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-s13504" xml:space="preserve">
              <pb o="406" file="0444" n="445" rhead="Archimedis"/>
            lelæ, & </s>
            <s xml:id="echoid-s13505" xml:space="preserve">quia B I æqualis eſt I A, erit B H æqualis ipſi H E, & </s>
            <s xml:id="echoid-s13506" xml:space="preserve">pro-
              <lb/>
            pter earum æqualitatem, & </s>
            <s xml:id="echoid-s13507" xml:space="preserve">quia B F eſt parallela ipſi H G, erit F G
              <lb/>
            æqualis ipſi G E, & </s>
            <s xml:id="echoid-s13508" xml:space="preserve">ex G C, G D æqualibus remanent F C, E D æqua-
              <lb/>
            les. </s>
            <s xml:id="echoid-s13509" xml:space="preserve">Et hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13510" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1164" type="section" level="1" n="379">
          <head xml:id="echoid-head471" xml:space="preserve">PROPOSITIO XIV.</head>
          <p>
            <s xml:id="echoid-s13511" xml:space="preserve">SI fuerit A B ſemicirculus, & </s>
            <s xml:id="echoid-s13512" xml:space="preserve">ex eius diametro A B diſſectæ
              <lb/>
            ſint A C, B D æquales, & </s>
            <s xml:id="echoid-s13513" xml:space="preserve">efficiantur ſuper lineas A C,
              <lb/>
            C D, D B ſemicirculi; </s>
            <s xml:id="echoid-s13514" xml:space="preserve">& </s>
            <s xml:id="echoid-s13515" xml:space="preserve">ſit centrum duorum ſemicirculorum
              <lb/>
            A B, C D punctum E, & </s>
            <s xml:id="echoid-s13516" xml:space="preserve">ſit E F perpendicularis ſuper A B,
              <lb/>
            & </s>
            <s xml:id="echoid-s13517" xml:space="preserve">producatur ad G: </s>
            <s xml:id="echoid-s13518" xml:space="preserve">vtique circulus, cuius diameter eſt F G
              <lb/>
            æqualis eſt ſuperficiei contentæ à ſemicirculo maiori, & </s>
            <s xml:id="echoid-s13519" xml:space="preserve">à duo-
              <lb/>
            bus ſemicirculis qui ſunt intra illum, & </s>
            <s xml:id="echoid-s13520" xml:space="preserve">à ſemicirculo medio qui
              <lb/>
            eſt extra illum, & </s>
            <s xml:id="echoid-s13521" xml:space="preserve">eſt figura, quam vocat Archimedes Salinon.</s>
            <s xml:id="echoid-s13522" xml:space="preserve"/>
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          <figure number="520">
            <image file="0444-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0444-01"/>
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          <p>
            <s xml:id="echoid-s13523" xml:space="preserve">Quia D C bifariam ſecatur in E, & </s>
            <s xml:id="echoid-s13524" xml:space="preserve">addita eſt illi C A, erunt duo
              <lb/>
            quadrata D A, C A dupla duorum quadratorum D E, E A, ſed F G
              <lb/>
            æqualis eſt ipſi D A, ergo duo quadrata F G, A C dupla ſunt duorum
              <lb/>
            quadratorum D E, E A: </s>
            <s xml:id="echoid-s13525" xml:space="preserve">& </s>
            <s xml:id="echoid-s13526" xml:space="preserve">quia A B dupla eſt A E, & </s>
            <s xml:id="echoid-s13527" xml:space="preserve">C D dupla.
              <lb/>
            </s>
            <s xml:id="echoid-s13528" xml:space="preserve">quoque E D, erunt duo quadrata A B, D C quadrupla duorum qua-
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            dratorum D E, E A, immo dupla duorum quadratorum G F, A C ſi-
              <lb/>
            militer etiam duo circuli, quorum diametri ſunt A B, D C dupli ſunt
              <lb/>
            eorum, quorum diametri ſunt G F, A C, & </s>
            <s xml:id="echoid-s13529" xml:space="preserve">dimidij eorum, quorum,
              <lb/>
            diametri ſunt A B, C D æquales duobus circulis, quorum diametri ſunt
              <lb/>
            G F, A C, ſed circulus, cuius diameter A C, eſt æqualis duobus </s>
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