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
281 243
282 244
283 245
284 246
285 247
286 248
287 249
288 250
289 251
290 252
291 253
292 254
293 255
294 256
295 257
296 258
297 259
298 260
299 261
300 262
301 263
302 264
303 265
304 266
305 267
306 268
307 269
308 270
309 271
310 272
< >
page |< < (174) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div625" type="section" level="1" n="209">
          <p style="it">
            <s xml:id="echoid-s6674" xml:space="preserve">
              <pb o="174" file="0212" n="212" rhead="Apollonij Pergæi"/>
            I, O L remanebunt I E, L K inæquales. </s>
            <s xml:id="echoid-s6675" xml:space="preserve">Quod eſt abſurdum: </s>
            <s xml:id="echoid-s6676" xml:space="preserve">oſtenſæ enim fue-
              <lb/>
            runt prius æquales inter ſe.</s>
            <s xml:id="echoid-s6677" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6678" xml:space="preserve">In figura autem tertia ducamus duas perpendiculares, &</s>
            <s xml:id="echoid-s6679" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6680" xml:space="preserve">In quarto
              <lb/>
              <note position="right" xlink:label="note-0212-01" xlink:href="note-0212-01a" xml:space="preserve">e</note>
            caſu ſupponuntur baſes A C, & </s>
            <s xml:id="echoid-s6681" xml:space="preserve">D F per centra circulorum tranſire, eo quod
              <lb/>
            anguli A B C, & </s>
            <s xml:id="echoid-s6682" xml:space="preserve">D E F recti ſupponuntur, atque rectæ lineæ B H, E I non
              <lb/>
            ſunt perpendiculares ſuper eaſdem baſes, licet intra circulos efficiant angulos B
              <lb/>
            H C, & </s>
            <s xml:id="echoid-s6683" xml:space="preserve">E I F inter ſe æqua-
              <lb/>
            les: </s>
            <s xml:id="echoid-s6684" xml:space="preserve">perſecta igitur conſiru-
              <lb/>
              <figure xlink:label="fig-0212-01" xlink:href="fig-0212-01a" number="235">
                <image file="0212-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0212-01"/>
              </figure>
            ctione, vt prius ad diame-
              <lb/>
            trũ D F, ducãtur ex punctis
              <lb/>
            E, & </s>
            <s xml:id="echoid-s6685" xml:space="preserve">K perpendiculares E
              <lb/>
            Q, K S, quæ diuidẽtur bi-
              <lb/>
            fariã, & </s>
            <s xml:id="echoid-s6686" xml:space="preserve">ad angulos rectos
              <lb/>
            in P, & </s>
            <s xml:id="echoid-s6687" xml:space="preserve">R. </s>
            <s xml:id="echoid-s6688" xml:space="preserve">Et quoniam
              <lb/>
            (vt in præcedenti caſu oſtẽ-
              <lb/>
            ſum eſt) G E ad E I ean-
              <lb/>
            dem proportionem habet,
              <lb/>
            quàm M K ad K L, cum-
              <lb/>
            que latera I E, L K ſint
              <lb/>
            parallela, pariterque P E, & </s>
            <s xml:id="echoid-s6689" xml:space="preserve">K R æquidiſtent, atque baſes I P, L R in dire-
              <lb/>
            ctum poſitæ ſint, erunt triangula I E P, & </s>
            <s xml:id="echoid-s6690" xml:space="preserve">L K R æquiangula, & </s>
            <s xml:id="echoid-s6691" xml:space="preserve">ſimilia: </s>
            <s xml:id="echoid-s6692" xml:space="preserve">& </s>
            <s xml:id="echoid-s6693" xml:space="preserve">
              <lb/>
            propterea I E ad E P erit, vt. </s>
            <s xml:id="echoid-s6694" xml:space="preserve">L K ad K R: </s>
            <s xml:id="echoid-s6695" xml:space="preserve">eſt verò P E ad eius duplam E Q,
              <lb/>
            vt R K ad eius duplam K S (cum diameter ſecet eas bifariam, quas perpendi-
              <lb/>
            culariter prius ſecabat) ergo, ex æquali ordinata, erit G E ad E Q, vt M K ad
              <lb/>
            K S; </s>
            <s xml:id="echoid-s6696" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s6697" xml:space="preserve">anguli verticales G E Q, & </s>
            <s xml:id="echoid-s6698" xml:space="preserve">M K S æquales, propterea quod conti-
              <lb/>
            nẽtur à rectis lineis quæ binæ binis ſunt æquidiſtantes; </s>
            <s xml:id="echoid-s6699" xml:space="preserve">ergo triangula G E Q, & </s>
            <s xml:id="echoid-s6700" xml:space="preserve">
              <lb/>
            M K S ſimilia ſunt inter ſe: </s>
            <s xml:id="echoid-s6701" xml:space="preserve">& </s>
            <s xml:id="echoid-s6702" xml:space="preserve">propterea angulus E G Q æqualis erit angulo K M S.</s>
            <s xml:id="echoid-s6703" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6704" xml:space="preserve">Et propterea ſegmentum E F Q maius ſimile erit ſegmento K F S mi-
              <lb/>
              <note position="right" xlink:label="note-0212-02" xlink:href="note-0212-02a" xml:space="preserve">f</note>
            nori: </s>
            <s xml:id="echoid-s6705" xml:space="preserve">quod eſt abſurdum, &</s>
            <s xml:id="echoid-s6706" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6707" xml:space="preserve">Legendum puto. </s>
            <s xml:id="echoid-s6708" xml:space="preserve">Et propterea periheriæ E F
              <lb/>
            Q, & </s>
            <s xml:id="echoid-s6709" xml:space="preserve">K F S, quibus inſiſtunt æquales erunt: </s>
            <s xml:id="echoid-s6710" xml:space="preserve">quod eſt abſurdum. </s>
            <s xml:id="echoid-s6711" xml:space="preserve">Eſt enim E
              <lb/>
            F Q ma
              <unsure/>
            ior, quàm K F S.</s>
            <s xml:id="echoid-s6712" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div633" type="section" level="1" n="210">
          <head xml:id="echoid-head265" xml:space="preserve">Notæ in Propoſit. Præmiſſ. VI.</head>
          <p style="it">
            <s xml:id="echoid-s6713" xml:space="preserve">DEinde ſint duo anguli B, E qualeſcumque; </s>
            <s xml:id="echoid-s6714" xml:space="preserve">ſed angulus A B H, vel
              <lb/>
              <note position="right" xlink:label="note-0212-03" xlink:href="note-0212-03a" xml:space="preserve">a</note>
            C B H æqualis angulo D E I vel F E I, & </s>
            <s xml:id="echoid-s6715" xml:space="preserve">condictiones, vti dixi-
              <lb/>
              <figure xlink:label="fig-0212-02" xlink:href="fig-0212-02a" number="236">
                <image file="0212-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0212-02"/>
              </figure>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum