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-div444" type="section" level="1" n="136">
          <pb o="120" file="0158" n="158" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s4754" xml:space="preserve">Nam ſi coniungamus A G, B G, B F,
              <lb/>
              <figure xlink:label="fig-0158-01" xlink:href="fig-0158-01a" number="150">
                <image file="0158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0158-01"/>
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              <note position="right" xlink:label="note-0158-01" xlink:href="note-0158-01a" xml:space="preserve">b</note>
            F C, &</s>
            <s xml:id="echoid-s4755" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4756" xml:space="preserve">Ideſt; </s>
            <s xml:id="echoid-s4757" xml:space="preserve">ſecetur C H æqualis com-
              <lb/>
            paratæ, ſeu ſemiſsi lateris recti axis A C;
              <lb/>
            </s>
            <s xml:id="echoid-s4758" xml:space="preserve">quia menſura E C ſuppoſita eſt maior compa-
              <lb/>
            rata, erit quoque E C maior, quàm C H, & </s>
            <s xml:id="echoid-s4759" xml:space="preserve">
              <lb/>
            propterea recta linea E F cadet infra H F; </s>
            <s xml:id="echoid-s4760" xml:space="preserve">
              <lb/>
            ideoque angulus C F E maior erit angulo C
              <lb/>
            F H: </s>
            <s xml:id="echoid-s4761" xml:space="preserve">eadem ratione angulus F B E maior
              <lb/>
            erit angulo F B H, atque angulus B F E mi-
              <lb/>
            nor erit angulo B F H, & </s>
            <s xml:id="echoid-s4762" xml:space="preserve">ſic de reliquis,
              <lb/>
            cumque C H ſit æqualis comparatæ, & </s>
            <s xml:id="echoid-s4763" xml:space="preserve">ſit
              <lb/>
            maior C D ſemiße axis recti minoris, omnium ramorum ex origine H ad elli-
              <lb/>
              <note position="left" xlink:label="note-0158-02" xlink:href="note-0158-02a" xml:space="preserve">16. 17. 18.
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              huius.</note>
            pſim C F B G, cadentium maximus erit H C; </s>
            <s xml:id="echoid-s4764" xml:space="preserve">& </s>
            <s xml:id="echoid-s4765" xml:space="preserve">propterea H C maior erit,
              <lb/>
            quàm H F, & </s>
            <s xml:id="echoid-s4766" xml:space="preserve">in triangulo H F C angulus H F C oppoſitus maiori lateri ma-
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            ior erit angulo C; </s>
            <s xml:id="echoid-s4767" xml:space="preserve">eſtque oſtenſus angulus E F C maior angulo H F C; </s>
            <s xml:id="echoid-s4768" xml:space="preserve">igitur
              <lb/>
            in triangulo C E F erit angulus C F E maior angulo F C E; </s>
            <s xml:id="echoid-s4769" xml:space="preserve">& </s>
            <s xml:id="echoid-s4770" xml:space="preserve">propterea ra-
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            mus E C maior erit, quàm E F: </s>
            <s xml:id="echoid-s4771" xml:space="preserve">ſimili modo, quia ramus H F propinquior ma-
              <lb/>
              <note position="left" xlink:label="note-0158-03" xlink:href="note-0158-03a" xml:space="preserve">Ibidem.</note>
            ximo maior eſt remotiore H B, erit angulus H F B minor angulo H B F: </s>
            <s xml:id="echoid-s4772" xml:space="preserve">ideo-
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            que angulus E F B, pars minoris, adbuc minor erit angulo E B F, maiorem
              <lb/>
            excedente; </s>
            <s xml:id="echoid-s4773" xml:space="preserve">& </s>
            <s xml:id="echoid-s4774" xml:space="preserve">propterea in triangulo E F B erit ramus E F propinquior maxi-
              <lb/>
            mo E C, maior remotiore E B, &</s>
            <s xml:id="echoid-s4775" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4776" xml:space="preserve"/>
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        <div xml:id="echoid-div447" type="section" level="1" n="137">
          <head xml:id="echoid-head183" xml:space="preserve">Notæ in Propoſit. XX. XXI. XXII.</head>
          <p>
            <s xml:id="echoid-s4777" xml:space="preserve">SI vero fuerit menſura I C minor comparata, quæ ſit C F, nempe ſe-
              <lb/>
              <note position="right" xlink:label="note-0158-04" xlink:href="note-0158-04a" xml:space="preserve">a</note>
            miſſe erecti, & </s>
            <s xml:id="echoid-s4778" xml:space="preserve">maior dimidio recti E C, & </s>
            <s xml:id="echoid-s4779" xml:space="preserve">origo ſit in recto, aut in
              <lb/>
            eius productione, vt in I; </s>
            <s xml:id="echoid-s4780" xml:space="preserve">tunc maximus ramorum egredientium ex origi-
              <lb/>
            ne, vt I A, I B, I K, I H eſt cuius inuerſi proportio E G (poſt abſolu-
              <lb/>
            tionem figuræ cum perpendicularibus, & </s>
            <s xml:id="echoid-s4781" xml:space="preserve">lineis præcedentibus) ad ab-
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              <figure xlink:label="fig-0158-02" xlink:href="fig-0158-02a" number="151">
                <image file="0158-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0158-02"/>
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            ſciſſam eius potentialis ex menſura cum origine, vt I G eſt, vt propor-
              <lb/>
            tio figuræ recti, vt D C ad erectum illius, & </s>
            <s xml:id="echoid-s4782" xml:space="preserve">quadratum eius, nẽpe </s>
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