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

Table of contents

< >
[91.] PROBL. XVI. PROP. XXXI.
[92.] THEOR. XIII. PROP. XXXII.
[93.] THEOR. IV. PROP. XXXIII.
[94.] MONITVM.
[95.] THEOR. XV. PROP. XXXIV.
[96.] THEOR. XVI. PROP. XXXV.
[97.] THEOR. XVII. PROP. XXXVI.
[98.] COROLL.
[99.] THEOR. XIII. PROP. XXXVII.
[100.] THEOR. XIX. PROP. XXXVIII.
[101.] LEMMA IV. PROP. XXXIX.
[102.] THEOR. XX. PROP. XXXX.
[103.] COROLL.
[104.] THEOR. XXI. PROP. XXXXI.
[105.] COROLL.
[106.] THEOR. XXII. PROP. XXXXII.
[107.] ALITER.
[108.] COROLL. I.
[109.] COROLL. II.
[110.] LEMMA V. PROP. XXXXIII.
[111.] THEOR. XXIII. PROP. XXXXIV.
[112.] COROLL.
[113.] Quod ſuperiùs promiſimus oſtendetur ſic.
[114.] THEOR. XXIV. PROP. XXXXV.
[115.] COROLL.
[116.] LEMMA VI. PROP. XXXXVI.
[117.] THEOR. XXV. PROP. XXXXVII.
[118.] ALITER.
[119.] COROLL. I.
[120.] COROLL. II.
< >
page |< < (128) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div414" type="section" level="1" n="174">
          <p>
            <s xml:id="echoid-s4302" xml:space="preserve">
              <pb o="128" file="0152" n="152" rhead=""/>
            tam AC deſcribatur Ellipſis ALCN. </s>
            <s xml:id="echoid-s4303" xml:space="preserve">Dico hanc eſſe _MAXIMAM_
              <note symbol="*" position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">Coroll.
                <lb/>
              57. h.</note>
            quæſitam.</s>
            <s xml:id="echoid-s4304" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4305" xml:space="preserve">Nam, in qualibet figura, cum
              <lb/>
            ſit rectangulum DHE, ſiue NGL
              <lb/>
              <figure xlink:label="fig-0152-01" xlink:href="fig-0152-01a" number="119">
                <image file="0152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0152-01"/>
              </figure>
            æquale quadrato HI, ſiue GF,
              <lb/>
            erit NG ad GF, vt GF ad GL, & </s>
            <s xml:id="echoid-s4306" xml:space="preserve">
              <lb/>
            componendo NG cum GF, hoc
              <lb/>
            eſt NK, erit ad GF, vt FG cum
              <lb/>
            GL, ſiue vt KL ad GL, & </s>
            <s xml:id="echoid-s4307" xml:space="preserve">permu-
              <lb/>
            tando NK ad KL, vt GF ad GL,
              <lb/>
            vel vt NG ad GF, vel vt NF
              <note symbol="a" position="left" xlink:label="note-0152-02" xlink:href="note-0152-02a" xml:space="preserve">Coroll.
                <lb/>
              12. h.</note>
            FL, quæ ſunt differentiæ, trium
              <lb/>
            proportionalium NG, GF, GL;
              <lb/>
            </s>
            <s xml:id="echoid-s4308" xml:space="preserve">ergo recta KAM tanget
              <note symbol="b" position="left" xlink:label="note-0152-03" xlink:href="note-0152-03a" xml:space="preserve">4. h.</note>
            pſim ALCN, ſiue hæc angulo
              <lb/>
            ABC erit inſcripta, ſed in alijs fi-
              <lb/>
            guris, ipſa KAM tangit quoque
              <lb/>
            datã ei ſimul adſcriptam ſectio-
              <lb/>
            nem ABC, (ex conſtructione)
              <lb/>
            adūdem terminum cõmunis ap-
              <lb/>
            plicatæ AC, quapropter Ellipſis ALCN datæ ſectioni, vel circulo
              <note symbol="c" position="left" xlink:label="note-0152-04" xlink:href="note-0152-04a" xml:space="preserve">61. h.</note>
            inſcripta.</s>
            <s xml:id="echoid-s4309" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4310" xml:space="preserve">Dico demum hanc eſſe _MAXIMAM_: </s>
            <s xml:id="echoid-s4311" xml:space="preserve">quoniam quæ ipſi adſcribitur per
              <lb/>
            eoſdem terminos applicatæ AC, & </s>
            <s xml:id="echoid-s4312" xml:space="preserve">cum tranſuerſa diametro æquali ipſi LN,
              <lb/>
            _licet minor fuerit eadem ALCN_, ſecat contingentem KAM, in A, atque
              <note symbol="d" position="left" xlink:label="note-0152-05" xlink:href="note-0152-05a" xml:space="preserve">81. h.</note>
            ad partes AK, ſi nempe vertex nouiter adſcriptæ cadat ſupra L; </s>
            <s xml:id="echoid-s4313" xml:space="preserve">vel ad par-
              <lb/>
            tes AM, ſi cadat infra, vt ex ipſa 81. </s>
            <s xml:id="echoid-s4314" xml:space="preserve">huius facilè elicitur: </s>
            <s xml:id="echoid-s4315" xml:space="preserve">cum ergo inouiter
              <lb/>
            adſcripta Ellipſis ſecet contingentem KAM, in ſe ipſam rediens, ſecabit om-
              <lb/>
            nino datam ſectionem ABC, quare Ellipſis ALCN, eſt _MAXIMA_ dato an-
              <lb/>
            gulo, vel ſectioni ABC inſcripta, circa datam applicatam, & </s>
            <s xml:id="echoid-s4316" xml:space="preserve">cum data
              <lb/>
            tranſuerſa diametro DE, immo potiùs ipſa ALCN eſt vnica huiuſmodi con-
              <lb/>
            ditionibus inſcriptibilius. </s>
            <s xml:id="echoid-s4317" xml:space="preserve">Quod faciendum, & </s>
            <s xml:id="echoid-s4318" xml:space="preserve">demonſtrandum erat.</s>
            <s xml:id="echoid-s4319" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div419" type="section" level="1" n="175">
          <head xml:id="echoid-head180" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s4320" xml:space="preserve">EX hac conſtat interceptum diametri ſegmentum inter quamlibet appli-
              <lb/>
            tam, & </s>
            <s xml:id="echoid-s4321" xml:space="preserve">verticem, æquale eſſe (in Parabola) intercepto ſegmento eiuſ-
              <lb/>
            dem diametri inter verticem, & </s>
            <s xml:id="echoid-s4322" xml:space="preserve">occurſum contingentis, ductæ ex termino
              <lb/>
            applicatæ, cum diametro: </s>
            <s xml:id="echoid-s4323" xml:space="preserve">in Hyperbola, verò maius, ſed in Ellipſi, vel cir-
              <lb/>
            culo minus eſſe.</s>
            <s xml:id="echoid-s4324" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4325" xml:space="preserve">Demonſtratum eſt enim, in ſecunda figura, KB æ qualem eſſe BF, in ter-
              <lb/>
            tia verò KB, minorem BF, & </s>
            <s xml:id="echoid-s4326" xml:space="preserve">in quarta KB maiorem BF.</s>
            <s xml:id="echoid-s4327" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>