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

Table of contents

< >
[191.] THEOR. XLV. PROP. XCI.
Page: 163 (139)
[192.] COROLL. I.
Page: 164 (140)
[193.] COROLL. II.
Page: 164 (140)
[194.] THEOR. XLVI. PROP. XCII.
Page: 165 (141)
[195.] THEOR. XLVIII. PROP. XCIII.
Page: 166 (142)
[196.] PROBL. XXXIV. PROP. XCIV.
Page: 168 (144)
[197.] PROBL. XXXV. PROP. XCV.
Page: 169 (145)
[198.] PROBL. XXXVI. PROP. XCVI.
Page: 169 (145)
[199.] THEOR. XLVIII. PROP. XCVII.
Page: 170 (146)
[200.] COROLL.
Page: 171 (147)
[201.] THEOR. IL. PROP. IIC.
Page: 172 (148)
[202.] THEOR. L. PROP. IC.
Page: 172 (148)
[203.] THEOR. LI. PROP. C.
Page: 173 (149)
[204.] PRIMI LIBRI FINIS.
Page: 174 (150)
[205.] ADDENDA LIB. I.
Page: 175 (151)
[206.] Pag. 74. ad finem Prim. Coroll.
Page: 175 (151)
[207.] Ad calcem Pag. 78. COROLL. II.
Page: 175 (151)
[208.] Pag. 87. ad finem Moniti.
Page: 175 (151)
[209.] Pag. 123. poſt Prop. 77. Aliter idem, ac Vniuerſaliùs.
Page: 175 (151)
[210.] COROLL.
Page: 177 (153)
[211.] Pag. 131. poſt Prop. 84.
Page: 177 (153)
[212.] Pag. 144. ad calcem Prop. 93.
Page: 177 (153)
[213.] SCHOLIVM.
Page: 177 (153)
[214.] Pag. 147. ad finem Prop. 97.
Page: 178 (154)
[215.] FINIS.
Page: 178 (154)
[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.
Page: 179
[217.] FLORENTIÆ MDCLIX. Apud Ioſeph Cocchini, Typis Nouis, ſub Signo STELLÆ. _SVPERIORVM PERMISSV._
Page: 179
[218.] SERENISSIMO PRINCIPI LEOPOLODO AB ETRVRIA.
Page: 181
[219.] VINCENTII VIVIANI DE MAXIMIS, ET MINIMIS Geometrica diuinatio in V. conic. Apoll. Pergæi. LIBER SECVNDVS. LEMMA I. PROP. I.
Page: 183 (1)
[220.] LEMMA II. PROP. II.
Page: 183 (1)
< >
page |< < (10) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div551" type="section" level="1" n="226">
          <p>
            <s xml:id="echoid-s5395" xml:space="preserve">
              <pb o="10" file="0192" n="192" rhead=""/>
            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
              <figure xlink:label="fig-0192-01" xlink:href="fig-0192-01a" number="152">
                <image file="0192-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0192-01"/>
              </figure>
              <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"/>
          </p>
          <p>
            <s xml:id="echoid-s5404" xml:space="preserve">Tandem ducatur G P minorem có-
              <lb/>
            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>
          <p style="it">
            <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-
              <lb/>
            mul, & </s>
            <s xml:id="echoid-s5416" xml:space="preserve">aliquid vltra, aliter, & </s>
            <s xml:id="echoid-s5417" xml:space="preserve">expeditiùs
              <lb/>
            demonſtrabitur.</s>
            <s xml:id="echoid-s5418" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum