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

Table of contents

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[211.] Pag. 131. poſt Prop. 84.
[212.] Pag. 144. ad calcem Prop. 93.
[213.] SCHOLIVM.
[214.] Pag. 147. ad finem Prop. 97.
[215.] FINIS.
[216.] DE MAXIMIS, ET MINIMIS GEOMETRICA DIVINATIO In Qvintvm Conicorvm APOLLONII PERGÆI _IAMDIV DESIDERATVM._ AD SER ENISSIMVM PRINCIPEM LEOPOLDVM AB ETRVRIA. LIBER SECVNDVS. _AVCTORE_ VINCENTIO VIVIANI.
[217.] FLORENTIÆ MDCLIX. Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. _SVPERIORVM PERMISSV._
[218.] SERENISSIMO PRINCIPI LEOPOLODO AB ETRVRIA.
[219.] VINCENTII VIVIANI DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER SECVNDVS. LEMMA I. PROP. I.
[220.] LEMMA II. PROP. II.
[221.] THEOR. I. PROP. III.
[222.] LEMMA III. PROP. IV.
[223.] THEOR. II. PROP. V.
[224.] THEOR. III. PROP. VI.
[225.] LEMMA IV. PROP. VII.
[226.] THEOR. IV. PROP. VIII.
[227.] THEOR. V. PROP. IX.
[228.] SCHOLIVM.
[229.] THEOR. VI. PROP. X.
[230.] THEOR. VII. PROP. XI.
[231.] THEOR. VIII. PROP. XII.
[232.] THEOR. IX. PROP. XIII.
[233.] THEOR. X. PROP. XIV.
[234.] THEOR. XI. PROP. XV.
[235.] LEMMA V. PROP. XVI.
[236.] COROLL.
[237.] THEOR. XII. PROP. XVII.
[238.] THEOR. XIII. PROP. XVIII.
[239.] THEOR. XIV. PROP. XIX.
[240.] PROBL. I. PROP. XX.
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            quadrato G N ſed rectangulum C G cum G N, in N C, vnà cum qua-
              <lb/>
            drato G N, conficit quadratum vnicæ C G, ergo quadratum G M
              <note symbol="a" position="left" xlink:label="note-0192-01" xlink:href="note-0192-01a" xml:space="preserve">1. h.</note>
            ius eſt quadrato G C, ſiue linea G M maior G C: </s>
            <s xml:id="echoid-s5396" xml:space="preserve">ex quò G C erit etiam
              <lb/>
            _MINIMA_ ductarum ex G ad peripheriam minoris portionis H C S. </s>
            <s xml:id="echoid-s5397" xml:space="preserve">Vn-
              <lb/>
            de ipſa G C erit _MINIMA_ ad totam peripheriam A B C D.</s>
            <s xml:id="echoid-s5398" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5399" xml:space="preserve">Inſuper rectangulum C G I ſuperat rectangulum C N O ſpatio minori,
              <lb/>
            quàm ſit quadratum N G, per ſecundam partem 7. </s>
            <s xml:id="echoid-s5400" xml:space="preserve">huius; </s>
            <s xml:id="echoid-s5401" xml:space="preserve">quare (alijs
              <lb/>
            ſumptis æqualibus) quadratum G
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                <image file="0192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0192-01"/>
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              <note symbol="b" position="left" xlink:label="note-0192-02" xlink:href="note-0192-02a" xml:space="preserve">Coroll.
                <lb/>
              primę pri.
                <lb/>
              mi huius.</note>
            ſuperabit quadratum M N maiori ex-
              <lb/>
            ceſſu quadrati G N; </s>
            <s xml:id="echoid-s5402" xml:space="preserve">ſed quadratum
              <lb/>
            G M ſuperat idem quadratum M N
              <lb/>
            quadrato tantùm G N, ergo exceſſus
              <lb/>
            quadrati G H ſupra N M, maior eſt
              <lb/>
            exceſſu quadrati G M ſupra idem qua-
              <lb/>
            dratum M N, quare quadratum G H
              <lb/>
            maius eſt quadrato G M, ſiue linea
              <lb/>
            G H maior G M.</s>
            <s xml:id="echoid-s5403" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5404" xml:space="preserve">Tandem ducatur G P minorem có-
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            ſtituens angulum cum _MINIMA_ G C
              <lb/>
            quàm G M, appliceturque PQR. </s>
            <s xml:id="echoid-s5405" xml:space="preserve">Erit
              <lb/>
            exceſſus rectanguli C Q R ſupra CNO
              <lb/>
            maior exceſſu quadrati N G ſupra
              <lb/>
            G Q, per tertiam partem 7. </s>
            <s xml:id="echoid-s5406" xml:space="preserve">huius,
              <lb/>
            ergo (permutatis æqualibus, &</s>
            <s xml:id="echoid-s5407" xml:space="preserve">c.)</s>
            <s xml:id="echoid-s5408" xml:space="preserve">
              <note symbol="c" position="left" xlink:label="note-0192-03" xlink:href="note-0192-03a" xml:space="preserve">ibidem.</note>
            quadratum P Q ſuperabit quadratum
              <lb/>
            M N maiori exceſſu, quàm quadrati N G ſupra G Q: </s>
            <s xml:id="echoid-s5409" xml:space="preserve">vnde aggregatum
              <lb/>
            extremorum quadratorum P Q, G Q, ſiue vnicum quadratum G P, ma-
              <lb/>
            ius erit aggregato mediorum M N, N G, ſiue vnico quadrato GM; </s>
            <s xml:id="echoid-s5410" xml:space="preserve">
              <note symbol="d" position="left" xlink:label="note-0192-04" xlink:href="note-0192-04a" xml:space="preserve">2. h.</note>
            eſt linea G P erit maior linea G M. </s>
            <s xml:id="echoid-s5411" xml:space="preserve">Quapropter linearum ex G ducibi-
              <lb/>
            lium ad minoris portionis peripheriam H C S, quæ minorem angulum
              <lb/>
            conſtituit cum _MINIMA_ minor eſt. </s>
            <s xml:id="echoid-s5412" xml:space="preserve">Quod erat vltimò demonſtrandum.</s>
            <s xml:id="echoid-s5413" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s5414" xml:space="preserve">Verùm prætermiſſa hac methodo mihi, vt fateor, moleſiiori, quod
              <lb/>
            in quatuor præcedentibus theorematibus, quò ad MAXI-
              <lb/>
            MAS tantùm, & </s>
            <s xml:id="echoid-s5415" xml:space="preserve">MINIMAS attinet, hic ſi-
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            mul, & </s>
            <s xml:id="echoid-s5416" xml:space="preserve">aliquid vltra, aliter, & </s>
            <s xml:id="echoid-s5417" xml:space="preserve">expeditiùs
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            demonſtrabitur.</s>
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