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-s13133" xml:space="preserve">
              <pb o="392" file="0430" n="431" rhead="Archimedis"/>
            A, C minoribus duobus
              <lb/>
            rectis, & </s>
            <s xml:id="echoid-s13134" xml:space="preserve">iungamus etiam
              <lb/>
            F E, E B, ergo E F B
              <lb/>
              <figure xlink:label="fig-0430-01" xlink:href="fig-0430-01a" number="496">
                <image file="0430-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0430-01"/>
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            eſt etiam recta, vti dixi-
              <lb/>
            mus, & </s>
            <s xml:id="echoid-s13135" xml:space="preserve">eſt perpendi-
              <lb/>
            cularis ſuper A D, eo
              <lb/>
            quod angulus A F B eſt
              <lb/>
            rectus, quia cadit in ſe-
              <lb/>
            micirculum A B, & </s>
            <s xml:id="echoid-s13136" xml:space="preserve">iun-
              <lb/>
            gamus H G, G C, erit
              <lb/>
            H C etiam recta; </s>
            <s xml:id="echoid-s13137" xml:space="preserve">& </s>
            <s xml:id="echoid-s13138" xml:space="preserve">iun-
              <lb/>
            gamus E G, G A, erit
              <lb/>
            E A recta, & </s>
            <s xml:id="echoid-s13139" xml:space="preserve">produca-
              <lb/>
            mus eam ad I, & </s>
            <s xml:id="echoid-s13140" xml:space="preserve">iun-
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            gamus B I, quæ ſit etiam
              <lb/>
            perpendicularis ſuper A I, & </s>
            <s xml:id="echoid-s13141" xml:space="preserve">iungamus D I; </s>
            <s xml:id="echoid-s13142" xml:space="preserve">& </s>
            <s xml:id="echoid-s13143" xml:space="preserve">quia A D, A B ſunt
              <lb/>
            duæ rectæ, & </s>
            <s xml:id="echoid-s13144" xml:space="preserve">educta ex D ad lineam A B perpendicularis D C, & </s>
            <s xml:id="echoid-s13145" xml:space="preserve">ex
              <lb/>
            B ad D A perpendicularis B F; </s>
            <s xml:id="echoid-s13146" xml:space="preserve">quæ ſe mutuo ſecant in E, & </s>
            <s xml:id="echoid-s13147" xml:space="preserve">educta A
              <lb/>
            E ad I eſt perpendicularis ſuper B I, erunt B I D rectæ, quemadmo-
              <lb/>
            dum oſtendimus in Propoſitionibus, quas confecimus in expoſitione tra-
              <lb/>
            ctatus de triangulis rectangulis: </s>
            <s xml:id="echoid-s13148" xml:space="preserve">& </s>
            <s xml:id="echoid-s13149" xml:space="preserve">quia duo anguli A G C, A I B ſunt
              <lb/>
            recti, vtique B D, C G ſunt parallelæ, & </s>
            <s xml:id="echoid-s13150" xml:space="preserve">proportio A D ad D H,
              <lb/>
            quæ eſt vt A C ad H E, eſt vt proportio A B ad B C, ergo rectangu-
              <lb/>
            lum A C in C B æquale eſt rectangulo A B in H E; </s>
            <s xml:id="echoid-s13151" xml:space="preserve">& </s>
            <s xml:id="echoid-s13152" xml:space="preserve">ſimiliter demon-
              <lb/>
            ſtratur in circulo L M N, quod rectangulum A C in C B æquale ſit re-
              <lb/>
            ctangulo A B in ſuam diametrum, & </s>
            <s xml:id="echoid-s13153" xml:space="preserve">demonſtratur inde etiam, quod
              <lb/>
            duæ diametri circulorum E F G, L M N, ſint æquales, ergo illi duo
              <lb/>
            circuli ſunt æquales. </s>
            <s xml:id="echoid-s13154" xml:space="preserve">Et hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13155" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1126" type="section" level="1" n="360">
          <head xml:id="echoid-head452" xml:space="preserve">SCHOLIVM ALMOCHTASSO.</head>
          <p>
            <s xml:id="echoid-s13156" xml:space="preserve">DIcit Doctor. </s>
            <s xml:id="echoid-s13157" xml:space="preserve">Clarum quidem eſt quod citauit ex expoſi-
              <lb/>
            tione triangulorum rectangulorum in præfatione; </s>
            <s xml:id="echoid-s13158" xml:space="preserve">& </s>
            <s xml:id="echoid-s13159" xml:space="preserve">eſt
              <lb/>
            quidem propoſitio vtilis in principijs, ac præſertim in triangulis
              <lb/>
            acutangulis, qua opus eſt in propoſit. </s>
            <s xml:id="echoid-s13160" xml:space="preserve">6. </s>
            <s xml:id="echoid-s13161" xml:space="preserve">huius libri, & </s>
            <s xml:id="echoid-s13162" xml:space="preserve">eſt hæc.
              <lb/>
            </s>
            <s xml:id="echoid-s13163" xml:space="preserve">Ex triangulo A B C eduxit perpendiculares B E, C D ſe mutuo
              <lb/>
            ſecantes in F, & </s>
            <s xml:id="echoid-s13164" xml:space="preserve">coniunxit A F, & </s>
            <s xml:id="echoid-s13165" xml:space="preserve">produxit ad G, hæc vti-
              <lb/>
            que erit perpendicularis ſuper B C.</s>
            <s xml:id="echoid-s13166" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s13167" xml:space="preserve">Iungamus itaque D E, erunt duo anguli D A F, D E F æquales,
              <lb/>
            quia circulus comprehendens triangulum A D F tranſit per punctum E,
              <lb/>
            eo quod angulus A E F eſt rectus, & </s>
            <s xml:id="echoid-s13168" xml:space="preserve">cadent in illo ſuper eundem ar-
              <lb/>
            cum, & </s>
            <s xml:id="echoid-s13169" xml:space="preserve">etiam angulus D E B æqualis eſt angulo D C B, quia circulus
              <lb/>
            continens triangulum B D C tranſit etiam per punctum E, ergo in duo-
              <lb/>
            bus triangulis A B G, C B D ſunt duo anguli B A G, B C D æquales;</s>
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