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-div1142" type="section" level="1" n="368">
          <pb o="400" file="0438" n="439" rhead="Archimedis"/>
          <p>
            <s xml:id="echoid-s13355" xml:space="preserve">Educamus igitur E G parallelam ipſi
              <lb/>
              <figure xlink:label="fig-0438-01" xlink:href="fig-0438-01a" number="507">
                <image file="0438-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0438-01"/>
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            A B, & </s>
            <s xml:id="echoid-s13356" xml:space="preserve">iungamus D B, D G: </s>
            <s xml:id="echoid-s13357" xml:space="preserve">& </s>
            <s xml:id="echoid-s13358" xml:space="preserve">quia duo
              <lb/>
            anguli D E G, D G E ſunt æquales, erit
              <lb/>
            angulus G D C duplus anguli D E G,
              <lb/>
            & </s>
            <s xml:id="echoid-s13359" xml:space="preserve">quia angulus B D C æqualis eſt angu-
              <lb/>
            lo B C D, & </s>
            <s xml:id="echoid-s13360" xml:space="preserve">angulus C E G æqualis eſt
              <lb/>
            angulo A C E, erit angulus G D C du-
              <lb/>
            plus anguli C D B, & </s>
            <s xml:id="echoid-s13361" xml:space="preserve">totus angulus B
              <lb/>
            D G triplus anguli B D C, & </s>
            <s xml:id="echoid-s13362" xml:space="preserve">arcus B G
              <lb/>
            æqualis arcui A E, triplus eſt arcus B F,
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            & </s>
            <s xml:id="echoid-s13363" xml:space="preserve">hoc eſt, quod voluimus.</s>
            <s xml:id="echoid-s13364" xml:space="preserve"/>
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        <div xml:id="echoid-div1144" type="section" level="1" n="369">
          <head xml:id="echoid-head461" xml:space="preserve">SCHOLIVM ALMOCHTASSO.</head>
          <p>
            <s xml:id="echoid-s13365" xml:space="preserve">DIcit Doctor Almoch-
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              <figure xlink:label="fig-0438-02" xlink:href="fig-0438-02a" number="508">
                <image file="0438-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0438-02"/>
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            taſſo. </s>
            <s xml:id="echoid-s13366" xml:space="preserve">Cum dicit ar-
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            cum B G æqualem eſſe ar-
              <lb/>
            cui A E, id ex eo eſt pro-
              <lb/>
            pter æquidiſtantiam duarum
              <lb/>
            cordarum. </s>
            <s xml:id="echoid-s13367" xml:space="preserve">Sint itaque in
              <lb/>
            circulo A B C cordæ A C,
              <lb/>
            B D parallelæ; </s>
            <s xml:id="echoid-s13368" xml:space="preserve">Dico quod
              <lb/>
            duo arcus A B, C D ſunt
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            æquales,</s>
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          <p>
            <s xml:id="echoid-s13369" xml:space="preserve">Iungamus A D, ergo duo anguli C A D, A D B ſunt æquales; </s>
            <s xml:id="echoid-s13370" xml:space="preserve">& </s>
            <s xml:id="echoid-s13371" xml:space="preserve">
              <lb/>
            propterea duo arcus ſunt æquales, & </s>
            <s xml:id="echoid-s13372" xml:space="preserve">conuerſum eodem modo demon-
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            ſtratur.</s>
            <s xml:id="echoid-s13373" xml:space="preserve"/>
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        <div xml:id="echoid-div1146" type="section" level="1" n="370">
          <head xml:id="echoid-head462" xml:space="preserve">Notæ in Propoſit. VIII.</head>
          <p style="it">
            <s xml:id="echoid-s13374" xml:space="preserve">HAEc quidem propoſitio elegantiſſima eſt, quæ ſi problematicè reſolui poſ-
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            ſet via plana, reperta iam eßet tripartitio cuiuſlibet anguli.</s>
            <s xml:id="echoid-s13375" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s13376" xml:space="preserve">Breuius tamen demonſtratio
              <lb/>
              <figure xlink:label="fig-0438-03" xlink:href="fig-0438-03a" number="509">
                <image file="0438-03" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0438-03"/>
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            perfici poteſt hac ratione. </s>
            <s xml:id="echoid-s13377" xml:space="preserve">Iuncta
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            recta E B, quia in triangulo Iſo-
              <lb/>
            ſcele B D C duo anguli C, & </s>
            <s xml:id="echoid-s13378" xml:space="preserve">C
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            D B æquales ſunt, eſtque pariter
              <lb/>
            externus angulus B D C duplus an-
              <lb/>
            guli D E B in triangulo Iſoſcelio
              <lb/>
            D E B, ergo angulus C duplus eſt
              <lb/>
            anguli B E C, & </s>
            <s xml:id="echoid-s13379" xml:space="preserve">propterea illi an-
              <lb/>
            guli ſimul ſumpti, ſeu externus an-
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            gulus A B E triplus erit anguli B
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            E F, & </s>
            <s xml:id="echoid-s13380" xml:space="preserve">circunferentia A E tripla ipſius B F.</s>
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