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 |< < (172) 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-s6585" xml:space="preserve">
              <pb o="172" file="0210" n="210" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0210-01" xlink:href="fig-0210-01a" number="232">
                <image file="0210-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0210-01"/>
              </figure>
            ſium eandem proportionem habeant, fuerintque anguli verticales inter ſe æquales,
              <lb/>
            vel qui à lateribus, & </s>
            <s xml:id="echoid-s6586" xml:space="preserve">à vertice ductis continentur, ſint æquales: </s>
            <s xml:id="echoid-s6587" xml:space="preserve">ſemper trian-
              <lb/>
            gula erunt ſimilia.</s>
            <s xml:id="echoid-s6588" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6589" xml:space="preserve">Dico iam, quod triangulum A B C ſimile eſt triangulo D E F, ſi enim
              <lb/>
              <note position="right" xlink:label="note-0210-01" xlink:href="note-0210-01a" xml:space="preserve">a</note>
            hoc verum non eſt, ſit angulus D maior, quàm angulus A, &</s>
            <s xml:id="echoid-s6590" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6591" xml:space="preserve">Textus
              <lb/>
            alterari debuit, nam duo triangula B A C, & </s>
            <s xml:id="echoid-s6592" xml:space="preserve">E D F ponuntur non ſimilia, & </s>
            <s xml:id="echoid-s6593" xml:space="preserve">
              <lb/>
            propterea æquiangula non erunt, ſcilicet non habebunt duos angulos æquales duo-
              <lb/>
            bus angulis alterius trianguli; </s>
            <s xml:id="echoid-s6594" xml:space="preserve">ſed ex hypotheſi anguli verticales A B C, & </s>
            <s xml:id="echoid-s6595" xml:space="preserve">D E
              <lb/>
            F æquales erant; </s>
            <s xml:id="echoid-s6596" xml:space="preserve">ergo angulus B A C non erit æqualis angulo E D F, neque
              <lb/>
            angulo E F D; </s>
            <s xml:id="echoid-s6597" xml:space="preserve">alias dicta triangula eßent æquiangula, & </s>
            <s xml:id="echoid-s6598" xml:space="preserve">ſimilia, quod non
              <lb/>
            ponitur; </s>
            <s xml:id="echoid-s6599" xml:space="preserve">igitur neceſſe eſt, vt angulus A non ſit æqualis vni duorum angulorum
              <lb/>
            D, vel F, poſtea rectangulorum A H C, & </s>
            <s xml:id="echoid-s6600" xml:space="preserve">D I F tam latus A H ipſius H C
              <lb/>
            non ſit maius, quàm D I ipſius I F, & </s>
            <s xml:id="echoid-s6601" xml:space="preserve">ad punctũ D fiat angulus F D K æqua-
              <lb/>
            lis angulo A.</s>
            <s xml:id="echoid-s6602" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6603" xml:space="preserve">Quare K L F ſimile quoq; </s>
            <s xml:id="echoid-s6604" xml:space="preserve">erit B H C, &</s>
            <s xml:id="echoid-s6605" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6606" xml:space="preserve">Luoniã angulus F D K æqualis
              <lb/>
              <note position="right" xlink:label="note-0210-02" xlink:href="note-0210-02a" xml:space="preserve">b</note>
            eſt factus angulo C A B, & </s>
            <s xml:id="echoid-s6607" xml:space="preserve">angulus F K D ſeu ei æqualis F E. </s>
            <s xml:id="echoid-s6608" xml:space="preserve">D eſt ipſi angu-
              <lb/>
            lo A B C æqualis (cum in ſimilibus circulorum ſegmentis exiſtant), igitur in
              <lb/>
            triangulis F K D, & </s>
            <s xml:id="echoid-s6609" xml:space="preserve">C B A tertius angulus K F D æqualis erit tertio angulo
              <lb/>
            C; </s>
            <s xml:id="echoid-s6610" xml:space="preserve">& </s>
            <s xml:id="echoid-s6611" xml:space="preserve">propter parallelas K L, E I eſt angulus D L K æqualis angulo D I E; </s>
            <s xml:id="echoid-s6612" xml:space="preserve">eſt
              <lb/>
            verò angulus A H B ex hypotheſi æqualis eidem angulo D I E; </s>
            <s xml:id="echoid-s6613" xml:space="preserve">ergò angulus D
              <lb/>
            L K æqualis eſt angulo A H B, & </s>
            <s xml:id="echoid-s6614" xml:space="preserve">F L K æqualis angulo C H B: </s>
            <s xml:id="echoid-s6615" xml:space="preserve">at oſtenſus fuit
              <lb/>
            angulus K F L æqualis angulo B C H; </s>
            <s xml:id="echoid-s6616" xml:space="preserve">ergo angulo C B H æqualis eſt angulus
              <lb/>
            F K L; </s>
            <s xml:id="echoid-s6617" xml:space="preserve">ideoque triangula C B H, & </s>
            <s xml:id="echoid-s6618" xml:space="preserve">F K L ſimilia erunt. </s>
            <s xml:id="echoid-s6619" xml:space="preserve">Pariterq; </s>
            <s xml:id="echoid-s6620" xml:space="preserve">duo trian-
              <lb/>
            gula B A H, & </s>
            <s xml:id="echoid-s6621" xml:space="preserve">K D L ſimilia erunt, cum angulus L æqualis ſit angulo H, & </s>
            <s xml:id="echoid-s6622" xml:space="preserve">
              <lb/>
            angulus K D L æqualis ſit interno B A H.</s>
            <s xml:id="echoid-s6623" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s6624" xml:space="preserve">Et hoc eſt abſurdum in prima figura, &</s>
            <s xml:id="echoid-s6625" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6626" xml:space="preserve">Luoniam ſunt rectæ lineæ in
              <lb/>
              <note position="right" xlink:label="note-0210-03" xlink:href="note-0210-03a" xml:space="preserve">c</note>
            circulo applicatæ K M, E G parallelæ inter ſe; </s>
            <s xml:id="echoid-s6627" xml:space="preserve">ergo coniunctæ rectæ lineæ E K,
              <lb/>
            G M parallelæ erunt inter ſe, aut conuenient extra circulum cum diametro bifa-
              <lb/>
            riam, & </s>
            <s xml:id="echoid-s6628" xml:space="preserve">ad angulos rectos diuidente applicatas E G, K M; </s>
            <s xml:id="echoid-s6629" xml:space="preserve">ſed eadem rectæ lineæ
              <lb/>
            G M ſecat trianguli baſim F A I intra circulũ, aut extra ipſum inter puncta I, A, & </s>
            <s xml:id="echoid-s6630" xml:space="preserve">
              <lb/>
            F (propterea quod angulus E I F conſtituitur à duabus in circulo applicatis extra
              <lb/>
            ipſum concurrentibus); </s>
            <s xml:id="echoid-s6631" xml:space="preserve">ergo tres coniunctæ rectæ lineæ K E, M G, & </s>
            <s xml:id="echoid-s6632" xml:space="preserve">I L, nec ſunt
              <lb/>
            omnes inter ſe parallelæ, nec in vno puncto cõueniunt, & </s>
            <s xml:id="echoid-s6633" xml:space="preserve">propterea E I, & </s>
            <s xml:id="echoid-s6634" xml:space="preserve">K </s>
          </p>
        </div>
      </text>
    </echo>
Impressum