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
241 203
242 204
243 205
244 206
245 207
246 208
247 209
248 210
249 211
250 212
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
< >
page |< < (173) 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-s6634" xml:space="preserve">
              <pb o="173" file="0211" n="211" rhead="Conicor. Lib. VI."/>
            ſectæ non erunt proportionaliter in punctis G, [
              <unsure/>
            & </s>
            <s xml:id="echoid-s6635" xml:space="preserve">M, ſed prius oſtenſa fuit E
              <lb/>
            I ad I G vt K L ad L M; </s>
            <s xml:id="echoid-s6636" xml:space="preserve">quod eſt abſurdum.</s>
            <s xml:id="echoid-s6637" xml:space="preserve"/>
          </p>
          <figure number="233">
            <image file="0211-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0211-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s6638" xml:space="preserve">In ſecunda verò ſecentur bifariam E G, K M in N O, &</s>
            <s xml:id="echoid-s6639" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6640" xml:space="preserve">Sunt enim
              <lb/>
              <note position="left" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">d</note>
            in tertio caſu K M, & </s>
            <s xml:id="echoid-s6641" xml:space="preserve">E G perpendiculares ad baſim D F; </s>
            <s xml:id="echoid-s6642" xml:space="preserve">igitur ſi ſecentur
              <lb/>
            bifariam in O, & </s>
            <s xml:id="echoid-s6643" xml:space="preserve">N coniuncta recta linea N O diameter circuli erit, quando-
              <lb/>
            quidem diuidit bifariam duas equidiſtantes in circulo applicatas; </s>
            <s xml:id="echoid-s6644" xml:space="preserve">& </s>
            <s xml:id="echoid-s6645" xml:space="preserve">ideo eas
              <lb/>
            ſecat ad angulos rectos, ſicuti D F eaſdem perpendiculariter ſecabat; </s>
            <s xml:id="echoid-s6646" xml:space="preserve">& </s>
            <s xml:id="echoid-s6647" xml:space="preserve">propte-
              <lb/>
            rea I N O L parallelogram-
              <lb/>
            mum erit, cuius latera op-
              <lb/>
              <figure xlink:label="fig-0211-02" xlink:href="fig-0211-02a" number="234">
                <image file="0211-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0211-02"/>
              </figure>
            poſita N I, & </s>
            <s xml:id="echoid-s6648" xml:space="preserve">O L æqualia
              <lb/>
            crunt. </s>
            <s xml:id="echoid-s6649" xml:space="preserve">Poſtea quia oſtenſa
              <lb/>
            fuit I G ad I E, vt L M
              <lb/>
            ad L K; </s>
            <s xml:id="echoid-s6650" xml:space="preserve">ergo ſummæ termi-
              <lb/>
              <note position="right" xlink:label="note-0211-02" xlink:href="note-0211-02a" xml:space="preserve">Lem. 1.</note>
            norum ad conſequentespro
              <lb/>
            portionales erunt; </s>
            <s xml:id="echoid-s6651" xml:space="preserve">ſcilice
              <lb/>
            G E ad E I erit vt M K ad
              <lb/>
            K L, & </s>
            <s xml:id="echoid-s6652" xml:space="preserve">antecedentiũ ſemiſ-
              <lb/>
            ſes N E ad E I, vt O K ad
              <lb/>
            K L: </s>
            <s xml:id="echoid-s6653" xml:space="preserve">& </s>
            <s xml:id="echoid-s6654" xml:space="preserve">diuidendo, duæ æ-
              <lb/>
            quates N I, O L eandem
              <lb/>
            proportionem habebunt ad I E, & </s>
            <s xml:id="echoid-s6655" xml:space="preserve">L K; </s>
            <s xml:id="echoid-s6656" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s6657" xml:space="preserve">I E æqualis eſt L K. </s>
            <s xml:id="echoid-s6658" xml:space="preserve">Et quoniã
              <lb/>
            triangulum A B H ſimile eſt triangulo D K L; </s>
            <s xml:id="echoid-s6659" xml:space="preserve">ergo A H ad H B eandem pro-
              <lb/>
            portionem habet, quàm D L ad L K; </s>
            <s xml:id="echoid-s6660" xml:space="preserve">eſtque triangulum B H C ſimile triangu-
              <lb/>
            lo K L F; </s>
            <s xml:id="echoid-s6661" xml:space="preserve">ergo B H ad H C eſt vt K L ad L F, & </s>
            <s xml:id="echoid-s6662" xml:space="preserve">ex æqualitate vt A H ad H C
              <lb/>
            ita eſt D L ad L F; </s>
            <s xml:id="echoid-s6663" xml:space="preserve">erat autem ſegmentum A H non maius ſegmento H C; </s>
            <s xml:id="echoid-s6664" xml:space="preserve">ergo
              <lb/>
            D L maius non erit ſegmento L F; </s>
            <s xml:id="echoid-s6665" xml:space="preserve">ſed erat ſegmentum D I non maius ſegmen-
              <lb/>
            to I F, igitur duo ſegmenta D I, & </s>
            <s xml:id="echoid-s6666" xml:space="preserve">D L non ſunt maiora, ideſt non ſunt ma-
              <lb/>
            iora medietate totius D F, ſed diameter parallela ipſis K M, & </s>
            <s xml:id="echoid-s6667" xml:space="preserve">E G ſecat D F
              <lb/>
            biſariam; </s>
            <s xml:id="echoid-s6668" xml:space="preserve">ergo K M, E G ad eaſdem partes diametri cadunt verſus D, & </s>
            <s xml:id="echoid-s6669" xml:space="preserve">ſunt
              <lb/>
            inter ſe parallelæ; </s>
            <s xml:id="echoid-s6670" xml:space="preserve">ergo inæqualiter à centro diſtant; </s>
            <s xml:id="echoid-s6671" xml:space="preserve">ideoque inæquales erunt in-
              <lb/>
            ter ſe, & </s>
            <s xml:id="echoid-s6672" xml:space="preserve">earum meditates N E, O K inæquales erunt; </s>
            <s xml:id="echoid-s6673" xml:space="preserve">& </s>
            <s xml:id="echoid-s6674" xml:space="preserve">ablatis æqualibus </s>
          </p>
        </div>
      </text>
    </echo>
Impressum