            <s xml:id="echoid-s7313" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7314" xml:space="preserve">Pro huius lineæ indagatione, generalis conſtructio in ſingulis figuris
              <lb/>
            quarti Schematiſmi, talis eſt.</s>
            <s xml:id="echoid-s7315" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7316" xml:space="preserve">Secetur Sphæroides A B C D plano per axem B D, ac per datum </s>
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