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

Page concordance

< >
Scan Original
101 77
102 78
103 79
104 80
105 81
106 82
107 83
108 84
109 85
110 86
111 87
112 88
113 89
114 90
115 91
116 92
117 93
118 94
119 95
120 96
121 97
122 98
123 99
124 100
125 101
126 102
127 103
128 104
129 105
130 106
< >
page |< < (50) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div149" type="section" level="1" n="82">
          <p>
            <s xml:id="echoid-s1717" xml:space="preserve">
              <pb o="50" file="0074" n="74" rhead=""/>
            adſcribatur per B Hyperbole ABC, quæ ipſi HBI erit ſimilis (cum
              <note symbol="a" position="left" xlink:label="note-0074-01" xlink:href="note-0074-01a" xml:space="preserve">5. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            latera ſint proportionalia) eritque ei circumſcripta (cum ſit maiorum late- rum) & </s>
            <s xml:id="echoid-s1718" xml:space="preserve">erit _MINIMA_ quæſita. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">Nam quælibet alia adſcripta cum recto BE,
              <lb/>
              <note symbol="b" position="left" xlink:label="note-0074-02" xlink:href="note-0074-02a" xml:space="preserve">3. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ſed cum tranſuerſo, quod ipſo BD ſit minus eſt maior ipfa ABC; </s>
            <s xml:id="echoid-s1720" xml:space="preserve">quælibet verò adſcripta cum eodem recto BE, ſed cum tranſuerſo BM, quod excedat
              <lb/>
              <note symbol="c" position="left" xlink:label="note-0074-03" xlink:href="note-0074-03a" xml:space="preserve">ibidem.</note>
            BD eſt quidem minor ipſa ABC, ſed omnino ſecat Hyperbolen HBI, cum
              <lb/>
            iuncta regula ME, & </s>
            <s xml:id="echoid-s1721" xml:space="preserve">producta omnino ſecet regulam GF infra contingen-
              <lb/>
            tem BE. </s>
            <s xml:id="echoid-s1722" xml:space="preserve">Vnde ipſa ABC erit _MINIMA_ circumſcripta cum dato recto BE,
              <lb/>
            vti quærebatur. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">Quod vltimò faciendum erat.</s>
            <s xml:id="echoid-s1724" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div152" type="section" level="1" n="83">
          <head xml:id="echoid-head88" xml:space="preserve">PROBL. X. PROP. XXV.</head>
          <p>
            <s xml:id="echoid-s1725" xml:space="preserve">Datæ Ellipſi, cum dato latere, quodminus ſit eius recto, per ip-
              <lb/>
            ſius verticem MAXIMAM Ellipſim inſcribere: </s>
            <s xml:id="echoid-s1726" xml:space="preserve">& </s>
            <s xml:id="echoid-s1727" xml:space="preserve">è contra.</s>
            <s xml:id="echoid-s1728" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1729" xml:space="preserve">Datæ Ellipſi, cum dato recto latere, quod maius ſit eius recto,
              <lb/>
            per ipſius verticem MINIMAM Ellipſim circumſcribere.</s>
            <s xml:id="echoid-s1730" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1731" xml:space="preserve">SIt data Ellipſis ABC, cuius tranſuerſum BD, rectum BE, regula DE:
              <lb/>
            </s>
            <s xml:id="echoid-s1732" xml:space="preserve">oportet per verticem B, cum dato recto BF _MAXIMAM_ Ellipſim inſcri-
              <lb/>
            bere, neceſſe eſt autem, quod rectum datum BF
              <lb/>
              <figure xlink:label="fig-0074-01" xlink:href="fig-0074-01a" number="44">
                <image file="0074-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0074-01"/>
              </figure>
            minus ſit recto BE (ſi enim ei æquale eſſet, vel
              <lb/>
              <note symbol="a" position="left" xlink:label="note-0074-04" xlink:href="note-0074-04a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            maius, etiam deſcribenda Ellipſis, vel eſſet ea- dem cum data ABC, vel hanc ipſam ſecaret, vt
              <lb/>
            ſatis patet, cum vel ipſarum regulæ ſimul con-
              <lb/>
            gruerent, vel ſe mutuò ſecarent.)</s>
            <s xml:id="echoid-s1733" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1734" xml:space="preserve">Adſcribatur cum eodem trãſuerſo BD,
              <note symbol="b" position="left" xlink:label="note-0074-05" xlink:href="note-0074-05a" xml:space="preserve">7. huius.</note>
            que dato recto BF, per verticem B, Ellipſis GBL:
              <lb/>
            </s>
            <s xml:id="echoid-s1735" xml:space="preserve">& </s>
            <s xml:id="echoid-s1736" xml:space="preserve">hæc erit _MAXIMA_ quæſita. </s>
            <s xml:id="echoid-s1737" xml:space="preserve">Nam quælibet alia
              <lb/>
            eidem ABC adſcripta cum recto BF, ſed cum
              <lb/>
            tranſuerſo, quod minus ſit BD, eſt minor
              <note symbol="c" position="left" xlink:label="note-0074-06" xlink:href="note-0074-06a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            GBL, quælibet verò adſcripta cum tranſuerſo
              <lb/>
            BM, quod excedat BD eſt quidem maior
              <note symbol="d" position="left" xlink:label="note-0074-07" xlink:href="note-0074-07a" xml:space="preserve">ibidem.</note>
            GBL, ſed omnino ſecat Ellipſim datam ABC cum & </s>
            <s xml:id="echoid-s1738" xml:space="preserve">iuncta regula
              <note symbol="e" position="left" xlink:label="note-0074-08" xlink:href="note-0074-08a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            omnino ſecet regulam ED. </s>
            <s xml:id="echoid-s1739" xml:space="preserve">Quare Ellipſis GBL erit _MAXIMA_ quæſita in-
              <lb/>
            ſcripta cum recto dato BF. </s>
            <s xml:id="echoid-s1740" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s1741" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1742" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1743" xml:space="preserve">Sit iam data Ellipſis GBL, cuius tranſuerſum BD, rectum BF, regula DF,
              <lb/>
            & </s>
            <s xml:id="echoid-s1744" xml:space="preserve">circumſcribenda ſit ci _MINIMA_ Ellipſis cum dato recto BE, quod debet
              <lb/>
            quidem eſſe maius recto BF (nam ſi æquale, vel minus eſſet, deſcribenda
              <lb/>
            quoque Ellipſis, vel eadem eſſet cum data GBL, vel huic eſſet
              <note symbol="f" position="left" xlink:label="note-0074-09" xlink:href="note-0074-09a" xml:space="preserve">ibidem.</note>
            cum vel harum regulæ ſimul congruerent, vel regula deſcribendæ caderet
              <lb/>
            tota intra regulam deſcriptæ GBL.)</s>
            <s xml:id="echoid-s1745" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1746" xml:space="preserve">Adſcribatur cum tranſuerſo BD, datoque recto BE, per verticem B,
              <note symbol="g" position="left" xlink:label="note-0074-10" xlink:href="note-0074-10a" xml:space="preserve">7. huius.</note>
            lipſis ABC, quæ erit _MINIMA_ circumſcripta quæſita. </s>
            <s xml:id="echoid-s1747" xml:space="preserve">Quoniam quæcun-
              <lb/>
            que alia adſcripta datæ GBL cum recto BE, ſed cum tranſuerſo, quod maius
              <lb/>
              <note symbol="h" position="left" xlink:label="note-0074-11" xlink:href="note-0074-11a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            ſit BD, maior eſt ipſa GBL; </s>
            <s xml:id="echoid-s1748" xml:space="preserve">quælibet verò adſcripta cum tranſuerſo BN, quod minus ſit tranſuerſo BD, eſt quidem minor ipſa ABC, ſed omnino
              <note symbol="i" position="left" xlink:label="note-0074-12" xlink:href="note-0074-12a" xml:space="preserve">ibidem.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum