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="407" file="0445" n="446" rhead="Aſſumpt. Liber."/>
            micirculis A C, B D, ergo ſi auferamus ex illis duos ſemicirculos A C,
              <lb/>
            B D, qui ſunt communes, remanet figura contenta à quatuor ſemicircu-
              <lb/>
            lis A B, C D, D B, A C, (quæ ea eſt, quàm vocat Archimedes Sali-
              <lb/>
            non) æqualis circulo, cuius diameter eſt F G, & </s>
            <s xml:id="echoid-s13530" xml:space="preserve">hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13531" xml:space="preserve"/>
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        <div xml:id="echoid-div1165" type="section" level="1" n="380">
          <head xml:id="echoid-head472" xml:space="preserve">PROPOSITIO XV.</head>
          <p>
            <s xml:id="echoid-s13532" xml:space="preserve">SI fuerit A B ſemicirculus, & </s>
            <s xml:id="echoid-s13533" xml:space="preserve">A C corda Pentagoni, & </s>
            <s xml:id="echoid-s13534" xml:space="preserve">ſe-
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            miſſis arcus A C ſit A D, iungatur C D, & </s>
            <s xml:id="echoid-s13535" xml:space="preserve">producatur
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            vt cadat ſuper E, & </s>
            <s xml:id="echoid-s13536" xml:space="preserve">iungatur D B, quæ ſecet C A in F, & </s>
            <s xml:id="echoid-s13537" xml:space="preserve">
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            ducatur ex F perpendicularis F G ſuper A B, erit linea E G
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            æqualis ſemidiametro circuli.</s>
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          <figure number="521">
            <image file="0445-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0445-01"/>
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            <s xml:id="echoid-s13539" xml:space="preserve">Iungamus itaque lineam C B, & </s>
            <s xml:id="echoid-s13540" xml:space="preserve">ſit centrum H, & </s>
            <s xml:id="echoid-s13541" xml:space="preserve">iungamus H D,
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            D G, & </s>
            <s xml:id="echoid-s13542" xml:space="preserve">A D. </s>
            <s xml:id="echoid-s13543" xml:space="preserve">Et quia angulus A B C, cuius baſis eſt latus Pentagoni,
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            eſt duæ quintæ partes recti, quilibet duorum angulorum C B D, D B
              <lb/>
            A eſt quinta pars recti, & </s>
            <s xml:id="echoid-s13544" xml:space="preserve">angulus D H A duplus eſt anguli D B H,
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            ergo angulus D H A eſt duæ quinte partes recti. </s>
            <s xml:id="echoid-s13545" xml:space="preserve">Et quia in duobus trian-
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            gulis C B F, G B F duo anguli B ſunt æquales, & </s>
            <s xml:id="echoid-s13546" xml:space="preserve">G, C recti, & </s>
            <s xml:id="echoid-s13547" xml:space="preserve">latus
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            F B commune, erit B C æquale ipſi B G: </s>
            <s xml:id="echoid-s13548" xml:space="preserve">& </s>
            <s xml:id="echoid-s13549" xml:space="preserve">quia in duobus triangulis
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            C B D, G B D duo latera C B, B G ſunt æqualia, & </s>
            <s xml:id="echoid-s13550" xml:space="preserve">ſimiliter duo an-
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            guli ad B, & </s>
            <s xml:id="echoid-s13551" xml:space="preserve">latus B D commune, erunt duo anguli B C D, B G D
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            æquales, & </s>
            <s xml:id="echoid-s13552" xml:space="preserve">quilibet eorum eſt ſex quintæ partes recti, & </s>
            <s xml:id="echoid-s13553" xml:space="preserve">eſt æqualis an-
              <lb/>
            gulo D A E externo quadrilateri B A D C, quod eſt in circulo, ergo
              <lb/>
            remanet angulus D A B æqualis angulo D G A, & </s>
            <s xml:id="echoid-s13554" xml:space="preserve">erit D A æqualis ip-
              <lb/>
            ſi D G. </s>
            <s xml:id="echoid-s13555" xml:space="preserve">Et quia angulus D H G eſt duæ quintæ partes recti, & </s>
            <s xml:id="echoid-s13556" xml:space="preserve">angulus
              <lb/>
            D G H ſex quintæ partes recti, remanet angulus H D G duæ quintæ par-
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            tes recti, & </s>
            <s xml:id="echoid-s13557" xml:space="preserve">erit D G æqualis G H. </s>
            <s xml:id="echoid-s13558" xml:space="preserve">Et quia A D E externus quadrila-
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            teri A D C B, quod eſt in circulo, eſt æqualis angulo C B A, & </s>
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