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
201 163
202 164
203 165
204 166
205 167
206 168
207 169
208 170
209 171
210 172
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
< >
page |< < (254) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div797" type="section" level="1" n="246">
          <pb o="254" file="0292" n="292" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div804" type="section" level="1" n="247">
          <head xml:id="echoid-head310" xml:space="preserve">Notæ in Propoſit. XXX.</head>
          <p style="it">
            <s xml:id="echoid-s9520" xml:space="preserve">ITa vt non ſit proportio quadrati axis coni, B Q ad quadratum ſemi-
              <lb/>
              <note position="right" xlink:label="note-0292-01" xlink:href="note-0292-01a" xml:space="preserve">a</note>
            diametri baſis illius vt C Q minor proportione figuræ ſectionis, &</s>
            <s xml:id="echoid-s9521" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s9522" xml:space="preserve">Rurſus datus ſit conus rectus A B C, cuius axis B Q ſemidiameter circuli ba-
              <lb/>
              <figure xlink:label="fig-0292-01" xlink:href="fig-0292-01a" number="340">
                <image file="0292-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0292-01"/>
              </figure>
            ſis ſit C Q, exhiberi aebet alius conus ſimilis dato, qui datam byperbolen D E
              <lb/>
            F contineat; </s>
            <s xml:id="echoid-s9523" xml:space="preserve">oportet autem, vt quadratum axis coni B Q ad quadratum ſemi-
              <lb/>
            diametri illius Q A non babeat maiorem proportionem, quàm habet axis tran-
              <lb/>
            ſuerſus H E ad latus rectum E I.</s>
            <s xml:id="echoid-s9524" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9525" xml:space="preserve">Et producamus L H ad E I occurret in K perpendiculari rectæ ad pun-
              <lb/>
              <note position="right" xlink:label="note-0292-02" xlink:href="note-0292-02a" xml:space="preserve">b</note>
            ctum E linea H, &</s>
            <s xml:id="echoid-s9526" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9527" xml:space="preserve">Ideſt ſi ducatur recta linea E K in plano circuli H L E
              <lb/>
            perpendicularis ad H E, ſeu parallela ipſi L N coniuncta recta linea H L ſeca-
              <lb/>
            bit reliquam æquidiſtantium E K in K.</s>
            <s xml:id="echoid-s9528" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9529" xml:space="preserve">Quapropter K L E ſimile eſt A B C, quia æquicrus etiam eſt: </s>
            <s xml:id="echoid-s9530" xml:space="preserve">ſi au-
              <lb/>
              <note position="right" xlink:label="note-0292-03" xlink:href="note-0292-03a" xml:space="preserve">c</note>
            tem ponamus K L E triangulum coni, cuius vertex L, & </s>
            <s xml:id="echoid-s9531" xml:space="preserve">planum trian-
              <lb/>
            guli illius erectum ad planum D E F; </s>
            <s xml:id="echoid-s9532" xml:space="preserve">vtique planum, quod eſt in ſectione
              <lb/>
            producit in cono ſectionẽ hyperbolicã, cuius axis E G, & </s>
            <s xml:id="echoid-s9533" xml:space="preserve">inclinatus E H,
              <lb/>
            &</s>
            <s xml:id="echoid-s9534" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9535" xml:space="preserve">Quoniam in duobus triangulis A B C, & </s>
            <s xml:id="echoid-s9536" xml:space="preserve">E L K ſunt anguli verticales B, & </s>
            <s xml:id="echoid-s9537" xml:space="preserve">
              <lb/>
            L æquales inter ſe, cũ externi M B C, & </s>
            <s xml:id="echoid-s9538" xml:space="preserve">H L E æquales facti ſint; </s>
            <s xml:id="echoid-s9539" xml:space="preserve">& </s>
            <s xml:id="echoid-s9540" xml:space="preserve">angulus H
              <lb/>
            L N æqualis ſit interno, & </s>
            <s xml:id="echoid-s9541" xml:space="preserve">oppoſito K, & </s>
            <s xml:id="echoid-s9542" xml:space="preserve">angulus N L E æqualis eſt alterno angulo
              <lb/>
            L E K propter parallelas N L, E K, & </s>
            <s xml:id="echoid-s9543" xml:space="preserve">quilibet eorũ eſt medietas externi anguli
              <lb/>
            H L E; </s>
            <s xml:id="echoid-s9544" xml:space="preserve">ergo angulus K æqualis erit angulo L E K, & </s>
            <s xml:id="echoid-s9545" xml:space="preserve">trianguliũ L E K erit iſoſceliũ,
              <lb/>
            ſed triangulum A B C per axim coni recti ductum eſt quoque iſoſcelium; </s>
            <s xml:id="echoid-s9546" xml:space="preserve">igitur
              <lb/>
            duo anguli ſupra baſim A, & </s>
            <s xml:id="echoid-s9547" xml:space="preserve">C æquales ſunt inter ſe; </s>
            <s xml:id="echoid-s9548" xml:space="preserve">erant autem prius ver-
              <lb/>
            ticales anguli B, & </s>
            <s xml:id="echoid-s9549" xml:space="preserve">L æquales; </s>
            <s xml:id="echoid-s9550" xml:space="preserve">igitur triangula A B C, & </s>
            <s xml:id="echoid-s9551" xml:space="preserve">E L K æquiangula,
              <lb/>
            & </s>
            <s xml:id="echoid-s9552" xml:space="preserve">ſimilia ſunt. </s>
            <s xml:id="echoid-s9553" xml:space="preserve">Ducatur poſtea recta linea L P perpendicularis ad baſim E K,
              <lb/>
            quæ eam ſecabit bifariam in P, & </s>
            <s xml:id="echoid-s9554" xml:space="preserve">ducatur planum per E K perpendiculare ad
              <lb/>
            planum E L K, & </s>
            <s xml:id="echoid-s9555" xml:space="preserve">in eo diametro E K fiat circulus, qui ſit baſis coni, cuius
              <lb/>
            vertex L, & </s>
            <s xml:id="echoid-s9556" xml:space="preserve">ducatur planum F D a æquidiſtans plano circuli E K; </s>
            <s xml:id="echoid-s9557" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum