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

Table of figures

< >
[Figure 171]
Page: 209
[Figure 172]
Page: 209
[Figure 173]
Page: 210
[Figure 174]
Page: 211
[Figure 175]
Page: 212
[Figure 176]
Page: 214
[Figure 177]
Page: 216
[Figure 178]
Page: 217
[Figure 179]
Page: 218
[Figure 180]
Page: 219
[Figure 181]
Page: 220
[Figure 182]
Page: 220
[Figure 183]
Page: 221
[Figure 184]
Page: 222
[Figure 185]
Page: 223
[Figure 186]
Page: 224
[Figure 187]
Page: 225
[Figure 188]
Page: 225
[Figure 189]
Page: 226
[Figure 190]
Page: 227
[Figure 191]
Page: 228
[Figure 192]
Page: 229
[Figure 193]
Page: 231
[Figure 194]
Page: 232
[Figure 195]
Page: 234
[Figure 196]
Page: 238
[Figure 197]
Page: 239
[Figure 198]
Page: 240
[Figure 199]
Page: 241
[Figure 200]
Page: 242
< >
page |< < (147) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div492" type="section" level="1" n="199">
          <p>
            <s xml:id="echoid-s4904" xml:space="preserve">
              <pb o="147" file="0171" n="171" rhead=""/>
            reliquo BFC æqualis, qui ſunt anguli ad
              <lb/>
              <figure xlink:label="fig-0171-01" xlink:href="fig-0171-01a" number="137">
                <image file="0171-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0171-01"/>
              </figure>
            centra D, F: </s>
            <s xml:id="echoid-s4905" xml:space="preserve">ergo ipſorum dimidia ad
              <lb/>
            circumferentias, hoc eſt anguli B G L,
              <lb/>
            B I C æquales erunt, vnde G L æquidi-
              <lb/>
            ſtabit I C: </s>
            <s xml:id="echoid-s4906" xml:space="preserve">quare, vt C B ad B L, ita I B,
              <lb/>
            ad BG, vel ſumpta communi altitudine
              <lb/>
            BH, ita rectangulum IBH, ſiue quadra-
              <lb/>
            tum B C, ad rectangulum H B G, vel ad
              <lb/>
            quadratum BM: </s>
            <s xml:id="echoid-s4907" xml:space="preserve">cum ergo ſit CB ad BL,
              <lb/>
            vt quadratum C B ad quadratum B M,
              <lb/>
            erunt tres contingentes BC, BM, BL,
              <lb/>
            in eadem ratione geometrica, ſed C B
              <lb/>
            ad B M, eſt vt C F ad M E, & </s>
            <s xml:id="echoid-s4908" xml:space="preserve">M B ad
              <lb/>
            B L, vt M E ad L D; </s>
            <s xml:id="echoid-s4909" xml:space="preserve">ergo C F, M E,
              <lb/>
            L D, vti etiam ipſarum quadrata, ſiue
              <lb/>
            _MAXIMI_ circuli ex FC, EM, DL erunt
              <lb/>
            in eadem ratione geometrica, quę pro-
              <lb/>
            cedit iuxta quadrata contingentium
              <lb/>
            B C, B M, B L. </s>
            <s xml:id="echoid-s4910" xml:space="preserve">Quod oſtendere pro-
              <lb/>
            ponebatur.</s>
            <s xml:id="echoid-s4911" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div494" type="section" level="1" n="200">
          <head xml:id="echoid-head205" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s4912" xml:space="preserve">HInc elicitur, quod ſi datus angulus fuerit angulus trianguli æquilateri,
              <lb/>
            ſiue duæ tertiæ vnius recti, prædicti _MAXIMI_ circuli erunt inter ſe
              <lb/>
            in continua progreſſione nonupla. </s>
            <s xml:id="echoid-s4913" xml:space="preserve">Tunc enim in triangulo ęquilatero BNO,
              <lb/>
            _MAXIMVS_ inſcriptus circulus ex DG ſingula latera ad puncta contactuum
              <lb/>
            bifariam ſecabit, quare BL æquabitur LN, ſiue NG, ſiue NM, (cum circu-
              <lb/>
            lum contingentes, ex eodem puncto ſint æquales) hoc eſt BM erit tripla
              <lb/>
            BL, & </s>
            <s xml:id="echoid-s4914" xml:space="preserve">quadratum BM nonuplum quadrati B L, vel circulus ex EM nonu-
              <lb/>
            plus circuli ex DL, itemque circulus ex F C nonuplus circuli ex E M, cum
              <lb/>
            ſint in eadem proportione geometrica, & </s>
            <s xml:id="echoid-s4915" xml:space="preserve">hoc ſemper, quotcunq; </s>
            <s xml:id="echoid-s4916" xml:space="preserve">ſint huiuſ-
              <lb/>
            modi circuli ſe mutuò, & </s>
            <s xml:id="echoid-s4917" xml:space="preserve">prædicti anguli latera contingentes.</s>
            <s xml:id="echoid-s4918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4919" xml:space="preserve">Hic autem notandum eſt inter hos _MAXIMOS_ circulos non dari _MAXI-_
              <lb/>
            _MVM_, cum infra circulum FC alij infiniti in eadem progreſſione dato angu-
              <lb/>
            lo inſcribi poſſint, eò quod ipſe ad partes L ſit infinitæ extenſionis.</s>
            <s xml:id="echoid-s4920" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4921" xml:space="preserve">Item inter eoſdem _MAXIMOS_ circulos non dari _MINIMVM_; </s>
            <s xml:id="echoid-s4922" xml:space="preserve">quoniam
              <lb/>
            ad partes verticis B, ſupra circulum DL, reſiduo trilineo, licet terminato,
              <lb/>
            alij infiniti circuli perpetuò decreſcentes inſcribi poſſunt.</s>
            <s xml:id="echoid-s4923" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum