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-div1110" type="section" level="1" n="351">
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              <pb o="387" file="0425" n="426" rhead="Aſſumpt. Liber."/>
            licet non laboret vitio Arabici textus, non tamen illa omnino ſincera eſt: </s>
            <s xml:id="echoid-s12966" xml:space="preserve">con-
              <lb/>
            ueniunt tamen in vniuerſalitate propoſitionis, quàm valde peruersè ſcholiaſtes
              <lb/>
            Arabicus expoſuit; </s>
            <s xml:id="echoid-s12967" xml:space="preserve">allucinatur enim quando ait, & </s>
            <s xml:id="echoid-s12968" xml:space="preserve">quia duo anguli E G
              <lb/>
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            D, & </s>
            <s xml:id="echoid-s12969" xml:space="preserve">E F B ſunt recti, &</s>
            <s xml:id="echoid-s12970" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12971" xml:space="preserve">Nam inferius citatur, & </s>
            <s xml:id="echoid-s12972" xml:space="preserve">vſurpatur hæc prima
              <lb/>
            propoſitio vniuerſaliſſimè, ſcilicet exiſtentibus angulis G, & </s>
            <s xml:id="echoid-s12973" xml:space="preserve">F acutis, vel ob-
              <lb/>
            tuſis, & </s>
            <s xml:id="echoid-s12974" xml:space="preserve">ſic reuera ſonant verba propoſitionis, vbi ait, quorum diametri A
              <lb/>
            B, C D ſunt parallelæ, & </s>
            <s xml:id="echoid-s12975" xml:space="preserve">ſic pariter habetur in prædicta propoſitione Pappi;
              <lb/>
            </s>
            <s xml:id="echoid-s12976" xml:space="preserve">quare textus omnino corrigi debuit, vt pronuncientur anguli E G D, & </s>
            <s xml:id="echoid-s12977" xml:space="preserve">E F
              <lb/>
            B æquales, non recti. </s>
            <s xml:id="echoid-s12978" xml:space="preserve">Neſcio tamen quomodo expoſitio Almochtaſſi excuſari poſ-
              <lb/>
            ſit, qui ſupponit diametros A B, & </s>
            <s xml:id="echoid-s12979" xml:space="preserve">C D perpendiculares ad rectam lineam
              <lb/>
            F G E, quod quidem in vnico caſu veriſicatur, vt dictum eſt. </s>
            <s xml:id="echoid-s12980" xml:space="preserve">Peccat poſtea
              <lb/>
            demonſtratio Pappi lib. </s>
            <s xml:id="echoid-s12981" xml:space="preserve">7. </s>
            <s xml:id="echoid-s12982" xml:space="preserve">pr. </s>
            <s xml:id="echoid-s12983" xml:space="preserve">110.</s>
            <s xml:id="echoid-s12984" xml:space="preserve">, vbi conatur oſtendere duo centra, & </s>
            <s xml:id="echoid-s12985" xml:space="preserve">pun-
              <lb/>
            ctum contactus circulorum eſſe in vnica recta linea; </s>
            <s xml:id="echoid-s12986" xml:space="preserve">quod quidem in 3. </s>
            <s xml:id="echoid-s12987" xml:space="preserve">Ele-
              <lb/>
            ment. </s>
            <s xml:id="echoid-s12988" xml:space="preserve">Eucl. </s>
            <s xml:id="echoid-s12989" xml:space="preserve">oſtenſum ſupponi debuerat.</s>
            <s xml:id="echoid-s12990" xml:space="preserve"/>
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        <div xml:id="echoid-div1112" type="section" level="1" n="352">
          <head xml:id="echoid-head444" xml:space="preserve">PROPOSITIO II.</head>
          <p>
            <s xml:id="echoid-s12991" xml:space="preserve">SIt C B A ſemicirculus, quem D C, D B tangant, & </s>
            <s xml:id="echoid-s12992" xml:space="preserve">B E
              <lb/>
            perpendicularis ſuper A C, & </s>
            <s xml:id="echoid-s12993" xml:space="preserve">iungamus A D, erit B F
              <lb/>
            æqualis ipſi F E.</s>
            <s xml:id="echoid-s12994" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s12995" xml:space="preserve">Demonſtratio. </s>
            <s xml:id="echoid-s12996" xml:space="preserve">Iungamus A B, eamque producamus in directum, & </s>
            <s xml:id="echoid-s12997" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0425-02" xlink:href="fig-0425-02a" number="489">
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            educamus C D, quouſque illi occurrat
              <lb/>
            in G, & </s>
            <s xml:id="echoid-s12998" xml:space="preserve">iungamus C B. </s>
            <s xml:id="echoid-s12999" xml:space="preserve">Et quia angu-
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            lus C B A eſt in ſemicirculo, erit re-
              <lb/>
            ctus, remanet C B G rectus, & </s>
            <s xml:id="echoid-s13000" xml:space="preserve">D B E
              <lb/>
            C eſt parallelogrammum rectangulum,
              <lb/>
            ergo in triangulo G B C rectangulo edu-
              <lb/>
            citur perpendicularis B D ex B erecta
              <lb/>
            ſuper baſim, & </s>
            <s xml:id="echoid-s13001" xml:space="preserve">B D, D C erunt æqua-
              <lb/>
            les, eo quod tangunt circulum, ergo C
              <lb/>
            D eſt etiam æqualis ipſi D G, quemad-
              <lb/>
            modum oſtendimus in </s>
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