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

Page concordance

< >
Scan Original
91 67
92 68
93 69
94 70
95 71
96 72
97 73
98 74
99 75
100 76
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
< >
page |< < (72) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div233" type="section" level="1" n="106">
          <p>
            <s xml:id="echoid-s2478" xml:space="preserve">
              <pb o="72" file="0096" n="96" rhead=""/>
            in ipſa DEF, quocunque puncto D, per ipſum ordinatim applicetur ODS,
              <lb/>
            alteram ſectionem ſecans in S: </s>
            <s xml:id="echoid-s2479" xml:space="preserve">erit quadratum SO æquale rectãgulo
              <note symbol="a" position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">1. huius.</note>
            & </s>
            <s xml:id="echoid-s2480" xml:space="preserve">quadratum DO rectangulo OEH, ſed rectangulum OBG maius eſt rectã-
              <lb/>
            gulo OEH, cum latitudo BG æqualis ſit EH, altitudo verò BO maior EO,
              <lb/>
            quare SO quadratum, maius eſt quadrato DO; </s>
            <s xml:id="echoid-s2481" xml:space="preserve">vnde punctum D cadit intra
              <lb/>
            Parabolen BA, & </s>
            <s xml:id="echoid-s2482" xml:space="preserve">ſic de quibuslibet alijs pũctis Parabolæ DEF; </s>
            <s xml:id="echoid-s2483" xml:space="preserve">ergo huiuſ-
              <lb/>
            modi ſectiones inter ſe nunquam conueniunt. </s>
            <s xml:id="echoid-s2484" xml:space="preserve">Quod primò, &</s>
            <s xml:id="echoid-s2485" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2487" xml:space="preserve">Has tamen dico, licet in infinitum productas, infra contingentem EA ad
              <lb/>
            ſe propiùs accedere: </s>
            <s xml:id="echoid-s2488" xml:space="preserve">Ducta enim DM parallela ad ON, & </s>
            <s xml:id="echoid-s2489" xml:space="preserve">per M applicata
              <lb/>
            MN, fiet parallelogrammum DN, cuius oppoſita latera MN, DO æqualia
              <lb/>
            erunt. </s>
            <s xml:id="echoid-s2490" xml:space="preserve">Iam quadratum MN, ſiue rectangulum NBG æquatur
              <note symbol="b" position="left" xlink:label="note-0096-02" xlink:href="note-0096-02a" xml:space="preserve">ibidem.</note>
            DO, ſiue rectangulo OEH, ſed horum latera BG, EH æqualia ſunt,
              <note symbol="c" position="left" xlink:label="note-0096-03" xlink:href="note-0096-03a" xml:space="preserve">ibidem.</note>
            & </s>
            <s xml:id="echoid-s2491" xml:space="preserve">latera BN, EO æqualia erunt: </s>
            <s xml:id="echoid-s2492" xml:space="preserve">itaque per proſtaphereſim, erit BE æqualis
              <lb/>
            NO, ſed eſt quoque MD æqualis eidem NO, igitur BE, & </s>
            <s xml:id="echoid-s2493" xml:space="preserve">MD inter ſe ſunt
              <lb/>
              <figure xlink:label="fig-0096-01" xlink:href="fig-0096-01a" number="65">
                <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0096-01"/>
              </figure>
            æquales, at ſunt quoque parallelæ, igitur coniunctæ BM, & </s>
            <s xml:id="echoid-s2494" xml:space="preserve">ED æquales
              <lb/>
            erunt, & </s>
            <s xml:id="echoid-s2495" xml:space="preserve">parallelæ, ſed BM ſecat NM, quare producta ſecabit quoque alte-
              <lb/>
            ram parallelarum OD, ſed extra ſectionem BMA (cum ſit BM intra ſectio-
              <lb/>
            nem, producta verò, tota cadat extra) ſit ergo occurſus cum ODS in P, & </s>
            <s xml:id="echoid-s2496" xml:space="preserve">
              <lb/>
            cum contingente EA in T; </s>
            <s xml:id="echoid-s2497" xml:space="preserve">& </s>
            <s xml:id="echoid-s2498" xml:space="preserve">in ſecunda figura, in qua contingens EA cadit
              <lb/>
            inter applicatas MN, OS, iungatur SM ſecans EA in V.</s>
            <s xml:id="echoid-s2499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2500" xml:space="preserve">Iam in prima figura, cum in parallelogrammo PE latera ET, DP, ſint æ-
              <lb/>
            qualia, ſitque EA maius ET, erit EA quoque maius DP, eſtque DP maius
              <lb/>
            intercepto ſegmento DS, quare AE, eò maius erit ipſo DS. </s>
            <s xml:id="echoid-s2501" xml:space="preserve">In ſecunda au-
              <lb/>
            tem figura, cum pariter ET, DP ſint æquales, ſitque ablata TV minor abla-
              <lb/>
            ta PS, erit reliqua EV maior reliqua DS, & </s>
            <s xml:id="echoid-s2502" xml:space="preserve">eò magis EA maior eadem DS.
              <lb/>
            </s>
            <s xml:id="echoid-s2503" xml:space="preserve">Non abſimili modò oſtendetur quamcunque interceptam XY infra SD, mi-
              <lb/>
            norem eſſe ipſa SD; </s>
            <s xml:id="echoid-s2504" xml:space="preserve">ducta enim YZ æquidiſtanter EB, demonſtrabitur item
              <lb/>
            YZ æqualis eidem BE, ideoque YZ, & </s>
            <s xml:id="echoid-s2505" xml:space="preserve">DM inter ſe æquales erunt, & </s>
            <s xml:id="echoid-s2506" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum