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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          <p>
            <s xml:id="echoid-s13425" xml:space="preserve">
              <pb o="403" file="0441" n="442" rhead="Aſſumpt. Liber."/>
            quadrata A E, E C æquantur quadrato C A, & </s>
            <s xml:id="echoid-s13426" xml:space="preserve">duo quadrata C F, C A
              <lb/>
            æquantur quadrato F A, nempe diametri, igitur quadrata A E, E B, C E,
              <lb/>
            E D omnia ſunt æqualia quadrato diametri, & </s>
            <s xml:id="echoid-s13427" xml:space="preserve">hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13428" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1154" type="section" level="1" n="374">
          <head xml:id="echoid-head466" xml:space="preserve">SCHOLIVM ALMOCHTASSO.</head>
          <p>
            <s xml:id="echoid-s13429" xml:space="preserve">DIcit Doctor. </s>
            <s xml:id="echoid-s13430" xml:space="preserve">Huius eſt alia facilior demonſtratio ea, quam attulit
              <lb/>
            Archimedes; </s>
            <s xml:id="echoid-s13431" xml:space="preserve">quæ eſt huiuſmodi. </s>
            <s xml:id="echoid-s13432" xml:space="preserve">Iungamus A D, C B, B D; </s>
            <s xml:id="echoid-s13433" xml:space="preserve">& </s>
            <s xml:id="echoid-s13434" xml:space="preserve">quia
              <lb/>
            angulus B E D eſt rectus, erunt duo
              <lb/>
              <figure xlink:label="fig-0441-01" xlink:href="fig-0441-01a" number="514">
                <image file="0441-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0441-01"/>
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            anguli E B D, E D B æquales vni
              <lb/>
            recto, & </s>
            <s xml:id="echoid-s13435" xml:space="preserve">duo A D, B C, æqua-
              <lb/>
            les ſemicirculo, ergo duæ cordæ eo-
              <lb/>
            rum in potentia ſunt æquales diame-
              <lb/>
            tro; </s>
            <s xml:id="echoid-s13436" xml:space="preserve">ſed duo quadrata A E, D E
              <lb/>
            æqualia quadrato A D, & </s>
            <s xml:id="echoid-s13437" xml:space="preserve">duo qua-
              <lb/>
            drata C E, B E ſunt æqualia qua-
              <lb/>
            drato C B, ergo quadrata A E, E
              <lb/>
            B, C E, E D æqualia ſunt quadra-
              <lb/>
            to diametri; </s>
            <s xml:id="echoid-s13438" xml:space="preserve">& </s>
            <s xml:id="echoid-s13439" xml:space="preserve">hoc eſt quod vo-
              <lb/>
            luimus.</s>
            <s xml:id="echoid-s13440" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1156" type="section" level="1" n="375">
          <head xml:id="echoid-head467" xml:space="preserve">PROPOSITIO XII.</head>
          <p>
            <s xml:id="echoid-s13441" xml:space="preserve">SI fuerit ſemicirculus ſuper diametrum A B, & </s>
            <s xml:id="echoid-s13442" xml:space="preserve">eductæ fue-
              <lb/>
            rint ex C duæ lineæ tangentes illum in duobus punctis D,
              <lb/>
            E, & </s>
            <s xml:id="echoid-s13443" xml:space="preserve">iunctæ fuerint E A, D B ſe muto ſecantes in F, & </s>
            <s xml:id="echoid-s13444" xml:space="preserve">iun cta
              <lb/>
            fuerit C F, & </s>
            <s xml:id="echoid-s13445" xml:space="preserve">producatur ad G, erit C G perpendicularis ad A B.</s>
            <s xml:id="echoid-s13446" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13447" xml:space="preserve">Iungamus D A, E B. </s>
            <s xml:id="echoid-s13448" xml:space="preserve">Et quia,
              <lb/>
            angulus B D A eſt rectus, erunt duo
              <lb/>
              <figure xlink:label="fig-0441-02" xlink:href="fig-0441-02a" number="515">
                <image file="0441-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0441-02"/>
              </figure>
            anguli D A B, D B A reliqui in,
              <lb/>
            triangulo D A B æquales vni recto,
              <lb/>
            & </s>
            <s xml:id="echoid-s13449" xml:space="preserve">angulus A E B rectus, igitur ſunt
              <lb/>
            æquales ei, & </s>
            <s xml:id="echoid-s13450" xml:space="preserve">ponamus angulum
              <lb/>
            F B E communem, ambo anguli D
              <lb/>
            A B, A B E ſunt æquales F B E,
              <lb/>
            F B E, immo angulo D F E exter-
              <lb/>
            no in F B E. </s>
            <s xml:id="echoid-s13451" xml:space="preserve">Et quia C D eſt tan-
              <lb/>
            gens circulum, & </s>
            <s xml:id="echoid-s13452" xml:space="preserve">D B ſecans illum,
              <lb/>
            angulus C D B æquatur angulo D
              <lb/>
            A B, & </s>
            <s xml:id="echoid-s13453" xml:space="preserve">pariter angulus C E F æ-
              <lb/>
            quatur angulo E B A, ergo duo an-
              <lb/>
            guli C E F, C D F ſimul æquales
              <lb/>
            ſunt angulo D F E. </s>
            <s xml:id="echoid-s13454" xml:space="preserve">Et iam quidem
              <lb/>
            planum fit ex noſtro tractatu de fi-
              <lb/>
            guris quadrilateris, quod ſi </s>
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