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

Table of contents

< >
[111.] THEOR. XXIII. PROP. XXXXIV.
Page: 100 (76)
[112.] COROLL.
Page: 102 (78)
[113.] Quod ſuperiùs promiſimus oſtendetur ſic.
Page: 102 (78)
[114.] THEOR. XXIV. PROP. XXXXV.
Page: 103 (79)
[115.] COROLL.
Page: 105 (81)
[116.] LEMMA VI. PROP. XXXXVI.
Page: 105 (81)
[117.] THEOR. XXV. PROP. XXXXVII.
Page: 105 (81)
[118.] ALITER.
Page: 107 (83)
[119.] COROLL. I.
Page: 107 (83)
[120.] COROLL. II.
Page: 107 (83)
[121.] THEOR. XXVI. PROP. XXXXVIII.
Page: 108 (84)
[122.] MONITVM.
Page: 111 (87)
[123.] THEOR. XXVII. PROP. XXXXIX.
Page: 112 (88)
[124.] THEOR. XXVIII. PROP. L.
Page: 113 (89)
[125.] COROLL.
Page: 113 (89)
[126.] PROBL. XVII. PROP. LI.
Page: 114 (90)
[127.] PROBL. XVIII. PROP. LII.
Page: 115 (91)
[128.] ALITER.
Page: 116 (92)
[129.] ALITER breuiùs.
Page: 117 (93)
[130.] PROBL. XIX. PROP. LIII.
Page: 117 (93)
[131.] ALITER.
Page: 118 (94)
[132.] ALITER breuiùs.
Page: 119 (95)
[133.] PROBL. XX. PROP. LIV.
Page: 119 (95)
[134.] ALITER breuiùs.
Page: 120 (96)
[135.] PROBL. XXI. PROP. LV.
Page: 121 (97)
[136.] PROBL. XXII. PROP. LVI.
Page: 123 (99)
[137.] COROLL. I.
Page: 125 (101)
[138.] COROLL. II.
Page: 125 (101)
[139.] PROBL. XXIII. PROP. LVII.
Page: 125 (101)
[140.] COROLL.
Page: 126 (102)
< >
page |< < (93) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div291" type="section" level="1" n="128">
          <p>
            <s xml:id="echoid-s3139" xml:space="preserve">
              <pb o="93" file="0117" n="117" rhead=""/>
            diametro vltra centrum 2 in D, quare ſi eadem D 5 producatur, neceſſa-
              <lb/>
            riò ſecabit Hyperbolen SPEQ, ſed ipſa D 5 tota cadit extra
              <note symbol="a" position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">35. h.</note>
            ABC, cum ſit eius aſymptotos, quapropter occurſus rectæ D 5 cum Hyper-
              <lb/>
            bola SPEQ ſiet extra ABC, ideoque ſectio EP ſecabit priùs Hyperbolen
              <lb/>
            ABC, & </s>
            <s xml:id="echoid-s3140" xml:space="preserve">ſic Hyperbole IEL erit _MAXIMA_ inſcripta quæſita. </s>
            <s xml:id="echoid-s3141" xml:space="preserve">Quod facien-
              <lb/>
            dum, ac demonſtrandum erat.</s>
            <s xml:id="echoid-s3142" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div294" type="section" level="1" n="129">
          <head xml:id="echoid-head134" xml:space="preserve">ALITER breuiùs.</head>
          <p>
            <s xml:id="echoid-s3143" xml:space="preserve">PRoducatur contingens HE vſque ad circumſcriptã ſectionem ABC in K.
              <lb/>
            </s>
            <s xml:id="echoid-s3144" xml:space="preserve">Cum Hyperbolę ABC, IEL ſimiles ſint per diuerſos vertices, & </s>
            <s xml:id="echoid-s3145" xml:space="preserve">ad ean-
              <lb/>
            dem regulam ſimul adſcriptæ erunt infra EK ad ſe propiùs accedentes,
              <note symbol="b" position="right" xlink:label="note-0117-02" xlink:href="note-0117-02a" xml:space="preserve">45. h.</note>
            mirum ſectio KAT recedet ab EI per interuallum minus ipſo EK; </s>
            <s xml:id="echoid-s3146" xml:space="preserve">Verùm
              <lb/>
            cum Hyperbolę PEQ, IEL ſint concentricæ, & </s>
            <s xml:id="echoid-s3147" xml:space="preserve">per eundem verticem ſimul
              <lb/>
            adſcriptæ, erunt ſemper magis recedentes, & </s>
            <s xml:id="echoid-s3148" xml:space="preserve">ad interuallũ peruenient maius
              <lb/>
            quocunq; </s>
            <s xml:id="echoid-s3149" xml:space="preserve">dato interuallo, videlicet ſectio EPS recedet ab eadem EI per
              <note symbol="*" position="right" xlink:label="note-0117-03" xlink:href="note-0117-03a" xml:space="preserve">37. h.</note>
            teruallũ omnino maius eodẽ EK: </s>
            <s xml:id="echoid-s3150" xml:space="preserve">quapropter ſectiones KAT, EPS neceſſariò
              <lb/>
            ſe mutuò ſecabunt: </s>
            <s xml:id="echoid-s3151" xml:space="preserve">Vnde Hyperbole IEL erit _MAXIMA_ inſcripta quæſita.</s>
            <s xml:id="echoid-s3152" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div296" type="section" level="1" n="130">
          <head xml:id="echoid-head135" xml:space="preserve">PROBL. XIX. PROP. LIII.</head>
          <p>
            <s xml:id="echoid-s3153" xml:space="preserve">Datæ Hyperbolæ per punctum extra ipſam datum MINIMAM
              <lb/>
            Hyperbolen circumſcribere, quarum eadem ſit regula.</s>
            <s xml:id="echoid-s3154" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3155" xml:space="preserve">Oportet autem datum punctum, vel eſſe in angulo aſymptotis
              <lb/>
            contento, vel in eo, quod
              <unsure/>
            eſt ad verticem, dummodo in hoc caſu,
              <lb/>
            ipſius diſtantia à centro datæ ſectionis, minor ſit eius ſemi-tranſ-
              <lb/>
            uerſo latere per datum punctum tranſeunte.</s>
            <s xml:id="echoid-s3156" xml:space="preserve"/>
          </p>
          <figure number="82">
            <image file="0117-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0117-01"/>
          </figure>
          <p>
            <s xml:id="echoid-s3157" xml:space="preserve">ESto data Hyperbole ABC, cuius centrum D, aſymptoti DF, DG, & </s>
            <s xml:id="echoid-s3158" xml:space="preserve">da-
              <lb/>
            tum extra ipſam punctum ſit E, quod tamen ſit in angulo aſymptotali
              <lb/>
            FDG, vt in prima figura; </s>
            <s xml:id="echoid-s3159" xml:space="preserve">vel in eò qui ipſi eſt ad verticem, vt in ſecunda,
              <lb/>
            dummodo coniuncta ED, & </s>
            <s xml:id="echoid-s3160" xml:space="preserve">producta vſque ad ſectionem in B, ipſa ED </s>
          </p>
        </div>
      </text>
    </echo>
Impressum