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-div1146" type="section" level="1" n="370">
          <pb o="401" file="0439" n="440" rhead="Aſſumpt. Liber."/>
        </div>
        <div xml:id="echoid-div1148" type="section" level="1" n="371">
          <head xml:id="echoid-head463" xml:space="preserve">PROPOSITIO IX.</head>
          <p>
            <s xml:id="echoid-s13382" xml:space="preserve">SI mutuo ſe ſecuerint in circulo duæ lineæ A B, C D, (ſed
              <lb/>
            non in centro) ad angulos rectos, vtique duo arcus A D,
              <lb/>
            C B ſunt æquales duobus arcubus A C, D B.</s>
            <s xml:id="echoid-s13383" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13384" xml:space="preserve">Educamus diametrum E F parallelam ipſi A B, quæ ſecet C D biſa-
              <lb/>
            riam in G, erit E C æqualis ipſi E D; </s>
            <s xml:id="echoid-s13385" xml:space="preserve">& </s>
            <s xml:id="echoid-s13386" xml:space="preserve">quia tam arcus E D F, quam
              <lb/>
            E C F eſt ſemicirculus, & </s>
            <s xml:id="echoid-s13387" xml:space="preserve">arcus
              <lb/>
            E D æqualis arcui E A cum
              <lb/>
              <figure xlink:label="fig-0439-01" xlink:href="fig-0439-01a" number="510">
                <image file="0439-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0439-01"/>
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            arcu A D, erit arcus C F cum
              <lb/>
            duobus arcubus E A, A D æ-
              <lb/>
            qualis ſemicirculo, & </s>
            <s xml:id="echoid-s13388" xml:space="preserve">arcus E
              <lb/>
            A æqualis arcui B F, ergo ar-
              <lb/>
            cus C B cum arcu A D æqualis
              <lb/>
            eſt ſemicirculo, & </s>
            <s xml:id="echoid-s13389" xml:space="preserve">remanent duo
              <lb/>
            arcus E C, E A nempe arcus A
              <lb/>
            C cum arcu D B æquales illi,
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            & </s>
            <s xml:id="echoid-s13390" xml:space="preserve">hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13391" xml:space="preserve"/>
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        <div xml:id="echoid-div1150" type="section" level="1" n="372">
          <head xml:id="echoid-head464" xml:space="preserve">PROPOSITIO X.</head>
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            <s xml:id="echoid-s13392" xml:space="preserve">SI fuerit circulus A B C, & </s>
            <s xml:id="echoid-s13393" xml:space="preserve">D A tangens illum, & </s>
            <s xml:id="echoid-s13394" xml:space="preserve">D B ſe-
              <lb/>
            cans illum, & </s>
            <s xml:id="echoid-s13395" xml:space="preserve">D C etiam tangens, & </s>
            <s xml:id="echoid-s13396" xml:space="preserve">educta fuerit C E
              <lb/>
            parallela ipſi D B, & </s>
            <s xml:id="echoid-s13397" xml:space="preserve">iuncta fuerit E A ſecans D B in F, & </s>
            <s xml:id="echoid-s13398" xml:space="preserve">
              <lb/>
            educta fuerit ex F perpendicularis F G ſuper C E; </s>
            <s xml:id="echoid-s13399" xml:space="preserve">vtique bifa-
              <lb/>
            riam ſecabit illam in G.</s>
            <s xml:id="echoid-s13400" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13401" xml:space="preserve">Iungamus A C, & </s>
            <s xml:id="echoid-s13402" xml:space="preserve">quia D A eſt tangens, & </s>
            <s xml:id="echoid-s13403" xml:space="preserve">A C ſecans circulum
              <lb/>
            erit angulus D A C æqualis angulo cadenti in alterno ſegmento A C
              <lb/>
              <figure xlink:label="fig-0439-02" xlink:href="fig-0439-02a" number="511">
                <image file="0439-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0439-02"/>
              </figure>
            </s>
          </p>
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