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-div1130" type="section" level="1" n="362">
          <p>
            <s xml:id="echoid-s13212" xml:space="preserve">
              <pb o="395" file="0433" n="434" rhead="Aſſump. Liber."/>
            tium eos, quæ ſunt æquales idem ſequetur.</s>
            <s xml:id="echoid-s13213" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13214" xml:space="preserve">Sint itaque ſemicirculi A B C, A D E, F G C, vti diſpoſuimus, & </s>
            <s xml:id="echoid-s13215" xml:space="preserve">
              <lb/>
            duæ lineæ N G, N D tangentes illos duos ſemicirculos in G, D, & </s>
            <s xml:id="echoid-s13216" xml:space="preserve">æ-
              <lb/>
            quales, ſibique occurrentes in N, & </s>
            <s xml:id="echoid-s13217" xml:space="preserve">linea B N tranſiens per punctum
              <lb/>
            N perpendiculariter erecta ſuper A C, & </s>
            <s xml:id="echoid-s13218" xml:space="preserve">tangat illam circulus M N I
              <lb/>
            in I, & </s>
            <s xml:id="echoid-s13219" xml:space="preserve">idem tangat circulum A B C in H, & </s>
            <s xml:id="echoid-s13220" xml:space="preserve">circulum A D E in L,
              <lb/>
              <figure xlink:label="fig-0433-01" xlink:href="fig-0433-01a" number="501">
                <image file="0433-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0433-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s13221" xml:space="preserve">educamus diametrum I M parallelam ipſi A C, & </s>
            <s xml:id="echoid-s13222" xml:space="preserve">iungamus C H,
              <lb/>
            quæ tranſibit per I, & </s>
            <s xml:id="echoid-s13223" xml:space="preserve">iungamus M E tranſibit per L, & </s>
            <s xml:id="echoid-s13224" xml:space="preserve">iungamus A I
              <lb/>
              <note position="right" xlink:label="note-0433-01" xlink:href="note-0433-01a" xml:space="preserve">Prop. I.
                <lb/>
              huius.
                <lb/>
              Ibidem,
                <lb/>
              Scholium
                <lb/>
              præc.
                <lb/>
              Almoc.</note>
            tranſibit per L, & </s>
            <s xml:id="echoid-s13225" xml:space="preserve">producamus eam ad P, & </s>
            <s xml:id="echoid-s13226" xml:space="preserve">iungamus C O tranſibit
              <lb/>
            per P, eritque parallela ipſi E M, & </s>
            <s xml:id="echoid-s13227" xml:space="preserve">erit proportio A O ad O M, nem-
              <lb/>
            pe proportio A N ad M I vt proportio A C ad C E, & </s>
            <s xml:id="echoid-s13228" xml:space="preserve">rectangulum A
              <lb/>
            N in C E æquale rectangulo A C in I M. </s>
            <s xml:id="echoid-s13229" xml:space="preserve">Et eodem modo oſtendetur,
              <lb/>
            quod rectangulum C N in F A ſit æquale rectangulo A C in diametrum
              <lb/>
            circuli, qui eſt ex altera parte; </s>
            <s xml:id="echoid-s13230" xml:space="preserve">& </s>
            <s xml:id="echoid-s13231" xml:space="preserve">quia rectangulum C N in N F æqua-
              <lb/>
            le eſt quadrato G N, & </s>
            <s xml:id="echoid-s13232" xml:space="preserve">eſt æquale quadrato D N, quod eſt æquale re-
              <lb/>
            ctangulo A N in N E erit rectangulum C N in N F æquale rectangulo
              <lb/>
            A N in N E, & </s>
            <s xml:id="echoid-s13233" xml:space="preserve">proportio C N ad A N vt E N ad N F, & </s>
            <s xml:id="echoid-s13234" xml:space="preserve">vt propor-
              <lb/>
            tio totius C E ad totum A F, ergo rectangulum A N in C E æquale eſt
              <lb/>
            rectangulo C N in F A, & </s>
            <s xml:id="echoid-s13235" xml:space="preserve">iam oſtenſum eſt, quod A N in C E æqua-
              <lb/>
            le eſt rectangulo A C in I M, & </s>
            <s xml:id="echoid-s13236" xml:space="preserve">quod rectangulum C N in F A ſit æqua-
              <lb/>
            le rectangulo A C in diametrum alterius circuli: </s>
            <s xml:id="echoid-s13237" xml:space="preserve">ergo duæ diametri ſunt
              <lb/>
            æquales, & </s>
            <s xml:id="echoid-s13238" xml:space="preserve">duo circuli æquales, & </s>
            <s xml:id="echoid-s13239" xml:space="preserve">hoc eſt quæſitum.</s>
            <s xml:id="echoid-s13240" xml:space="preserve"/>
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        <div xml:id="echoid-div1132" type="section" level="1" n="363">
          <head xml:id="echoid-head455" xml:space="preserve">Notæ in Propoſit. V.</head>
          <p style="it">
            <s xml:id="echoid-s13241" xml:space="preserve">HAEc propoſitio parum quidem differt à poſtrema parte propoſit. </s>
            <s xml:id="echoid-s13242" xml:space="preserve">14, 16.
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            </s>
            <s xml:id="echoid-s13243" xml:space="preserve">& </s>
            <s xml:id="echoid-s13244" xml:space="preserve">17. </s>
            <s xml:id="echoid-s13245" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13246" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13247" xml:space="preserve">Pappi Alex.</s>
            <s xml:id="echoid-s13248" xml:space="preserve">, ſi figuram, conſtructionem, & </s>
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