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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              <pb o="404" file="0442" n="443" rhead="Archimedis"/>
            tur inter duas lineas æquales ſibi oc-
              <lb/>
              <figure xlink:label="fig-0442-01" xlink:href="fig-0442-01a" number="516">
                <image file="0442-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0442-01"/>
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            currentes in aliquo puncto, vti ſunt
              <lb/>
            duæ lineæ C D, C E, duæ lineæ ſe
              <lb/>
            mutuo ſecantes, vti ſunt duæ lineæ
              <lb/>
            D F, E F, & </s>
            <s xml:id="echoid-s13455" xml:space="preserve">ſuerit angulus ab illis
              <lb/>
            contentus vt eſt angulus F æqualis
              <lb/>
            duobus angulis, qui occurrunt dua-
              <lb/>
            bus [lineis] ſe inuicem ſecanti-
              <lb/>
            bus, vti ſunt duo anguli E, D ſimul,
              <lb/>
            erit linea egrediens à puncto con-
              <lb/>
            curſus ad punctum ſectionis, vti eſt
              <lb/>
            linea C F æqualis cuilibet linearum
              <lb/>
            ſibi occurrentium, vt C D, vel C
              <lb/>
            E, propterea erit C F æqualis ipſi
              <lb/>
            C D, ergo angulus C F D eſt æqua-
              <lb/>
            lis angulo C D F, nempe angulo
              <lb/>
            D A G, ſed angulus C F D cum an-
              <lb/>
            gulo D F G eſt æqualis duobus re-
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            ctis, ergo angulus D A G cum angulo D F G æqualis eſt duobus rectis,
              <lb/>
            & </s>
            <s xml:id="echoid-s13456" xml:space="preserve">remanent in quadrilatero A D F G duo anguli A D F, A G F æqua-
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            les duobus rectis, ſed angulus A D B rectus eſt, ergo angulus A G C
              <lb/>
            eſt rectus, & </s>
            <s xml:id="echoid-s13457" xml:space="preserve">C G perpendicularis ad A B, & </s>
            <s xml:id="echoid-s13458" xml:space="preserve">hoc eſt quod voluimus.</s>
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          <head xml:id="echoid-head468" xml:space="preserve">SCHOLIVM ALMOCHTASSO.</head>
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            <s xml:id="echoid-s13460" xml:space="preserve">DIcit Doctor de demonſtratione, quàm citat ex tractatu
              <lb/>
            de figuris quadrilateris. </s>
            <s xml:id="echoid-s13461" xml:space="preserve">Sint duæ lineæ æquales ſibi oc-
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            currentes A B, A C, & </s>
            <s xml:id="echoid-s13462" xml:space="preserve">punctum concurſus A, & </s>
            <s xml:id="echoid-s13463" xml:space="preserve">ſe inuicem
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            ſecantes B D, D C, & </s>
            <s xml:id="echoid-s13464" xml:space="preserve">punctum ſectionis D, & </s>
            <s xml:id="echoid-s13465" xml:space="preserve">ſit angulus B
              <lb/>
            D C æqualis duobus angulis A B D, A C D, & </s>
            <s xml:id="echoid-s13466" xml:space="preserve">iungamus A
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            D; </s>
            <s xml:id="echoid-s13467" xml:space="preserve">Dico quod ſit æqualis A B.</s>
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            <s xml:id="echoid-s13469" xml:space="preserve">Alioquin vel eſt minor A B, vel maior
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            illa, & </s>
            <s xml:id="echoid-s13470" xml:space="preserve">ſit maior, & </s>
            <s xml:id="echoid-s13471" xml:space="preserve">abſcindatur A E æqua-
              <lb/>
            lis A B, & </s>
            <s xml:id="echoid-s13472" xml:space="preserve">iungamus B E, ergo duo anguli
              <lb/>
            A E B, A B E ſunt æquales; </s>
            <s xml:id="echoid-s13473" xml:space="preserve">ſed angulus
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            A E B maior eſt angulo A D B, & </s>
            <s xml:id="echoid-s13474" xml:space="preserve">pariter
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            angulus A E C, qui eſt æqualis A C E ma-
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            ior eſt angulo A D C, omnes ergo anguli
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            B E C, vel duo anguli ſimul A B E, B C E
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            maiores ſunt duobus angulis A B D, A C
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            D, pars ſuo toto, quod eſt abſurdum. </s>
            <s xml:id="echoid-s13475" xml:space="preserve">Dein-
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            de ſit A D minor quàm A B, & </s>
            <s xml:id="echoid-s13476" xml:space="preserve">ponamus
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            A F æqualem A B, & </s>
            <s xml:id="echoid-s13477" xml:space="preserve">iungamus B F, F C,
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            remanet, vt dictum eſt, quod angulus </s>
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