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
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
241 203
242 204
243 205
244 206
245 207
246 208
247 209
248 210
249 211
250 212
< >
page |< < (253) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div796" type="section" level="1" n="245">
          <pb o="253" file="0291" n="291" rhead="Conicor. Lib. VI."/>
        </div>
        <div xml:id="echoid-div797" type="section" level="1" n="246">
          <head xml:id="echoid-head309" xml:space="preserve">Notæ in Propoſit. XXIX.</head>
          <p>
            <s xml:id="echoid-s9456" xml:space="preserve">ET faciamus ſuper E K triangulum ſimile triangulo A B C, &</s>
            <s xml:id="echoid-s9457" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9458" xml:space="preserve">
              <note position="left" xlink:label="note-0291-01" xlink:href="note-0291-01a" xml:space="preserve">a</note>
            mirum, fiat angulus K E L æqualis angulo A, & </s>
            <s xml:id="echoid-s9459" xml:space="preserve">angulus L fiat æqualis angulo B.</s>
            <s xml:id="echoid-s9460" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9461" xml:space="preserve">Ergo L K, quæ eſt latus trianguli tranſeuntis per axim E G para llelũ
              <lb/>
              <note position="left" xlink:label="note-0291-02" xlink:href="note-0291-02a" xml:space="preserve">b</note>
            eſt E G, &</s>
            <s xml:id="echoid-s9462" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9463" xml:space="preserve">Legi debet, vt in textu videre eſt. </s>
            <s xml:id="echoid-s9464" xml:space="preserve">Hoc conſtat ex conſtructio-
              <lb/>
            ne; </s>
            <s xml:id="echoid-s9465" xml:space="preserve">nam duo anguli alterni G E K,, & </s>
            <s xml:id="echoid-s9466" xml:space="preserve">L K E æquales ſunt eidem angulo C.</s>
            <s xml:id="echoid-s9467" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9468" xml:space="preserve">Et propterea planum, in quo eſt ſectio D E
              <lb/>
              <note position="left" xlink:label="note-0291-03" xlink:href="note-0291-03a" xml:space="preserve">C</note>
              <figure xlink:label="fig-0291-01" xlink:href="fig-0291-01a" number="339">
                <image file="0291-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0291-01"/>
              </figure>
            F producit in cono ſectionem parabolicam, &</s>
            <s xml:id="echoid-s9469" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s9470" xml:space="preserve">Quoniam planum circuli, cuius diameter E K
              <lb/>
            perpendiculare eſt ad planum trianguli L E K: </s>
            <s xml:id="echoid-s9471" xml:space="preserve">igi-
              <lb/>
            tur ſi ducatur planum N F O æquidiſtans circulo E
              <lb/>
            K ſecans planum D E F in recta linea D G F, erit
              <lb/>
            quoque circulus, & </s>
            <s xml:id="echoid-s9472" xml:space="preserve">perpendicularis ad planum triã-
              <lb/>
            guli per axim L E K: </s>
            <s xml:id="echoid-s9473" xml:space="preserve">ſed ex conſtructione planum
              <lb/>
            D E F perpendiculare quoque erat ad idem trian-
              <lb/>
            gulum per axim E L K; </s>
            <s xml:id="echoid-s9474" xml:space="preserve">igitur D F communis ſectio
              <lb/>
            eorundem planorum perpendicularis quoque erit ad
              <lb/>
            idem planum L N O, & </s>
            <s xml:id="echoid-s9475" xml:space="preserve">efficiet angulos rectos cum
              <lb/>
            diametro circuli N O, & </s>
            <s xml:id="echoid-s9476" xml:space="preserve">cum E G, quæ in eodẽ pla-
              <lb/>
            no exiſtunt, & </s>
            <s xml:id="echoid-s9477" xml:space="preserve">cũ illo conueniunt in puncto G; </s>
            <s xml:id="echoid-s9478" xml:space="preserve">ſuntq; </s>
            <s xml:id="echoid-s9479" xml:space="preserve">E G, & </s>
            <s xml:id="echoid-s9480" xml:space="preserve">L O parallelæ: </s>
            <s xml:id="echoid-s9481" xml:space="preserve">igitur
              <lb/>
              <note position="right" xlink:label="note-0291-04" xlink:href="note-0291-04a" xml:space="preserve">11. lib. 1.</note>
            planum ſectionis D E F producit neceſſariò in cono L N O producto parabolam.</s>
            <s xml:id="echoid-s9482" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9483" xml:space="preserve">Igitur H E ad E L, quæ eſt æqualis ipſi L K eamdem proportionem,
              <lb/>
              <note position="left" xlink:label="note-0291-05" xlink:href="note-0291-05a" xml:space="preserve">d</note>
            habet, quàm quadratum E K ad quadratum K L, &</s>
            <s xml:id="echoid-s9484" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9485" xml:space="preserve">Quoniam conus
              <lb/>
            L E K ſimilis eſt cono recto A B C erit quoque rectus: </s>
            <s xml:id="echoid-s9486" xml:space="preserve">& </s>
            <s xml:id="echoid-s9487" xml:space="preserve">propterea duo latera
              <lb/>
            trianguli per axim E L, & </s>
            <s xml:id="echoid-s9488" xml:space="preserve">L K æqualia erunt inter ſe, & </s>
            <s xml:id="echoid-s9489" xml:space="preserve">ideo E K ad K L,
              <lb/>
            atque ad E L eandem proportionem habebit, &</s>
            <s xml:id="echoid-s9490" xml:space="preserve">c.</s>
            <s xml:id="echoid-s9491" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9492" xml:space="preserve">Et dico, quod ſectio D E F non reperitur in alio cono ſimili cono A
              <lb/>
              <note position="left" xlink:label="note-0291-06" xlink:href="note-0291-06a" xml:space="preserve">e</note>
            B C, cuius vertex ſit ex parte plani ſectionis præter hunc conum, &</s>
            <s xml:id="echoid-s9493" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s9494" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s9495" xml:space="preserve">Nullus alius conus rectus continebit eandem parabolam D E F, qui ſit
              <lb/>
            ſinilis cono A B C, & </s>
            <s xml:id="echoid-s9496" xml:space="preserve">vertex E parabole magis, aut minus recedat à vertice
              <lb/>
            coni, quàm E L.</s>
            <s xml:id="echoid-s9497" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9498" xml:space="preserve">Ergo E M eſt indirectum ipſi E L, &</s>
            <s xml:id="echoid-s9499" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9500" xml:space="preserve">Quia D G baſis ſectionis conicæ
              <lb/>
              <note position="left" xlink:label="note-0291-07" xlink:href="note-0291-07a" xml:space="preserve">f</note>
            perpendicularis eße debet ad G O, & </s>
            <s xml:id="echoid-s9501" xml:space="preserve">ad G E, & </s>
            <s xml:id="echoid-s9502" xml:space="preserve">ideo ad triangulum per axim
              <lb/>
            vtriuſque coni recti L E K, & </s>
            <s xml:id="echoid-s9503" xml:space="preserve">M E I; </s>
            <s xml:id="echoid-s9504" xml:space="preserve">& </s>
            <s xml:id="echoid-s9505" xml:space="preserve">conueniunt plana eorundem trian-
              <lb/>
            gulorum in E G axi conicæ ſectionis geniti ab eis; </s>
            <s xml:id="echoid-s9506" xml:space="preserve">ergo dicta triangula in eo-
              <lb/>
            dem plano exiſtunt per rectas E G, & </s>
            <s xml:id="echoid-s9507" xml:space="preserve">G O ducto; </s>
            <s xml:id="echoid-s9508" xml:space="preserve">& </s>
            <s xml:id="echoid-s9509" xml:space="preserve">in vtroquè cono triangu-
              <lb/>
            lorum per axes latera L K, & </s>
            <s xml:id="echoid-s9510" xml:space="preserve">M I parallela ſunt eidem axi E G paraboles:
              <lb/>
            </s>
            <s xml:id="echoid-s9511" xml:space="preserve">ergo L K, M I parallelæ ſunt inter ſe, & </s>
            <s xml:id="echoid-s9512" xml:space="preserve">anguli L, & </s>
            <s xml:id="echoid-s9513" xml:space="preserve">M æquales ſunt pro-
              <lb/>
            pter ſimilitudinem triangulorum per axes in conis ſimilibus: </s>
            <s xml:id="echoid-s9514" xml:space="preserve">igitur L E, & </s>
            <s xml:id="echoid-s9515" xml:space="preserve">M
              <lb/>
            E ſunt quoq; </s>
            <s xml:id="echoid-s9516" xml:space="preserve">parallelæ, & </s>
            <s xml:id="echoid-s9517" xml:space="preserve">conueniunt in E vertice paraboles; </s>
            <s xml:id="echoid-s9518" xml:space="preserve">ergo in directum
              <lb/>
            ſunt conſtitutæ.</s>
            <s xml:id="echoid-s9519" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum