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-div1158" type="section" level="1" n="376">
          <p>
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              <pb o="405" file="0443" n="444" rhead="Aſſump. Liber."/>
            immo duo anguli A B F, A C F minores ſint duobus angulis A B D,
              <lb/>
            A C D, totum ſua parte, & </s>
            <s xml:id="echoid-s13478" xml:space="preserve">hoc eſt abſurdum, ergo manet propoſitum.</s>
            <s xml:id="echoid-s13479" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1160" type="section" level="1" n="377">
          <head xml:id="echoid-head469" xml:space="preserve">Notæ in Propoſit. XII.</head>
          <p style="it">
            <s xml:id="echoid-s13480" xml:space="preserve">LEmma aſſumptum in demonſtratione huius pulcherrimæ propoſitionis poteſt
              <lb/>
            directè oſtendi hac ratione.</s>
            <s xml:id="echoid-s13481" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s13482" xml:space="preserve">Si in quadrilatero A C D B duo latera A C, & </s>
            <s xml:id="echoid-s13483" xml:space="preserve">A B æqualia fuerint, atque
              <lb/>
            angulus C D B æqualis duobus angulis C, & </s>
            <s xml:id="echoid-s13484" xml:space="preserve">B ſimul ſumptis. </s>
            <s xml:id="echoid-s13485" xml:space="preserve">Dico rectam A
              <lb/>
            D ipſi A C, vel A B æqualẽ eſſe. </s>
            <s xml:id="echoid-s13486" xml:space="preserve">Producatur C A, in E, vt A E fiat æqualis
              <lb/>
            A B, iungaturque B E. </s>
            <s xml:id="echoid-s13487" xml:space="preserve">Quia in triangulo Iſo-
              <lb/>
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                <image file="0443-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0443-01"/>
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            ſcelio B A E angulus E æqualis eſt angulo A B
              <lb/>
            E, & </s>
            <s xml:id="echoid-s13488" xml:space="preserve">angulus C D B æqualis eſt duobus angulis
              <lb/>
            C, & </s>
            <s xml:id="echoid-s13489" xml:space="preserve">D B A ſimul ſumptis, ergo duo anguli C D
              <lb/>
            B, & </s>
            <s xml:id="echoid-s13490" xml:space="preserve">E (oppoſiti in quadrilatero C D B E)
              <lb/>
            æquales ſunt tribus angulis C, D B A, & </s>
            <s xml:id="echoid-s13491" xml:space="preserve">A B
              <lb/>
            E, ſeu duobus angulis C, & </s>
            <s xml:id="echoid-s13492" xml:space="preserve">D B E, ſed qua-
              <lb/>
            tuor anguli quadrilateri E C D B æquales ſunt
              <lb/>
            quatuor rectis, ergo duo anguli oppoſiti E, C D
              <lb/>
            B duobus rectis æquales ſunt, & </s>
            <s xml:id="echoid-s13493" xml:space="preserve">propterea qua-
              <lb/>
            drilaterum ipſum circulo inſcribi poteſt, cuius
              <lb/>
            circuli centrum erit A, cum tres rectæ lineæ
              <lb/>
            C A, A B, A E æquales poſitæ ſint, & </s>
            <s xml:id="echoid-s13494" xml:space="preserve">propte-
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            rea A D radius quoque circuli erit æqualis ipſi C A.</s>
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        <div xml:id="echoid-div1162" type="section" level="1" n="378">
          <head xml:id="echoid-head470" xml:space="preserve">PROPOSITIO XIII.</head>
          <p>
            <s xml:id="echoid-s13496" xml:space="preserve">SI mutuo ſe ſecent duæ lineæ A B, C D in circulo, & </s>
            <s xml:id="echoid-s13497" xml:space="preserve">fue-
              <lb/>
            rit A B diameter illius, at non C D, & </s>
            <s xml:id="echoid-s13498" xml:space="preserve">educantur ex duo-
              <lb/>
            bus punctis A, B duæ per-
              <lb/>
              <figure xlink:label="fig-0443-02" xlink:href="fig-0443-02a" number="519">
                <image file="0443-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0443-02"/>
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            pendiculares ad C D, quæ
              <lb/>
            ſint A E, B F, vtique ab-
              <lb/>
            ſcindent ex illa C F, D E
              <lb/>
            æquales.</s>
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          </p>
          <p>
            <s xml:id="echoid-s13500" xml:space="preserve">Iungamus E B, & </s>
            <s xml:id="echoid-s13501" xml:space="preserve">educamus
              <lb/>
            ex I, quod eſt centrum, per-
              <lb/>
            pendicularem I G ſuper C D,
              <lb/>
            & </s>
            <s xml:id="echoid-s13502" xml:space="preserve">producamus eam ad H in E
              <lb/>
            B. </s>
            <s xml:id="echoid-s13503" xml:space="preserve">Et quia I G eſt perpendicu-
              <lb/>
            laris ex centro ad C D illam bi-
              <lb/>
            fariam diuidet in G, & </s>
            <s xml:id="echoid-s13504" xml:space="preserve">quia I
              <lb/>
            G, A E ſunt duæ perpendicu-
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            lares ſuper illam, erunt </s>
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