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-div1128" type="section" level="1" n="361">
          <p>
            <s xml:id="echoid-s13186" xml:space="preserve">
              <pb o="394" file="0432" n="433" rhead="Archimedis"/>
            & </s>
            <s xml:id="echoid-s13187" xml:space="preserve">circulus I H L tangat circulum A B C in H, & </s>
            <s xml:id="echoid-s13188" xml:space="preserve">circulum A D E in
              <lb/>
            L, & </s>
            <s xml:id="echoid-s13189" xml:space="preserve">perpendicularem in I. </s>
            <s xml:id="echoid-s13190" xml:space="preserve">Dico eſſe æqualem circulo, qui eſt in al-
              <lb/>
            tera parte. </s>
            <s xml:id="echoid-s13191" xml:space="preserve">Hoc modo, Educamus I M parallelam ipſi A C, & </s>
            <s xml:id="echoid-s13192" xml:space="preserve">iungamus
              <lb/>
            A H, quæ tranſibit per M, quemadmodum demonſtrauit Archimedes,
              <lb/>
              <note position="left" xlink:label="note-0432-01" xlink:href="note-0432-01a" xml:space="preserve">Prop. I.
                <lb/>
              huius.</note>
              <figure xlink:label="fig-0432-01" xlink:href="fig-0432-01a" number="500">
                <image file="0432-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0432-01"/>
              </figure>
            & </s>
            <s xml:id="echoid-s13193" xml:space="preserve">producamus eam quouſque occurrat perpendiculari N G in N, & </s>
            <s xml:id="echoid-s13194" xml:space="preserve">
              <lb/>
            iungamus I A, quæ tranſibit per L, & </s>
            <s xml:id="echoid-s13195" xml:space="preserve">producamus illam ad O, & </s>
            <s xml:id="echoid-s13196" xml:space="preserve">iun-
              <lb/>
            gamus C O, O N, quæ erit linea recta, & </s>
            <s xml:id="echoid-s13197" xml:space="preserve">iungamus M E, quæ tranſi-
              <lb/>
            bit per L, & </s>
            <s xml:id="echoid-s13198" xml:space="preserve">iungamus C H, quæ tranſibit per I; </s>
            <s xml:id="echoid-s13199" xml:space="preserve">& </s>
            <s xml:id="echoid-s13200" xml:space="preserve">linea C O N pa-
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              <gap/>
            a eſt lineæ E M, & </s>
            <s xml:id="echoid-s13201" xml:space="preserve">proportio A N ad N M, nempe proportio A
              <lb/>
            G ad I M eſt vt C A ad C E, ergo rectangulum A G in C E æquale
              <lb/>
            eſt rectangulo C A in I M; </s>
            <s xml:id="echoid-s13202" xml:space="preserve">& </s>
            <s xml:id="echoid-s13203" xml:space="preserve">quia G D eſt perpendicularis in duobus
              <lb/>
            circulis C D F, E D A ſuper duas diametros C F, E A, erit rectangu-
              <lb/>
            lum C G in G F æquale quadrato G D, & </s>
            <s xml:id="echoid-s13204" xml:space="preserve">rectangulum A G in G E
              <lb/>
            æquale etiam eſt illi, ergo rectangulum C G in G F æquale eſt rectan-
              <lb/>
            lo A G in G E, & </s>
            <s xml:id="echoid-s13205" xml:space="preserve">proportio C G ad G A eſt vt proportio E G ad G
              <lb/>
            F, immo vt proportio C E ad F A reſiduam; </s>
            <s xml:id="echoid-s13206" xml:space="preserve">ergo rectangulum C G in
              <lb/>
            F A, eſt æquale rectangulo C A in I M cui æquale eſt rectangulum G
              <lb/>
            A in C E. </s>
            <s xml:id="echoid-s13207" xml:space="preserve">Et ſi fuerit in altera parte circulus modo præfato eadem ra-
              <lb/>
            tione oſtendemus, quod reſtangulum C A in diametrum illius circuli
              <lb/>
            æquale ſit rectangulo C G in A F, & </s>
            <s xml:id="echoid-s13208" xml:space="preserve">oſtendetur quod duæ diametri duo-
              <lb/>
            rum circulorum ſint æquales.</s>
            <s xml:id="echoid-s13209" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1130" type="section" level="1" n="362">
          <head xml:id="echoid-head454" xml:space="preserve">SCHOLIVM SECVNDVM ALKAVHI.</head>
          <p>
            <s xml:id="echoid-s13210" xml:space="preserve">POrrò ſecunda eſt hæc. </s>
            <s xml:id="echoid-s13211" xml:space="preserve">Dicit quod ſi duo ſemicirculi non
              <lb/>
            ſint tangentes, nec ſe mutuo ſecantes, ſed ſeparati, & </s>
            <s xml:id="echoid-s13212" xml:space="preserve">
              <lb/>
            perpendicularis tranſeat per concurſum duarum linearum </s>
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