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

Page concordance

< >
Scan Original
41 21
42 22
43 23
44 24
45 25
46 26
47 27
48 28
49 29
50 30
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59
60
61
62
63 39
64 40
65 41
66 42
67 43
68 44
69 45
70 46
< >
page |< < (27) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div74" type="section" level="1" n="45">
          <pb o="27" file="0047" n="47" rhead=""/>
        </div>
        <div xml:id="echoid-div76" type="section" level="1" n="46">
          <head xml:id="echoid-head51" xml:space="preserve">ITER VM aliter breuiùs, ſed negatiuè.</head>
          <p>
            <s xml:id="echoid-s987" xml:space="preserve">Sifuerit vt recta AD ad DC, ita quadratum AB ad BC, erunt
              <lb/>
            AD, DB, DC in continua ratione geometrica.</s>
            <s xml:id="echoid-s988" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s989" xml:space="preserve">SIenim DB non eſt media proportionalis inter AD, DC, eſto ſi fieri po-
              <lb/>
            teſt media quæcunque DE; </s>
            <s xml:id="echoid-s990" xml:space="preserve">erit igitur, in prima figura, tota AD ad to-
              <lb/>
            tam DE, vt pars DE ad partem DC, ergo reliqua AE ad reliquam EC, erit
              <lb/>
              <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">Vni-
                <lb/>
              uerſalius
                <lb/>
              quàm à
                <lb/>
              Caual. in
                <lb/>
              3. prop.
                <lb/>
              exerc. 6.</note>
            vt pars ED ad DC, vel vt tota AD ad totam DE: </s>
            <s xml:id="echoid-s991" xml:space="preserve">(ex cõ-
              <lb/>
            ſtructione) in ſecunda verò cum ſit AD ad DE vt DE ad
              <lb/>
              <figure xlink:label="fig-0047-01" xlink:href="fig-0047-01a" number="23">
                <image file="0047-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0047-01"/>
              </figure>
            DC, erit componendo AE ad ED, vt EC ad CD, & </s>
            <s xml:id="echoid-s992" xml:space="preserve">per-
              <lb/>
            mutando AE ad EC, vt ED ad DC, vel vt AD ad DE
              <lb/>
            (ex conſtructione) cum ergo in vtraque figura ſit AE ad
              <lb/>
            EC, vt AD ad DE, erit quadratum AE ad EC, vt qua-
              <lb/>
            dratum AD ad DE, vel vt recta AD ad DC, vel vt qua-
              <lb/>
            dratum AB ad BC (ex ſuppoſitione) vel recta AE ad
              <lb/>
            EC, vt recta AB ad BC, & </s>
            <s xml:id="echoid-s993" xml:space="preserve">in prima figura componen-
              <lb/>
            do, at in ſecunda diuidendo, AC ad CE, vt AC ad CB,
              <lb/>
            quare CE, CB inter ſe ſunt &</s>
            <s xml:id="echoid-s994" xml:space="preserve">quales, totum, & </s>
            <s xml:id="echoid-s995" xml:space="preserve">pars,
              <lb/>
            quod eſt abſurdum: </s>
            <s xml:id="echoid-s996" xml:space="preserve">non eſt ergo media inter AD, & </s>
            <s xml:id="echoid-s997" xml:space="preserve">
              <lb/>
            DC, quæ ſit maior, vel minor DB; </s>
            <s xml:id="echoid-s998" xml:space="preserve">vnde ipſa DB erit
              <lb/>
            media proportionalis inter AD, & </s>
            <s xml:id="echoid-s999" xml:space="preserve">DC. </s>
            <s xml:id="echoid-s1000" xml:space="preserve">Quod demon-
              <lb/>
            ſtrare oportebat.</s>
            <s xml:id="echoid-s1001" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div78" type="section" level="1" n="47">
          <head xml:id="echoid-head52" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s1002" xml:space="preserve">HInc patet, quod, cum fuerint tres magnitudines continuè proportio-
              <lb/>
            nales, tùm exceſſus quibus differunt, tùm earum aggregata, erunt in
              <lb/>
            eadem ratione, in qua ſunt datæ magnitudines: </s>
            <s xml:id="echoid-s1003" xml:space="preserve">quando enim poſitum fuit
              <lb/>
            eſſe AD ad DE, vt DE ad DC oſtenſum quoque fuit AE ad EC eſſe vt AD
              <lb/>
            ad DE, ſed in prima figura AE, EC ſunt exceſſus datarum magnitudinum,
              <lb/>
            in ſecunda verò ſunt aggregata primæ cum ſecunda, & </s>
            <s xml:id="echoid-s1004" xml:space="preserve">ſecundæ cum tertia;
              <lb/>
            </s>
            <s xml:id="echoid-s1005" xml:space="preserve">quare patet, &</s>
            <s xml:id="echoid-s1006" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1007" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div79" type="section" level="1" n="48">
          <head xml:id="echoid-head53" xml:space="preserve">THEOR. V. PROP. XIII.</head>
          <p>
            <s xml:id="echoid-s1008" xml:space="preserve">Si duæ Parabolæ ad eaſdem partes deſcriptæ ad idem punctum
              <lb/>
            ſimul occurrant, ſintque earum diametri inter ſe æquidiſtantes, & </s>
            <s xml:id="echoid-s1009" xml:space="preserve">
              <lb/>
            applicatæ ſint eædem, ac ipſarum vertices ſint in eadem recta, quæ
              <lb/>
            ducitur ex occurſu; </s>
            <s xml:id="echoid-s1010" xml:space="preserve">ipſæ in nullo alio puncto ſimul conuenient, & </s>
            <s xml:id="echoid-s1011" xml:space="preserve">
              <lb/>
            omnes, quæ ex contactu in ipſis ducuntur in eadem ratione à ſe-
              <lb/>
            ctionibus diuidentur.</s>
            <s xml:id="echoid-s1012" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1013" xml:space="preserve">ESto Parabole ABC, cuius diameter BF, & </s>
            <s xml:id="echoid-s1014" xml:space="preserve">ducta BA, ſit quælibet DE
              <lb/>
            ipſi BF æquidiſtans, & </s>
            <s xml:id="echoid-s1015" xml:space="preserve">AC ordinatim applicata BF, & </s>
            <s xml:id="echoid-s1016" xml:space="preserve">per verticem </s>
          </p>
        </div>
      </text>
    </echo>
Impressum