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

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        <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"/>
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            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"/>
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          <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>
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