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="173" file="0211" n="211" rhead="Conicor. Lib. VI."/>
            ſectæ non erunt proportionaliter in punctis G, [
              <unsure/>
            & </s>
            <s xml:id="echoid-s6635" xml:space="preserve">M, ſed prius oſtenſa fuit E
              <lb/>
            I ad I G vt K L ad L M; </s>
            <s xml:id="echoid-s6636" xml:space="preserve">quod eſt abſurdum.</s>
            <s xml:id="echoid-s6637" xml:space="preserve"/>
          </p>
          <figure number="233">
            <image file="0211-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0211-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s6638" xml:space="preserve">In ſecunda verò ſecentur bifariam E G, K M in N O, &</s>
            <s xml:id="echoid-s6639" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6640" xml:space="preserve">Sunt enim
              <lb/>
              <note position="left" xlink:label="note-0211-01" xlink:href="note-0211-01a" xml:space="preserve">d</note>
            in tertio caſu K M, & </s>
            <s xml:id="echoid-s6641" xml:space="preserve">E G perpendiculares ad baſim D F; </s>
            <s xml:id="echoid-s6642" xml:space="preserve">igitur ſi ſecentur
              <lb/>
            bifariam in O, & </s>
            <s xml:id="echoid-s6643" xml:space="preserve">N coniuncta recta linea N O diameter circuli erit, quando-
              <lb/>
            quidem diuidit bifariam duas equidiſtantes in circulo applicatas; </s>
            <s xml:id="echoid-s6644" xml:space="preserve">& </s>
            <s xml:id="echoid-s6645" xml:space="preserve">ideo eas
              <lb/>
            ſecat ad angulos rectos, ſicuti D F eaſdem perpendiculariter ſecabat; </s>
            <s xml:id="echoid-s6646" xml:space="preserve">& </s>
            <s xml:id="echoid-s6647" xml:space="preserve">propte-
              <lb/>
            rea I N O L parallelogram-
              <lb/>
            mum erit, cuius latera op-
              <lb/>
              <figure xlink:label="fig-0211-02" xlink:href="fig-0211-02a" number="234">
                <image file="0211-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0211-02"/>
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            poſita N I, & </s>
            <s xml:id="echoid-s6648" xml:space="preserve">O L æqualia
              <lb/>
            crunt. </s>
            <s xml:id="echoid-s6649" xml:space="preserve">Poſtea quia oſtenſa
              <lb/>
            fuit I G ad I E, vt L M
              <lb/>
            ad L K; </s>
            <s xml:id="echoid-s6650" xml:space="preserve">ergo ſummæ termi-
              <lb/>
              <note position="right" xlink:label="note-0211-02" xlink:href="note-0211-02a" xml:space="preserve">Lem. 1.</note>
            norum ad conſequentespro
              <lb/>
            portionales erunt; </s>
            <s xml:id="echoid-s6651" xml:space="preserve">ſcilice
              <lb/>
            G E ad E I erit vt M K ad
              <lb/>
            K L, & </s>
            <s xml:id="echoid-s6652" xml:space="preserve">antecedentiũ ſemiſ-
              <lb/>
            ſes N E ad E I, vt O K ad
              <lb/>
            K L: </s>
            <s xml:id="echoid-s6653" xml:space="preserve">& </s>
            <s xml:id="echoid-s6654" xml:space="preserve">diuidendo, duæ æ-
              <lb/>
            quates N I, O L eandem
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            proportionem habebunt ad I E, & </s>
            <s xml:id="echoid-s6655" xml:space="preserve">L K; </s>
            <s xml:id="echoid-s6656" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s6657" xml:space="preserve">I E æqualis eſt L K. </s>
            <s xml:id="echoid-s6658" xml:space="preserve">Et quoniã
              <lb/>
            triangulum A B H ſimile eſt triangulo D K L; </s>
            <s xml:id="echoid-s6659" xml:space="preserve">ergo A H ad H B eandem pro-
              <lb/>
            portionem habet, quàm D L ad L K; </s>
            <s xml:id="echoid-s6660" xml:space="preserve">eſtque triangulum B H C ſimile triangu-
              <lb/>
            lo K L F; </s>
            <s xml:id="echoid-s6661" xml:space="preserve">ergo B H ad H C eſt vt K L ad L F, & </s>
            <s xml:id="echoid-s6662" xml:space="preserve">ex æqualitate vt A H ad H C
              <lb/>
            ita eſt D L ad L F; </s>
            <s xml:id="echoid-s6663" xml:space="preserve">erat autem ſegmentum A H non maius ſegmento H C; </s>
            <s xml:id="echoid-s6664" xml:space="preserve">ergo
              <lb/>
            D L maius non erit ſegmento L F; </s>
            <s xml:id="echoid-s6665" xml:space="preserve">ſed erat ſegmentum D I non maius ſegmen-
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            to I F, igitur duo ſegmenta D I, & </s>
            <s xml:id="echoid-s6666" xml:space="preserve">D L non ſunt maiora, ideſt non ſunt ma-
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            iora medietate totius D F, ſed diameter parallela ipſis K M, & </s>
            <s xml:id="echoid-s6667" xml:space="preserve">E G ſecat D F
              <lb/>
            biſariam; </s>
            <s xml:id="echoid-s6668" xml:space="preserve">ergo K M, E G ad eaſdem partes diametri cadunt verſus D, & </s>
            <s xml:id="echoid-s6669" xml:space="preserve">ſunt
              <lb/>
            inter ſe parallelæ; </s>
            <s xml:id="echoid-s6670" xml:space="preserve">ergo inæqualiter à centro diſtant; </s>
            <s xml:id="echoid-s6671" xml:space="preserve">ideoque inæquales erunt in-
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            ter ſe, & </s>
            <s xml:id="echoid-s6672" xml:space="preserve">earum meditates N E, O K inæquales erunt; </s>
            <s xml:id="echoid-s6673" xml:space="preserve">& </s>
            <s xml:id="echoid-s6674" xml:space="preserve">ablatis æqualibus </s>
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