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

Table of figures

< >
[Figure 141]
Page: 176
[Figure 142]
Page: 179
[Figure 143]
Page: 183
[Figure 144]
Page: 184
[Figure 145]
Page: 184
[Figure 146]
Page: 185
[Figure 147]
Page: 186
[Figure 148]
Page: 188
[Figure 149]
Page: 189
[Figure 150]
Page: 190
[Figure 151]
Page: 191
[Figure 152]
Page: 192
[Figure 153]
Page: 193
[Figure 154]
Page: 194
[Figure 155]
Page: 195
[Figure 156]
Page: 196
[Figure 157]
Page: 197
[Figure 158]
Page: 198
[Figure 159]
Page: 199
[Figure 160]
Page: 200
[Figure 161]
Page: 201
[Figure 162]
Page: 202
[Figure 163]
Page: 203
[Figure 164]
Page: 204
[Figure 165]
Page: 205
[Figure 166]
Page: 205
[Figure 167]
Page: 206
[Figure 168]
Page: 207
[Figure 169]
Page: 208
[Figure 170]
Page: 208
< >
page |< < (109) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div350" type="section" level="1" n="150">
          <p>
            <s xml:id="echoid-s3659" xml:space="preserve">
              <pb o="109" file="0133" n="133" rhead=""/>
            Cipſius latera BA, BC eum contingant; </s>
            <s xml:id="echoid-s3660" xml:space="preserve">& </s>
            <s xml:id="echoid-s3661" xml:space="preserve">erit _MAXIMVS_: </s>
            <s xml:id="echoid-s3662" xml:space="preserve">Nam licet fa-
              <lb/>
            cta ſupra EF eadem penitùs, conſtructione nempe ſumpta FG æquali ad FE,
              <lb/>
            & </s>
            <s xml:id="echoid-s3663" xml:space="preserve">ducta GH perpendiculari ad GA, oſtendetur pariter H eſſe centrum alte-
              <lb/>
            rius circuli dato angulo inſcripti, ſed is erit minor circulo ex DE, cum ob
              <lb/>
            parallelas GH, AD, ſit AB ad BG, vt DA ad HG, ſed eſt AB maior BG, vn-
              <lb/>
            de radius DA erit maior radio HG, ſiue circulus AEC maior circulo ex HE.
              <lb/>
            </s>
            <s xml:id="echoid-s3664" xml:space="preserve">Iam quilibet alius circulus per E, dato angulo adſcriptus, cuius diameter
              <lb/>
            minor ſit EI, minor eſt ipſo AEC, & </s>
            <s xml:id="echoid-s3665" xml:space="preserve">quilibet alius, cuius diameter ſit maior
              <lb/>
            ipſa EI, eſt quidem maior AEC, ſed omnino ſecat dati anguli latera, cum
              <lb/>
            hæc circulum contingant: </s>
            <s xml:id="echoid-s3666" xml:space="preserve">ex quo circulus ex DE erit _MAXIMVS_ inſcriptus
              <lb/>
            quæſitus. </s>
            <s xml:id="echoid-s3667" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s3668" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3669" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3670" xml:space="preserve">SIverò ad datum punctum B extra circulum AEC, cuius ſit centrum D, ſit
              <lb/>
            ei circumſcribendus _MINIMVS_ angulus rectilineus; </s>
            <s xml:id="echoid-s3671" xml:space="preserve">iam per ſe patet
              <lb/>
            angulum ABC, à ductis contingentibus ex B, eſſe _MINIMVM_ quæſitum.
              <lb/>
            </s>
            <s xml:id="echoid-s3672" xml:space="preserve">Quod vltimò faciendum, ac demonſtrandum erat.</s>
            <s xml:id="echoid-s3673" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div352" type="section" level="1" n="151">
          <head xml:id="echoid-head156" xml:space="preserve">LEMMA VII. PROP. LXVI.</head>
          <p>
            <s xml:id="echoid-s3674" xml:space="preserve">In dato angulo, à recta linea per verticem vtcunque ſecto, lineas
              <lb/>
            applicare, quæ à prædicta diuidantur in data ratione.</s>
            <s xml:id="echoid-s3675" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3676" xml:space="preserve">SIt datus angulus ABC, vtcunque ſectus à re-
              <lb/>
              <figure xlink:label="fig-0133-01" xlink:href="fig-0133-01a" number="99">
                <image file="0133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0133-01"/>
              </figure>
            cta BD, punctum in eo ſit D, ex quo opor-
              <lb/>
            tet rectam, qualis eſt ADC, applicare ita vt ip-
              <lb/>
            ſius partes AD, DC ſint in data ratione, veluti
              <lb/>
            E ad F.</s>
            <s xml:id="echoid-s3677" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3678" xml:space="preserve">Ducatur DG parallela ad alteram linearum,
              <lb/>
            angulum continentium, vt ad AB; </s>
            <s xml:id="echoid-s3679" xml:space="preserve">& </s>
            <s xml:id="echoid-s3680" xml:space="preserve">fiat vt E ad
              <lb/>
            F, ita BG ad GC, iungaturque CD, quæ cum
              <lb/>
            BA conueniat in A. </s>
            <s xml:id="echoid-s3681" xml:space="preserve">Dico factum eſſe, quod
              <lb/>
            proponebatur.</s>
            <s xml:id="echoid-s3682" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3683" xml:space="preserve">Et enim, ob parallelas, vt AD ad DC, ita BG
              <lb/>
            ad GC, vel E ad F. </s>
            <s xml:id="echoid-s3684" xml:space="preserve">Quod, &</s>
            <s xml:id="echoid-s3685" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3686" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div354" type="section" level="1" n="152">
          <head xml:id="echoid-head157" xml:space="preserve">SCHOLIVM.</head>
          <p>
            <s xml:id="echoid-s3687" xml:space="preserve">SI data ratio E ad F, fuerit ratio æqualitatis, tunc BD, licet præter morem,
              <lb/>
            vocetur dati anguli diameter, & </s>
            <s xml:id="echoid-s3688" xml:space="preserve">ſi bifariam, & </s>
            <s xml:id="echoid-s3689" xml:space="preserve">ad rectos angulos ipſas
              <lb/>
            applicatas ſecuerit, dicatur axis.</s>
            <s xml:id="echoid-s3690" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum