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 |< < (104) of 458 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div382" type="section" level="1" n="122">
          <p style="it">
            <s xml:id="echoid-s4202" xml:space="preserve">
              <pb o="104" file="0142" n="142" rhead="104 Apollonij Pergæi"/>
            nem: </s>
            <s xml:id="echoid-s4203" xml:space="preserve">Dico, quod circumpherentia Z γ ſecat tangentem rectam lineam
              <lb/>
            x A, & </s>
            <s xml:id="echoid-s4204" xml:space="preserve">coniſectionem B G in puncto A.</s>
            <s xml:id="echoid-s4205" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4206" xml:space="preserve">Quoniam perpendicularis D E ponitur ma-
              <lb/>
              <figure xlink:label="fig-0142-01" xlink:href="fig-0142-01a" number="127">
                <image file="0142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-01"/>
              </figure>
            ior trutina L; </s>
            <s xml:id="echoid-s4207" xml:space="preserve">ergo quilibet ramus D A cadit
              <lb/>
              <note position="left" xlink:label="note-0142-01" xlink:href="note-0142-01a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            ſupra breuiſsimam ex puncto A ad axim B E
              <lb/>
            ductam: </s>
            <s xml:id="echoid-s4208" xml:space="preserve">efficit vero breuiſsima cum tangente
              <lb/>
            A x angulum rectum; </s>
            <s xml:id="echoid-s4209" xml:space="preserve">ergo angulus D A x eſt
              <lb/>
              <note position="left" xlink:label="note-0142-02" xlink:href="note-0142-02a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            acutus; </s>
            <s xml:id="echoid-s4210" xml:space="preserve">& </s>
            <s xml:id="echoid-s4211" xml:space="preserve">propterea recta A x cadit intracir-
              <lb/>
            culum A Z; </s>
            <s xml:id="echoid-s4212" xml:space="preserve">ſed A x cadit extra coniſectio-
              <lb/>
              <note position="left" xlink:label="note-0142-03" xlink:href="note-0142-03a" xml:space="preserve">35. 36.
                <lb/>
              Lib. 1.</note>
            nem B A, quàm contingit; </s>
            <s xml:id="echoid-s4213" xml:space="preserve">ergo circumferen-
              <lb/>
            tia Z A cadit extra ſectionem B A, & </s>
            <s xml:id="echoid-s4214" xml:space="preserve">extra
              <lb/>
            tangentem A x: </s>
            <s xml:id="echoid-s4215" xml:space="preserve">poſtea ducatur quilibet ramus
              <lb/>
            D G infra ramum D A ſecans circumferentiã
              <lb/>
            circuli in r: </s>
            <s xml:id="echoid-s4216" xml:space="preserve">& </s>
            <s xml:id="echoid-s4217" xml:space="preserve">quia ramus D A propinquior
              <lb/>
            eſt vertici B, quàm D G, erit D A minor,
              <lb/>
              <note position="left" xlink:label="note-0142-04" xlink:href="note-0142-04a" xml:space="preserve">64. 65.
                <lb/>
              huius.</note>
            quàm D G; </s>
            <s xml:id="echoid-s4218" xml:space="preserve">eſtque D γ æqualis D A (cum ſint ambo radij eiuſdem circuli) ergo
              <lb/>
            D γ minor erit, quàm D G: </s>
            <s xml:id="echoid-s4219" xml:space="preserve">& </s>
            <s xml:id="echoid-s4220" xml:space="preserve">propterea quodlibet punctum γ peripheriæ cir-
              <lb/>
            cularis infra punctum A poſitum cadet intra coniſectionem B G; </s>
            <s xml:id="echoid-s4221" xml:space="preserve">& </s>
            <s xml:id="echoid-s4222" xml:space="preserve">ideo cir-
              <lb/>
            cumferentia Z A γ ſecat tangentẽ, & </s>
            <s xml:id="echoid-s4223" xml:space="preserve">coniſectionẽ in A, quod erat propoſitum.</s>
            <s xml:id="echoid-s4224" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4225" xml:space="preserve">Iſdem poſitis, ſit perpendicularis D E æqualis Trutinæ L, & </s>
            <s xml:id="echoid-s4226" xml:space="preserve">ſit D
              <lb/>
              <note position="left" xlink:label="note-0142-05" xlink:href="note-0142-05a" xml:space="preserve">PR. 10.
                <lb/>
              Addit.</note>
            A ſingularis ille ramus breuiſecans, qui ex concurſu D ad ſectionem
              <lb/>
            B G duci poteſt; </s>
            <s xml:id="echoid-s4227" xml:space="preserve">perficiaturque conſtructio, vt antea factum eſt; </s>
            <s xml:id="echoid-s4228" xml:space="preserve">Dico,
              <lb/>
              <note position="left" xlink:label="note-0142-06" xlink:href="note-0142-06a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            circulum Z A γ ſecare coniſectionem in A, & </s>
            <s xml:id="echoid-s4229" xml:space="preserve">contingere rectam Ax.</s>
            <s xml:id="echoid-s4230" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4231" xml:space="preserve">Ducatur quilibet ramus D F ſupra breuiſe-
              <lb/>
              <figure xlink:label="fig-0142-02" xlink:href="fig-0142-02a" number="128">
                <image file="0142-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-02"/>
              </figure>
            cantem D A, ſecans circuli peripheriam in Z,
              <lb/>
            & </s>
            <s xml:id="echoid-s4232" xml:space="preserve">quilibet alius ramus D G infra D A ſecans
              <lb/>
            eandem peripheriam in γ. </s>
            <s xml:id="echoid-s4233" xml:space="preserve">Et quia ex con-
              <lb/>
            curſu D ad ſectionem B G vnicus tantum bre-
              <lb/>
              <note position="left" xlink:label="note-0142-07" xlink:href="note-0142-07a" xml:space="preserve">Ibidem.</note>
            uiſecans D A duci poteſt; </s>
            <s xml:id="echoid-s4234" xml:space="preserve">igitur ramus D F
              <lb/>
            propinquio
              <unsure/>
            r vertici B minor eſt remotiore D
              <lb/>
              <note position="left" xlink:label="note-0142-08" xlink:href="note-0142-08a" xml:space="preserve">67. huius.</note>
            A, & </s>
            <s xml:id="echoid-s4235" xml:space="preserve">D A propinquior vertici B minor eſt
              <lb/>
            remotiore D G: </s>
            <s xml:id="echoid-s4236" xml:space="preserve">ſuntque rectæ D Z, D γ æ-
              <lb/>
            quales eidem D A (cum ſint radij eiuſdem,
              <lb/>
            circuli) ergo D Z maior eſt, quàm D F, & </s>
            <s xml:id="echoid-s4237" xml:space="preserve">
              <lb/>
            D γ minor, quàm D G; </s>
            <s xml:id="echoid-s4238" xml:space="preserve">& </s>
            <s xml:id="echoid-s4239" xml:space="preserve">propterea quodli-
              <lb/>
            bet punctum Z circuli ſupra A ſumptum ca-
              <lb/>
            dit extra coniſectionem B F A, & </s>
            <s xml:id="echoid-s4240" xml:space="preserve">quodlibet
              <lb/>
            infimum punctum γ eiuſdem circuli cadit intra eandem coniſectionem A G;
              <lb/>
            </s>
            <s xml:id="echoid-s4241" xml:space="preserve">quapropter circumferentia circuli Z A γ ſecat coniſectionem B A G in A. </s>
            <s xml:id="echoid-s4242" xml:space="preserve">Po-
              <lb/>
            ſtea quia recta A x contingens ſectionem in A perpendicularis eſt ad breuiſe-
              <lb/>
            cantem D A, cum I A ſit breuiſsima; </s>
            <s xml:id="echoid-s4243" xml:space="preserve">igitur recta linea x A, quæ perpendicu-
              <lb/>
              <note position="left" xlink:label="note-0142-09" xlink:href="note-0142-09a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            laris eſt ad radium D A, continget circulum Z Y γ. </s>
            <s xml:id="echoid-s4244" xml:space="preserve">Quapropter circulus Z
              <lb/>
            A γ ſecant coniſectionem B A G in A, & </s>
            <s xml:id="echoid-s4245" xml:space="preserve">tangit eandem rectam lineam A x,
              <lb/>
            quàm contingit ſectio conica B A G, & </s>
            <s xml:id="echoid-s4246" xml:space="preserve">in eodem puncto A, quod erat oſtendendũ.</s>
            <s xml:id="echoid-s4247" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum