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
251 213
252 214
253 215
254 216
255 217
256 218
257 219
258 220
259 221
260 222
261 223
262 224
263 225
264 226
265 227
266 228
267 229
268 230
269 231
270 232
271 233
272 234
273 235
274 236
275 237
276 238
277 239
278 240
279 241
280 242
< >
page |< < (132) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div493" type="section" level="1" n="154">
          <p style="it">
            <s xml:id="echoid-s5183" xml:space="preserve">
              <pb o="132" file="0170" n="170" rhead="Apollonij Pergæi"/>
            angulo D B E; </s>
            <s xml:id="echoid-s5184" xml:space="preserve">cadit verò F E infra rectam B E, quam ſecat in E, propter
              <lb/>
            curuitatem ſectionis F E B; </s>
            <s xml:id="echoid-s5185" xml:space="preserve">igitur angulus D E F obtuſus quoque erit, & </s>
            <s xml:id="echoid-s5186" xml:space="preserve">an-
              <lb/>
            gulus D F E acutus; </s>
            <s xml:id="echoid-s5187" xml:space="preserve">& </s>
            <s xml:id="echoid-s5188" xml:space="preserve">propterea recta linea D E minor erit, quàm D F; </s>
            <s xml:id="echoid-s5189" xml:space="preserve">ea-
              <lb/>
            dem ratione oſtendetur D F minor, quàm D A.</s>
            <s xml:id="echoid-s5190" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div495" type="section" level="1" n="155">
          <head xml:id="echoid-head204" xml:space="preserve">Notæ in Propoſit. XXXIX.</head>
          <p style="it">
            <s xml:id="echoid-s5191" xml:space="preserve">ALioquin ſecet illam, & </s>
            <s xml:id="echoid-s5192" xml:space="preserve">ſecemus ex,
              <lb/>
              <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a" number="168">
                <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0170-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s5193" xml:space="preserve">D G intra ſectionem, &</s>
            <s xml:id="echoid-s5194" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5195" xml:space="preserve">Si e-
              <lb/>
            nim recta F D non contingit ellipſim A B,
              <lb/>
            ſecet eam ſi fieri poteſt in D: </s>
            <s xml:id="echoid-s5196" xml:space="preserve">quare F D pro-
              <lb/>
            ducta in directum cadet intra ſectionem, & </s>
            <s xml:id="echoid-s5197" xml:space="preserve">
              <lb/>
            in producta recta linea F D G ſumatur quod-
              <lb/>
            libet punctum G dummodo intra ſectionem
              <lb/>
            exiſtat, & </s>
            <s xml:id="echoid-s5198" xml:space="preserve">per G ad concurſum C coniunga-
              <lb/>
            tur recta linea G C, quæ producta occurrat
              <lb/>
            ſectioni in B: </s>
            <s xml:id="echoid-s5199" xml:space="preserve">& </s>
            <s xml:id="echoid-s5200" xml:space="preserve">quia ex hypotheſi recta F
              <lb/>
            D G perpendicularis erat ad maximum ramum D C, ergo in triangulo D G C
              <lb/>
            rectangulo erit hypothenuſa G C maior quàm D C, & </s>
            <s xml:id="echoid-s5201" xml:space="preserve">ideo B C multo maior
              <lb/>
            erit quàm D C; </s>
            <s xml:id="echoid-s5202" xml:space="preserve">quod eſt abſurdum, ſuppoſita enim fuit D C omnium maxima
              <lb/>
            earum, quæ ex C ad ſectionem A B duci poſſunt.</s>
            <s xml:id="echoid-s5203" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div497" type="section" level="1" n="156">
          <head xml:id="echoid-head205" xml:space="preserve">Notæ in Propoſit. XXXXVIII.</head>
          <p style="it">
            <s xml:id="echoid-s5204" xml:space="preserve">ALioquin occurtant in O, quia iſtæ
              <lb/>
              <figure xlink:label="fig-0170-02" xlink:href="fig-0170-02a" number="169">
                <image file="0170-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0170-02"/>
              </figure>
            lineæ ſunt maximæ, &</s>
            <s xml:id="echoid-s5205" xml:space="preserve">c. </s>
            <s xml:id="echoid-s5206" xml:space="preserve">Secant e-
              <lb/>
            nim lineæ maximæ ſemiaxim maiorem D A
              <lb/>
            in punctis M, N, & </s>
            <s xml:id="echoid-s5207" xml:space="preserve">L: </s>
            <s xml:id="echoid-s5208" xml:space="preserve">& </s>
            <s xml:id="echoid-s5209" xml:space="preserve">ſiquidem tres li-
              <lb/>
            neæ maximæ conueniunt in vnico puncto O,
              <lb/>
            erunt ſegmenta inter axim maiorem, & </s>
            <s xml:id="echoid-s5210" xml:space="preserve">ſe-
              <lb/>
              <note position="left" xlink:label="note-0170-01" xlink:href="note-0170-01a" xml:space="preserve">32. buius.</note>
            ctionem intercepta, nimirum M K, N H, L
              <lb/>
            F lineæ breuiſſimæ; </s>
            <s xml:id="echoid-s5211" xml:space="preserve">quarum duæ quæquè L
              <lb/>
            F, N H educuntur ab eodem puncto concur-
              <lb/>
            ſus O: </s>
            <s xml:id="echoid-s5212" xml:space="preserve">igitur (ex 54. </s>
            <s xml:id="echoid-s5213" xml:space="preserve">55. </s>
            <s xml:id="echoid-s5214" xml:space="preserve">huius) tertius ra-
              <lb/>
            mus O K ab eodem concurſu O eductus non erit breuiſecans; </s>
            <s xml:id="echoid-s5215" xml:space="preserve">quod eſt contra
              <lb/>
            hypotheſim.</s>
            <s xml:id="echoid-s5216" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div499" type="section" level="1" n="157">
          <head xml:id="echoid-head206" xml:space="preserve">LIBRI QVINTI FINIS.</head>
        </div>
      </text>
    </echo>
Impressum