Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

Page concordance

< >
Scan Original
211 173
212 174
213 175
214 176
215 177
216 178
217 179
218 180
219 181
220 182
221 183
222 184
223 185
224 186
225 187
226 188
227 189
228 190
229 191
230 192
231 193
232 194
233 195
234 196
235 197
236 198
237 199
238 200
239 201
240 202
< >
page |< < (270) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div814" type="section" level="1" n="248">
          <pb o="270" file="0308" n="308" rhead="Apollonij Pergæi Conicor. Lib. VI."/>
          <p style="it">
            <s xml:id="echoid-s10100" xml:space="preserve">Sectionum conicarum circa axim communem poſitarum datam coniſe-
              <lb/>
              <note position="left" xlink:label="note-0308-01" xlink:href="note-0308-01a" xml:space="preserve">PROP.
                <lb/>
              22.
                <lb/>
              Addit.</note>
            ctionem abſcindentium non in eius vertice, quas omnes eadem recta li-
              <lb/>
            nea contingat, erunt ſingulares tantummodo parabolæ, & </s>
            <s xml:id="echoid-s10101" xml:space="preserve">circulus, elli-
              <lb/>
            pſes verò, & </s>
            <s xml:id="echoid-s10102" xml:space="preserve">hyperbole erunt infinitæ.</s>
            <s xml:id="echoid-s10103" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10104" xml:space="preserve">Quoniam circa communem axim D
              <lb/>
              <figure xlink:label="fig-0308-01" xlink:href="fig-0308-01a" number="356">
                <image file="0308-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0308-01"/>
              </figure>
            A conſtitui poßunt parabolæ, circulus,
              <lb/>
            infinitæ hyperbolæ, & </s>
            <s xml:id="echoid-s10105" xml:space="preserve">infinitæ ellipſes
              <lb/>
              <note position="left" xlink:label="note-0308-02" xlink:href="note-0308-02a" xml:space="preserve">Prop. 17.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            habentes ſemilatus rectum axis æqualẽ
              <lb/>
            ſingulari breuiſecanti D A in ſectione
              <lb/>
            conica B A C educto, & </s>
            <s xml:id="echoid-s10106" xml:space="preserve">hæ omnes ab-
              <lb/>
              <note position="left" xlink:label="note-0308-03" xlink:href="note-0308-03a" xml:space="preserve">Prop. 21.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            ſcindunt coniſectionem B A C in A.
              <lb/>
            </s>
            <s xml:id="echoid-s10107" xml:space="preserve">Ergo patet propoſitum.</s>
            <s xml:id="echoid-s10108" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10109" xml:space="preserve">Hinc colligitur dari non poſſe coniſe-
              <lb/>
            ctionem minimam extrinſecus tangen-
              <lb/>
            tium, neque maximam intrinſecus tã-
              <lb/>
            gentium eandem coniſectionem in pun-
              <lb/>
            cto A extra verticem axis poſito.</s>
            <s xml:id="echoid-s10110" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10111" xml:space="preserve">Nam quælibet coniſectio, cuius ſemie-
              <lb/>
            rectum axis minus eſt breuiſecante ſingulari D A intrinſecus tangit ſectionem
              <lb/>
              <note position="left" xlink:label="note-0308-04" xlink:href="note-0308-04a" xml:space="preserve">Prop. 18.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            B A C in A, & </s>
            <s xml:id="echoid-s10112" xml:space="preserve">ſi ſemierectum maius fuerit eadem D A extrinſecus eandem
              <lb/>
            ſectionem B A C continget, neque vnquam ceſſant prædicti contactus extrin-
              <lb/>
              <note position="left" xlink:label="note-0308-05" xlink:href="note-0308-05a" xml:space="preserve">Prop. 19.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            ſeci, vel intrinſeci quouſque ſemierectum axis efficitur æquale breuiſecanti D
              <lb/>
            A: </s>
            <s xml:id="echoid-s10113" xml:space="preserve">at tunc non amplius contingit, ſed ſecat eam in A. </s>
            <s xml:id="echoid-s10114" xml:space="preserve">Quare patet propoſi-
              <lb/>
              <note position="left" xlink:label="note-0308-06" xlink:href="note-0308-06a" xml:space="preserve">Prop. 21.
                <lb/>
              addit.
                <lb/>
              huius.</note>
            tum.</s>
            <s xml:id="echoid-s10115" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10116" xml:space="preserve">Conſtat etiam quod parabolarum vnica tantummodò, & </s>
            <s xml:id="echoid-s10117" xml:space="preserve">circulorum vnicus
              <lb/>
            etiam abſcindit coniſectionem B A C in A, & </s>
            <s xml:id="echoid-s10118" xml:space="preserve">contingit eandem contingentem
              <lb/>
            A G in A.</s>
            <s xml:id="echoid-s10119" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10120" xml:space="preserve">At hyperbolarum, atque ellipſium abſcindentium eandem ſectionem B A C in
              <lb/>
            A, quas omnes eadem recta linea A G tangit in A non poteſt affignari maxi-
              <lb/>
            ma, neque minima.</s>
            <s xml:id="echoid-s10121" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s10122" xml:space="preserve">Nam vt dictum eſt ad 17. </s>
            <s xml:id="echoid-s10123" xml:space="preserve">Additarum huius libri infinitæ hyperbolæ ſe ſe
              <lb/>
            contingentes in vertice axis deſinunt in parabolam vnicam, & </s>
            <s xml:id="echoid-s10124" xml:space="preserve">poſt parabolam
              <lb/>
            interius ſe ſe ſucceſſiuè contingunt infinitæ ellipſes ad axim maiorem adiacen-
              <lb/>
            tes, quæ deſinunt in circulum vnicum, ac poſt circulum interius eum contin-
              <lb/>
            gunt inſinitæ ellipſes ad axim minorem adiacentes, quarum omnium ſemiere-
              <lb/>
            cta latera axium æqualia ſunt breuiſecanti ſingulari D A datæ ſectionis B A C.
              <lb/>
            </s>
            <s xml:id="echoid-s10125" xml:space="preserve">Quare patet propoſitum.</s>
            <s xml:id="echoid-s10126" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div839" type="section" level="1" n="249">
          <head xml:id="echoid-head312" xml:space="preserve">LIBRI SEXTI FINIS.</head>
        </div>
      </text>
    </echo>
Impressum