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

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          <p>
            <s xml:id="echoid-s7212" xml:space="preserve">Ducatur enim in plano ſecante D A E, per punctum F ſectionem con-
              <lb/>
            tingens G F H, quæ, (vtielicitur ex propoſitionibus 20. </s>
            <s xml:id="echoid-s7213" xml:space="preserve">22. </s>
            <s xml:id="echoid-s7214" xml:space="preserve">ac 23. </s>
            <s xml:id="echoid-s7215" xml:space="preserve">huius)
              <lb/>
            cum _MINIMA_ C F rectos an-
              <lb/>
            gulos efficiet. </s>
            <s xml:id="echoid-s7216" xml:space="preserve">Concipiatur
              <lb/>
              <figure xlink:label="fig-0261-01" xlink:href="fig-0261-01a" number="217">
                <image file="0261-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0261-01"/>
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            denique per contingentem G
              <lb/>
            H, ductum planũ L M, quod
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            ad planum D A E, in quo iam
              <lb/>
            ponitur eſſe C F, rectum ſit.
              <lb/>
            </s>
            <s xml:id="echoid-s7217" xml:space="preserve">Cum ergo plana L M, D A E,
              <lb/>
            ſe mutuò ſecent per rectam G
              <lb/>
            H, cui in plano D A E ducta
              <lb/>
            eſt perpendicularis C F, erit
              <lb/>
            ipſa C F, recta quoque
              <note symbol="a" position="right" xlink:label="note-0261-01" xlink:href="note-0261-01a" xml:space="preserve">4. def.
                <lb/>
              II. Elem.</note>
            planum L M, ſiue ad idem planum ex puncto C erit _MINIMA_; </s>
            <s xml:id="echoid-s7218" xml:space="preserve">ſed
              <note symbol="b" position="right" xlink:label="note-0261-02" xlink:href="note-0261-02a" xml:space="preserve">52. h.</note>
            num L M conuexam ſolidi ſuperficiem contingit in puncto tantùm F, quę
              <lb/>
            cadit tota infra idem planum, ergo recta C F eò magis eſt _MINIMA_
              <note symbol="c" position="right" xlink:label="note-0261-03" xlink:href="note-0261-03a" xml:space="preserve">55. h.</note>
            conuexam ſolidi ſuperficiem D A E. </s>
            <s xml:id="echoid-s7219" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s7220" xml:space="preserve">c.</s>
            <s xml:id="echoid-s7221" xml:space="preserve"/>
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        <div xml:id="echoid-div760" type="section" level="1" n="301">
          <head xml:id="echoid-head310" xml:space="preserve">PROBL. X. PROP. LIX.</head>
          <p>
            <s xml:id="echoid-s7222" xml:space="preserve">A puncto non intra ſphæram dato, ad eius ſuperficiem, MA-
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            XIMAM rectam lineam ducere.</s>
            <s xml:id="echoid-s7223" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7224" xml:space="preserve">SIt data ſphæra, cuius centrum A, & </s>
            <s xml:id="echoid-s7225" xml:space="preserve">oporteat per punctum B non intra
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            ſphæram datum, ad eius ſuperficiẽ, _MAXIMAM_ rectam lineam ducere.
              <lb/>
            </s>
            <s xml:id="echoid-s7226" xml:space="preserve">Iungatur B A, & </s>
            <s xml:id="echoid-s7227" xml:space="preserve">producatur, donec
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              <figure xlink:label="fig-0261-02" xlink:href="fig-0261-02a" number="218">
                <image file="0261-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0261-02"/>
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            ſphæricæ ſuperficiei occurrat in D, & </s>
            <s xml:id="echoid-s7228" xml:space="preserve">E.
              <lb/>
            </s>
            <s xml:id="echoid-s7229" xml:space="preserve">Dico B E, in qua eſt centrum, eſſe _MAXI_-
              <lb/>
            _MAM._</s>
            <s xml:id="echoid-s7230" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7231" xml:space="preserve">Concipiatur per B E ductum planum,
              <lb/>
            quod in ſpæræ ſuperficie maximum circu-
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            lum deſignabit D F E, ad cuius periphe-
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            riam eſt recta B E _MAXIMA._</s>
            <s xml:id="echoid-s7232" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7233" xml:space="preserve">Iam in plano circuli D F E, cum radio
              <lb/>
            B E deſcripto circulo G E H, & </s>
            <s xml:id="echoid-s7234" xml:space="preserve">circa im-
              <lb/>
            motum axim B E reuoluto, ab ipſo deſcri-
              <lb/>
            betur ſphæra G E H, quæ datam ſphæram
              <lb/>
            D F E circa eundem axim deſcriptam comprehendet, ac ſe ſimul contingét
              <lb/>
            in ipſo circulorum contactu E, ſed quæ à centro B ad ſphæricam
              <note symbol="d" position="right" xlink:label="note-0261-04" xlink:href="note-0261-04a" xml:space="preserve">56. h.</note>
            ciem G E H ducuntur omnes ſunt æquales rectæ B E, ergo quæ ab eodem
              <lb/>
            puncto B ad interioris ſphæræ D F E ſuperficiem ducentur ipſa B E mino-
              <lb/>
            res erunt. </s>
            <s xml:id="echoid-s7235" xml:space="preserve">Vnde B E eſt _MAXIMA_ quæſita, &</s>
            <s xml:id="echoid-s7236" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7237" xml:space="preserve">Quod erat, &</s>
            <s xml:id="echoid-s7238" xml:space="preserve">c.</s>
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