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

Table of contents

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[261.] PROBL. IV. PROP. XXXIII.
[262.] PROBL. V. PROP. XXXIV.
[263.] DEFINITIONES. I.
[264.] II.
[265.] LEMMA X. PROP. XXXV.
[266.] THEOR. XXI. PROP. XXXVI.
[267.] THEOR. XXII. PROP. XXXVII.
[268.] SCHOLIVM.
[269.] LEMMA XI. PROP. XXXVIII.
[270.] LEMMA XII. PROP. XXXIX.
[271.] THEOR. XXIII. PROP. XXXX.
[272.] COROLL. I.
[273.] COROLL. II.
[274.] COROLL. III.
[275.] PROBL. VI. PROP. XXXXI.
[276.] PROBL. VII. PROP. XXXXII.
[277.] COROLL.
[278.] THEOR. XXIV. PROP. XXXXIII.
[279.] THEOR. XXV. PROP. XXXXIV.
[280.] SCHOLIVM.
[281.] THEOR. XXVI. PROP. XLV.
[282.] COROLL.
[283.] THEOR. XXVII. PROP. XLVI.
[284.] COROLL. I.
[285.] COROLL. II.
[286.] THEOR. XXVIII. PROP. XLVII.
[287.] THEOR. XXIX. PROP. XLVIII.
[288.] THEOR. XXX. PROP. XLIX.
[289.] THEOR. XXXI. PROP. L.
[290.] COROLL.
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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/>
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                <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
              <lb/>
            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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          <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-
              <lb/>
            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
              <lb/>
            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
              <lb/>
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                <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-
              <lb/>
            lum deſignabit D F E, ad cuius periphe-
              <lb/>
            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>
            <s xml:id="echoid-s7239" xml:space="preserve"/>
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