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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            <s xml:id="echoid-s2857" xml:space="preserve">
              <pb o="66" file="0104" n="104" rhead="Apollonij Pergæi"/>
            ad G F, vt latus tranuer ſum ad
              <lb/>
              <figure xlink:label="fig-0104-01" xlink:href="fig-0104-01a" number="84">
                <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0104-01"/>
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            rectum, & </s>
            <s xml:id="echoid-s2858" xml:space="preserve">ducatur ex E recta
              <lb/>
            E H parallela F A, quæ ſecetur
              <lb/>
            à rectis D K, G I ad axim per-
              <lb/>
            pendicularibus in K, & </s>
            <s xml:id="echoid-s2859" xml:space="preserve">I, & </s>
            <s xml:id="echoid-s2860" xml:space="preserve">
              <lb/>
            per D ducatur hyperbole D B
              <lb/>
              <note position="left" xlink:label="note-0104-01" xlink:href="note-0104-01a" xml:space="preserve">4. lib. 2.</note>
            circa aſymptotos H I G, occur-
              <lb/>
            ret hyperbole A B (vt in Prop.
              <lb/>
            </s>
            <s xml:id="echoid-s2861" xml:space="preserve">59. </s>
            <s xml:id="echoid-s2862" xml:space="preserve">62. </s>
            <s xml:id="echoid-s2863" xml:space="preserve">63. </s>
            <s xml:id="echoid-s2864" xml:space="preserve">oſtenſum eſt) ali-
              <lb/>
            cubi, vt in B, coniungatur rect a
              <lb/>
            linea B C, quæ occurrat axi in
              <lb/>
            L, & </s>
            <s xml:id="echoid-s2865" xml:space="preserve">ipſi E H in M, duca-
              <lb/>
            turque ex B perpendicularis ad
              <lb/>
            axim eum ſecans in N, & </s>
            <s xml:id="echoid-s2866" xml:space="preserve">re-
              <lb/>
            ctam E M in H. </s>
            <s xml:id="echoid-s2867" xml:space="preserve">Dico, quod B L eſt linea breuiſsima.</s>
            <s xml:id="echoid-s2868" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2869" xml:space="preserve">C E ad E F, nempe K D eſt, vt D G ad G F, &</s>
            <s xml:id="echoid-s2870" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2871" xml:space="preserve">Quoniam ex conſtru-
              <lb/>
              <note position="right" xlink:label="note-0104-02" xlink:href="note-0104-02a" xml:space="preserve">b</note>
            ctione C E ad E F, ſeu ad ei æqualem K D, in parallelogrammo D E, eſt vt
              <lb/>
            D G ad G F, ſcilicet vt latus @ anſuerſum ad rectum, eſtque K I ad I E, vt D
              <lb/>
            G ad G F propter parallelas D K, G I, F E; </s>
            <s xml:id="echoid-s2872" xml:space="preserve">ergo vt prima C E ad ſecundam
              <lb/>
            D K, ita eſt tertia K I ad quartam I E, & </s>
            <s xml:id="echoid-s2873" xml:space="preserve">propterea rectangulum C E I ſub
              <lb/>
            extremis contentum æquale eſt rectangulo D K I ſub intermedijs compræhenſo;
              <lb/>
            </s>
            <s xml:id="echoid-s2874" xml:space="preserve">eſt vero rectangulum B I æquale rectangulo D I cum compræhendantur ab hyper-
              <lb/>
            bole D B, & </s>
            <s xml:id="echoid-s2875" xml:space="preserve">aſymptotis H I G; </s>
            <s xml:id="echoid-s2876" xml:space="preserve">ergo rectangulum C E I æquale eſt rectangulo
              <lb/>
              <note position="left" xlink:label="note-0104-03" xlink:href="note-0104-03a" xml:space="preserve">12. lib. 2.</note>
            B H I; </s>
            <s xml:id="echoid-s2877" xml:space="preserve">& </s>
            <s xml:id="echoid-s2878" xml:space="preserve">propterea B H ad C E, nempe H M ad M E (propter ſimilitudinem
              <lb/>
            triangulorum B H M, C E M) eandem proportionem habebit, quàm E I ad I
              <lb/>
            H, & </s>
            <s xml:id="echoid-s2879" xml:space="preserve">componendo eadem H E ad H I, atque ad E M eandem proportioner
              <unsure/>
              <lb/>
            habebit; </s>
            <s xml:id="echoid-s2880" xml:space="preserve">& </s>
            <s xml:id="echoid-s2881" xml:space="preserve">ideo H I ſeu ei æqualis N G æqualis erit E M, quare eadem
              <lb/>
            L F ad N G, atque ad E M eandem proportionem habebit: </s>
            <s xml:id="echoid-s2882" xml:space="preserve">ſed propter ſimi-
              <lb/>
            litudinem triangulorum L C F, M C E eſt F C ad E C, vt F L ad M E,
              <lb/>
            ſeu ad N G, & </s>
            <s xml:id="echoid-s2883" xml:space="preserve">erat C E ad E F, necnon D G ad G F in eadem propor-
              <lb/>
            tione lateris tranſuerſi ad rectum, & </s>
            <s xml:id="echoid-s2884" xml:space="preserve">ſummæ terminorum ad antece-
              <lb/>
              <note position="left" xlink:label="note-0104-04" xlink:href="note-0104-04a" xml:space="preserve">Lem. 1.</note>
            dentes terminos, ſcilicet F C ad E C, necnon F D ad D G ean-
              <lb/>
            dem proportionem habent; </s>
            <s xml:id="echoid-s2885" xml:space="preserve">quare L F ad N G eandem
              <lb/>
            proportionem habet, quàm F D ad D G, & </s>
            <s xml:id="echoid-s2886" xml:space="preserve">compa-
              <lb/>
            rando homologorum differentias L D ad D N
              <lb/>
              <note position="left" xlink:label="note-0104-05" xlink:href="note-0104-05a" xml:space="preserve">Lem. 3.</note>
            eandem proportionem habebit, quàm F D
              <lb/>
            ad D G, & </s>
            <s xml:id="echoid-s2887" xml:space="preserve">comparando conſe-
              <lb/>
            quentes ad differentias termi-
              <lb/>
              <note position="left" xlink:label="note-0104-06" xlink:href="note-0104-06a" xml:space="preserve">Lem. 1.</note>
            norum D N ad L N erit,
              <lb/>
            vt D G ad F G,
              <lb/>
            ſcilicet
              <lb/>
            vt latus tranſuer ſum ad rectum;
              <lb/>
            </s>
            <s xml:id="echoid-s2888" xml:space="preserve">quapropter B L eſt linea
              <lb/>
              <note position="left" xlink:label="note-0104-07" xlink:href="note-0104-07a" xml:space="preserve">9. huius.</note>
            breuiſsima.</s>
            <s xml:id="echoid-s2889" xml:space="preserve"/>
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