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

Page concordance

< >
Scan Original
71 47
72 48
73 49
74 50
75 51
76 52
77 53
78 54
79 55
80 56
81 57
82 58
83 59
84 60
85 61
86 62
87 63
88 64
89 65
90 66
91 67
92 68
93 69
94 70
95 71
96 72
97 73
98 74
99 75
100 76
< >
page |< < (52) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div157" type="section" level="1" n="84">
          <p>
            <s xml:id="echoid-s1785" xml:space="preserve">
              <pb o="52" file="0076" n="76" rhead=""/>
            ſed omnino, vel Ellipſim ſecat, velintra eam cadit, cum punctum I ſit quo-
              <lb/>
            que intra. </s>
            <s xml:id="echoid-s1786" xml:space="preserve">Quare circulus GBH _MINIMV S_ eſt circumſcriptibilium per ver-
              <lb/>
            ticem B maioris axis datæ Ellipſis ABC. </s>
            <s xml:id="echoid-s1787" xml:space="preserve">Quod ſecundò faciendum erat.</s>
            <s xml:id="echoid-s1788" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div160" type="section" level="1" n="85">
          <head xml:id="echoid-head90" xml:space="preserve">SCHOLIVM I.</head>
          <p>
            <s xml:id="echoid-s1789" xml:space="preserve">HInc facilè eruitur pulcherrima de _MAXIMIS_, & </s>
            <s xml:id="echoid-s1790" xml:space="preserve">_MINIMIS_ circulis,
              <lb/>
            Ellipſi inſcriptis, & </s>
            <s xml:id="echoid-s1791" xml:space="preserve">circumſcriptis proprietas. </s>
            <s xml:id="echoid-s1792" xml:space="preserve">Nempe.</s>
            <s xml:id="echoid-s1793" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1794" xml:space="preserve">_MINIMV M_ circulum per verticem minoris axis AC Ellipſi circumſcri-
              <lb/>
            ptum, cuius diameter eſt rectum latus AB.</s>
            <s xml:id="echoid-s1795" xml:space="preserve"/>
          </p>
          <note symbol="a" position="left" xml:space="preserve">1. Co-
            <lb/>
          roll. 20. h.</note>
          <p>
            <s xml:id="echoid-s1796" xml:space="preserve">_MINIMV M_ circulum per verticem maioris axis DE circumſcriptũ, cuius
              <lb/>
            diameter eſt ipſe maior axis DE.</s>
            <s xml:id="echoid-s1797" xml:space="preserve"/>
          </p>
          <note symbol="b" position="left" xml:space="preserve">26. h.</note>
          <p>
            <s xml:id="echoid-s1798" xml:space="preserve">_MAXIMV M_ circulum per verticem minoris axis AC inſcriptum, cuius
              <lb/>
            diameter eſt ipſe minor axis AC.</s>
            <s xml:id="echoid-s1799" xml:space="preserve"/>
          </p>
          <note symbol="c" position="left" xml:space="preserve">26. h.</note>
          <p>
            <s xml:id="echoid-s1800" xml:space="preserve">Et _MAXIMV M_ circulũ per ver-
              <lb/>
              <figure xlink:label="fig-0076-01" xlink:href="fig-0076-01a" number="46">
                <image file="0076-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0076-01"/>
              </figure>
            ticem maioris axis DE inſcriptum,
              <lb/>
            cuius diameter eſt rectum
              <note symbol="d" position="left" xlink:label="note-0076-04" xlink:href="note-0076-04a" xml:space="preserve">1. Co-
                <lb/>
              roll. 20. h.</note>
            DF, eſſe quatuor circulos in conti-
              <lb/>
            nua eademque ratione geometri-
              <lb/>
            ca; </s>
            <s xml:id="echoid-s1801" xml:space="preserve">nam & </s>
            <s xml:id="echoid-s1802" xml:space="preserve">ipſorum diametri AB,
              <lb/>
            DE, AC, DF ſunt quatuor lineæ
              <lb/>
            continuè proportionales.</s>
            <s xml:id="echoid-s1803" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div162" type="section" level="1" n="86">
          <head xml:id="echoid-head91" xml:space="preserve">SCHOLIVM II.</head>
          <p>
            <s xml:id="echoid-s1804" xml:space="preserve">ELicitur quoque, Ellipſim quamcunque, mediam eſſe proportionalem
              <lb/>
            inter extremos prædictos circulos, mediamque inter medios. </s>
            <s xml:id="echoid-s1805" xml:space="preserve">Cum
              <lb/>
            enim quatuor lineæ AB, DE, AC, DF ſint continuè proportionales, erit
              <lb/>
            rectangulum ſub extremis AB, DF æquale rectangulo ſub medijs DE, AC,
              <lb/>
            nempè quadrato G, quæ ſit media proportionalis inter DE, AC; </s>
            <s xml:id="echoid-s1806" xml:space="preserve">hoc eſt vt
              <lb/>
            AB ad G, ita erit G ad DF; </s>
            <s xml:id="echoid-s1807" xml:space="preserve">quare circulus ex diametro AB, ad circulum ex
              <lb/>
            diametro G, erit vt circulus G, ad circulum ex DF. </s>
            <s xml:id="echoid-s1808" xml:space="preserve">Item cum ſit DE ad G,
              <lb/>
            ita G ad AC, erit circulus ex DE ad circulum ex G, vt circulus G ad circu-
              <lb/>
              <note symbol="e" position="left" xlink:label="note-0076-05" xlink:href="note-0076-05a" xml:space="preserve">5. Arch.
                <lb/>
              de Co-
                <lb/>
              noid. &
                <lb/>
              Sphęroid.</note>
            lum ex AC, ſed circulus ex G æquatur Ellipſi; </s>
            <s xml:id="echoid-s1809" xml:space="preserve">vnde Ellipſis DAEC eſt media proportionalis inter extremos prædictos circulos AB, DF mediaque
              <lb/>
            inter medios DE, AC.</s>
            <s xml:id="echoid-s1810" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum