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="170" file="0208" n="208" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0208-01" xlink:href="fig-0208-01a" number="229">
                <image file="0208-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0208-01"/>
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            litate, quod ſi fuerit A H in H C ad quadratum H B, vt D I in I F ad
              <lb/>
            quadratum I E, quod A H in H C ad quadratum H T ſit etiam, vt I D
              <lb/>
            in I F ad quadratum I G. </s>
            <s xml:id="echoid-s6527" xml:space="preserve">Dico iam, quod triangulum A B C ſimile eſt
              <lb/>
            triangulo D E F. </s>
            <s xml:id="echoid-s6528" xml:space="preserve">Si enim hoc verum non eſt, non erit angulus A æqua-
              <lb/>
            lis vni duorum angulorum D, vel F: </s>
            <s xml:id="echoid-s6529" xml:space="preserve">ſitque angulus D maior, quàm A,
              <lb/>
            & </s>
            <s xml:id="echoid-s6530" xml:space="preserve">fiat angulus K D F æqualis A, iungaturque F K; </s>
            <s xml:id="echoid-s6531" xml:space="preserve">quia angulus K, ve-
              <lb/>
            luti E, eſt æqualis angulo B; </s>
            <s xml:id="echoid-s6532" xml:space="preserve">ſimilia erunt triangula A B C, D K F, & </s>
            <s xml:id="echoid-s6533" xml:space="preserve">e-
              <lb/>
            ducamus K L parallelam E I: </s>
            <s xml:id="echoid-s6534" xml:space="preserve">quare K L F ſimile quoque erit B H C
              <lb/>
              <note position="right" xlink:label="note-0208-01" xlink:href="note-0208-01a" xml:space="preserve">b</note>
            ideoque H A ad H B eſt vt D L ad L K, & </s>
            <s xml:id="echoid-s6535" xml:space="preserve">H C ad H B, vt F L ad L
              <lb/>
            K; </s>
            <s xml:id="echoid-s6536" xml:space="preserve">igitur H A in H C, nempe B H in H T ad quadratum H B, quod eſt,
              <lb/>
            vt H T ad H B, quæ oſtenſa eſt; </s>
            <s xml:id="echoid-s6537" xml:space="preserve">vt I G ad I E, erit vt D L in L F, nẽ-
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            pe K L in L M ad qua-
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              <figure xlink:label="fig-0208-02" xlink:href="fig-0208-02a" number="230">
                <image file="0208-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0208-02"/>
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            dratum K L: </s>
            <s xml:id="echoid-s6538" xml:space="preserve">& </s>
            <s xml:id="echoid-s6539" xml:space="preserve">propte-
              <lb/>
            rea M L ad L K erit vt G
              <lb/>
            I ad I E in omnibus fi-
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            guris; </s>
            <s xml:id="echoid-s6540" xml:space="preserve">& </s>
            <s xml:id="echoid-s6541" xml:space="preserve">hoc eſt abſurdũ
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              <note position="right" xlink:label="note-0208-02" xlink:href="note-0208-02a" xml:space="preserve">c</note>
            in prima figura: </s>
            <s xml:id="echoid-s6542" xml:space="preserve">in ſecun-
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              <note position="right" xlink:label="note-0208-03" xlink:href="note-0208-03a" xml:space="preserve">d</note>
            da verò ſecentur bifariam
              <lb/>
            E G, K M in N, O, & </s>
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              <lb/>
            iungatur N O, quæ pa-
              <lb/>
            rallela erit L I, quia ſunt
              <lb/>
            duæ perpendiculares ſu-
              <lb/>
            per K M, E G, quæ ſunt
              <lb/>
            parallelæ; </s>
            <s xml:id="echoid-s6544" xml:space="preserve">ergo I N eſt
              <lb/>
            æqualis L O, & </s>
            <s xml:id="echoid-s6545" xml:space="preserve">quia E G ad E I iam oſtenſa eſt vt K M ad K L; </s>
            <s xml:id="echoid-s6546" xml:space="preserve">ergo
              <lb/>
            E N ad E I eſt, vt O K ad K L: </s>
            <s xml:id="echoid-s6547" xml:space="preserve">& </s>
            <s xml:id="echoid-s6548" xml:space="preserve">diuidendo erit N I ad I E, vt O L,
              <lb/>
            quæ eſt æqualis N I ad L K. </s>
            <s xml:id="echoid-s6549" xml:space="preserve">Et hoc quoque eſt abſurdum.</s>
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            <s xml:id="echoid-s6551" xml:space="preserve">In figura autem tertia educamus duas perpendiculares E P Q, K R S
              <lb/>
              <note position="right" xlink:label="note-0208-04" xlink:href="note-0208-04a" xml:space="preserve">e</note>
            ſuper diametrum D F, cui occurrant in P, R: </s>
            <s xml:id="echoid-s6552" xml:space="preserve">& </s>
            <s xml:id="echoid-s6553" xml:space="preserve">iungamus G Q, M S,
              <lb/>
            quia erat G E ad E I, vt M K ad L K, & </s>
            <s xml:id="echoid-s6554" xml:space="preserve">propter ſimilitudinem trian-
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            gulorum I E P, K L R, E I ad E P eſt, vt L K ad K R, atque E P ad E
              <lb/>
            Q eſt, vt R K ad K S, & </s>
            <s xml:id="echoid-s6555" xml:space="preserve">angulus G E Q æqualis eſt M K S; </s>
            <s xml:id="echoid-s6556" xml:space="preserve">ergo E </s>
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