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

Table of figures

< >
[Figure 111]
Page: 145
[Figure 112]
Page: 146
[Figure 113]
Page: 147
[Figure 114]
Page: 148
[Figure 115]
Page: 149
[Figure 116]
Page: 149
[Figure 117]
Page: 150
[Figure 118]
Page: 151
[Figure 119]
Page: 152
[Figure 120]
Page: 153
[Figure 121]
Page: 154
[Figure 122]
Page: 155
[Figure 123]
Page: 156
[Figure 124]
Page: 158
[Figure 125]
Page: 159
[Figure 126]
Page: 160
[Figure 127]
Page: 161
[Figure 128]
Page: 162
[Figure 129]
Page: 164
[Figure 130]
Page: 165
[Figure 131]
Page: 166
[Figure 132]
Page: 167
[Figure 133]
Page: 168
[Figure 134]
Page: 168
[Figure 135]
Page: 169
[Figure 136]
Page: 170
[Figure 137]
Page: 171
[Figure 138]
Page: 172
[Figure 139]
Page: 173
[Figure 140]
Page: 173
< >
page |< < (89) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div275" type="section" level="1" n="123">
          <p>
            <s xml:id="echoid-s3004" xml:space="preserve">
              <pb o="89" file="0113" n="113" rhead=""/>
            ipſam ABC in puncto L, ſed poſitum fuit eam quoque contingere in H: </s>
            <s xml:id="echoid-s3005" xml:space="preserve">Er-
              <lb/>
            go in duobus punctis H, L ſe contingent; </s>
            <s xml:id="echoid-s3006" xml:space="preserve">quod eſt falſum; </s>
            <s xml:id="echoid-s3007" xml:space="preserve">nam Parabole
              <lb/>
            Parabolen, ſiue Hyperbole Hyperbolen concentricam in duobus
              <note symbol="a" position="right" xlink:label="note-0113-01" xlink:href="note-0113-01a" xml:space="preserve">28. 31. 4.
                <lb/>
              conic.</note>
            non contingit. </s>
            <s xml:id="echoid-s3008" xml:space="preserve">Non ergo tales ſectiones ſe tangunt in H; </s>
            <s xml:id="echoid-s3009" xml:space="preserve">neque in L, ob ean-
              <lb/>
            dem rationem; </s>
            <s xml:id="echoid-s3010" xml:space="preserve">quare ipſæ in occurſibus H, & </s>
            <s xml:id="echoid-s3011" xml:space="preserve">L ſe mutuò ſecant. </s>
            <s xml:id="echoid-s3012" xml:space="preserve">Quod erat
              <lb/>
            oſtendendum.</s>
            <s xml:id="echoid-s3013" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div278" type="section" level="1" n="124">
          <head xml:id="echoid-head129" xml:space="preserve">THEOR. XXVIII. PROP. L.</head>
          <p>
            <s xml:id="echoid-s3014" xml:space="preserve">Impoſſibile eſt Hyperbolen Parabolæ, per eundem, vel per
              <lb/>
            diuerſos vertices inſcribere. </s>
            <s xml:id="echoid-s3015" xml:space="preserve">Item.</s>
            <s xml:id="echoid-s3016" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3017" xml:space="preserve">Impoſſibile eſt Parabolen Hyperbolæ, per eundem, vel per di-
              <lb/>
            uerſos vertices circumſcribere.</s>
            <s xml:id="echoid-s3018" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3019" xml:space="preserve">ESto Parabole ABC, cui per punctum D in ea ſumptum, vt in prima figu-
              <lb/>
            ra, vel intra ipſam, vt in ſecunda, adſcripta ſit quæcunque Hyperbole
              <lb/>
            EDF circa communem diametrum BDG, quæ per aliquas ſuæ peripheriæ
              <lb/>
            partes DE, DF, hinc inde à diametro ſumptas cadat intra Parabolen ABC.
              <lb/>
            </s>
            <s xml:id="echoid-s3020" xml:space="preserve">Dico ipſam Hyperbolen, ſi producatur, ex vtraque parte Parabolen ſecare.</s>
            <s xml:id="echoid-s3021" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3022" xml:space="preserve">Nam ductis ex D re-
              <lb/>
            ctis DA, DC vtrique
              <lb/>
              <figure xlink:label="fig-0113-01" xlink:href="fig-0113-01a" number="78">
                <image file="0113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0113-01"/>
              </figure>
            aſymptoto Hyperbolæ
              <lb/>
            EDF ęquidiſtãtibus, hę;
              <lb/>
            </s>
            <s xml:id="echoid-s3023" xml:space="preserve">neceſſariò Parabolen
              <lb/>
            ſecabunt, vt in A, C;</s>
            <s xml:id="echoid-s3024" xml:space="preserve">
              <note symbol="a" position="right" xlink:label="note-0113-02" xlink:href="note-0113-02a" xml:space="preserve">27. pri-
                <lb/>
              mi conic.</note>
            ſed cum Hyperbola in
              <lb/>
            alio puncto quàm D
              <lb/>
            nunquam conuenient:</s>
            <s xml:id="echoid-s3025" xml:space="preserve">
              <note symbol="b" position="right" xlink:label="note-0113-03" xlink:href="note-0113-03a" xml:space="preserve">Coroll.
                <lb/>
              11. huius.</note>
            quare, cum Hyperbola
              <lb/>
            EDF ex vtraque parte
              <lb/>
            in infinitum habeat, ſi
              <lb/>
            producatur, occurret
              <lb/>
            denique Parabolæ ABC inter puncta B, A, & </s>
            <s xml:id="echoid-s3026" xml:space="preserve">puncta B, C; </s>
            <s xml:id="echoid-s3027" xml:space="preserve">eamque ſeca-
              <lb/>
            bit, nam ſi tantùm eam tangeret, vel non, ſi vlteriùs producatur intra Para-
              <lb/>
            bolen, ſecaret aliquandò rectas DA, DC; </s>
            <s xml:id="echoid-s3028" xml:space="preserve">quod eſt impoſſibile. </s>
            <s xml:id="echoid-s3029" xml:space="preserve">Non
              <note symbol="c" position="right" xlink:label="note-0113-04" xlink:href="note-0113-04a" xml:space="preserve">ibidem.</note>
            tur inſcribi vnquam poteſt Hyperbole datæ Parabolæ, per punctum in ea,
              <lb/>
            vel intra ipſa datum, eadem ratione demonſtrabitur non poſſe circumſcribi
              <lb/>
            Parabolen datæ Hyperbolę per punctum in ea, vel extra ipſam datum. </s>
            <s xml:id="echoid-s3030" xml:space="preserve">Quod
              <lb/>
            erat, &</s>
            <s xml:id="echoid-s3031" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3032" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div280" type="section" level="1" n="125">
          <head xml:id="echoid-head130" xml:space="preserve">COROLL.</head>
          <p>
            <s xml:id="echoid-s3033" xml:space="preserve">HInc patet non dari _MAXIMAM_ Hyperbolen datæ Parabolæ, vel per
              <lb/>
            eundem verticem, vel per diuerſos inſcriptibilem; </s>
            <s xml:id="echoid-s3034" xml:space="preserve">itemque non dari
              <lb/>
            _MINIMAM_ Parabolen datæ Hyperbolæ, vel per eundem, vel per diuerſos
              <lb/>
            vertices circumſcriptibilem.</s>
            <s xml:id="echoid-s3035" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum