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-s13403" xml:space="preserve">
              <pb o="402" file="0440" n="441" rhead="Archimedis"/>
            nempe angulo A E C, & </s>
            <s xml:id="echoid-s13404" xml:space="preserve">eſt æqualis angulo A F D, eo quod C E,
              <lb/>
            B D ſunt parallelæ, ergo anguli D A C, A F D ſunt æquales, & </s>
            <s xml:id="echoid-s13405" xml:space="preserve">in
              <lb/>
            duobus triangulis D A F, A H D ſunt duo auguli A F D, H A D æquales,
              <lb/>
            & </s>
            <s xml:id="echoid-s13406" xml:space="preserve">angulus D communis, propterea erit rectãgulum F D in D H æquale
              <lb/>
              <figure xlink:label="fig-0440-01" xlink:href="fig-0440-01a" number="512">
                <image file="0440-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0440-01"/>
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            quadrato D A, immo quadrato D C, & </s>
            <s xml:id="echoid-s13407" xml:space="preserve">quia proportio F D ad D C eſt
              <lb/>
            eadem proportioni C D ad D H, & </s>
            <s xml:id="echoid-s13408" xml:space="preserve">angulus D communis, erunt triangula
              <lb/>
            D F C, D C H ſimilia, & </s>
            <s xml:id="echoid-s13409" xml:space="preserve">angulus D F C æqualis D C H, qui æqualis
              <lb/>
            eſt angulo D A H, & </s>
            <s xml:id="echoid-s13410" xml:space="preserve">hic eſt æqualis angulo A F D, ergo duo anguli A
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            F D, C F D ſunt æquales, & </s>
            <s xml:id="echoid-s13411" xml:space="preserve">D F C æqualis angulo F C E, & </s>
            <s xml:id="echoid-s13412" xml:space="preserve">erat D
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            F A æqualis angulo A E C, ergo in triangulo F E C ſunt duo anguli C,
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            E æquales, & </s>
            <s xml:id="echoid-s13413" xml:space="preserve">duo anguli G recti, & </s>
            <s xml:id="echoid-s13414" xml:space="preserve">latus G F commune, propterea
              <lb/>
            eri@ C G æqualis ipſi G E, ergo C E bifariam ſecatur in G, & </s>
            <s xml:id="echoid-s13415" xml:space="preserve">hoc eſt,
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            quod voluimus,</s>
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          <head xml:id="echoid-head465" xml:space="preserve">PROPOSITIO XI.</head>
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            <s xml:id="echoid-s13416" xml:space="preserve">SI mutuo ſe ſecuerint in circulo duæ lineæ A B, C D ad an-
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            gulos rectos in E, quod non ſit in centro, vtique omnia
              <lb/>
            quadrata A E, B E, E C, E D æqualia ſunt quadrato diametri.</s>
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          <p>
            <s xml:id="echoid-s13418" xml:space="preserve">Educamus diametrum A F,
              <lb/>
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            & </s>
            <s xml:id="echoid-s13419" xml:space="preserve">iungamus lineas A C, A D,
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            C F, D B; </s>
            <s xml:id="echoid-s13420" xml:space="preserve">Et quia angulus A
              <lb/>
            E D eſt rectus, erit æqualis an-
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            gulo A C F, & </s>
            <s xml:id="echoid-s13421" xml:space="preserve">angulus A D C
              <lb/>
            æqualis A F C, eo quod ſunt
              <lb/>
            ſuper arcum A C, & </s>
            <s xml:id="echoid-s13422" xml:space="preserve">remanent
              <lb/>
            in duobus triangulis A D E, A
              <lb/>
            F C duo anguli C A F, D A E
              <lb/>
            æquales erunt pariter duo arcus
              <lb/>
            C F, D B æquales immo, & </s>
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              <lb/>
            duæ cordæ eorum æquales, & </s>
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            duo quadrata D E, E B æquantur quadrato B D, nempe C F, & </s>
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