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-div1165" type="section" level="1" n="380">
          <p>
            <s xml:id="echoid-s13559" xml:space="preserve">
              <pb o="408" file="0446" n="447" rhead="Archimedis"/>
            duæ quintæ partes recti, & </s>
            <s xml:id="echoid-s13560" xml:space="preserve">æqualis angulo G D H. </s>
            <s xml:id="echoid-s13561" xml:space="preserve">Et quia in duobus
              <lb/>
            triangulis E D A, H D G ſunt duo anguli E D A, H D G æquales, & </s>
            <s xml:id="echoid-s13562" xml:space="preserve">
              <lb/>
            pariter duo anguli D G H, D A E, & </s>
            <s xml:id="echoid-s13563" xml:space="preserve">duo latera D A, D G, erit E A
              <lb/>
            æquale H G, & </s>
            <s xml:id="echoid-s13564" xml:space="preserve">ponamus A G commune, erit E G æquale A H, & </s>
            <s xml:id="echoid-s13565" xml:space="preserve">
              <lb/>
            hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13566" xml:space="preserve"/>
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          <figure number="522">
            <image file="0446-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0446-01"/>
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          <p>
            <s xml:id="echoid-s13567" xml:space="preserve">Et hinc patet, quod linea D E æqualis ſit ſemidiametro circuli, quia
              <lb/>
            angulus A æqualis eſt angulo D G H, ideo erit linea D H æqualis li-
              <lb/>
            neæ D E. </s>
            <s xml:id="echoid-s13568" xml:space="preserve">Et dico quod E C diuiditur media, & </s>
            <s xml:id="echoid-s13569" xml:space="preserve">extrema proportione
              <lb/>
            in D, & </s>
            <s xml:id="echoid-s13570" xml:space="preserve">maius ſegmentum eſt D E; </s>
            <s xml:id="echoid-s13571" xml:space="preserve">& </s>
            <s xml:id="echoid-s13572" xml:space="preserve">hoc quia E D eſt corda hexago-
              <lb/>
            ni, & </s>
            <s xml:id="echoid-s13573" xml:space="preserve">D C decagoni, & </s>
            <s xml:id="echoid-s13574" xml:space="preserve">hoc iam demonſtratum eſt in libro elemento-
              <lb/>
            rum, & </s>
            <s xml:id="echoid-s13575" xml:space="preserve">hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13576" xml:space="preserve"/>
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          <note position="left" xml:space="preserve">Impie vt
            <lb/>
          Mahume-
            <lb/>
          tanus Para
            <lb/>
          phr
            <unsure/>
          aſtes
            <lb/>
          loquit
            <unsure/>
          ur.</note>
          <p>
            <s xml:id="echoid-s13577" xml:space="preserve">Finis libri Aſſumptorum Archimedis. </s>
            <s xml:id="echoid-s13578" xml:space="preserve">Laus Deo ſoli, & </s>
            <s xml:id="echoid-s13579" xml:space="preserve">orationes eius
              <lb/>
            ſint ſuper Dominum noſtrum Mahometum, & </s>
            <s xml:id="echoid-s13580" xml:space="preserve">ſuos ſocios.</s>
            <s xml:id="echoid-s13581" xml:space="preserve"/>
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        <div xml:id="echoid-div1166" type="section" level="1" n="381">
          <head xml:id="echoid-head473" xml:space="preserve">Notæ in Propoſit. XV.</head>
          <p style="it">
            <s xml:id="echoid-s13582" xml:space="preserve">EX hac propoſitione non pauca colligi poſſunt; </s>
            <s xml:id="echoid-s13583" xml:space="preserve">Si enim coniungantur rectæ
              <lb/>
            lineæ C H, & </s>
            <s xml:id="echoid-s13584" xml:space="preserve">C G, erit triangulum B C E iſoſcelium ſimile triangulo
              <lb/>
            H D E, & </s>
            <s xml:id="echoid-s13585" xml:space="preserve">ſimiliter poſitum; </s>
            <s xml:id="echoid-s13586" xml:space="preserve">pariterque triangulum H C G ſimile quidem
              <lb/>
            erit ipſi G D A, & </s>
            <s xml:id="echoid-s13587" xml:space="preserve">in vtriſque baſes ſimiliter ſecantur, nam angulus B C E
              <lb/>
            in tres partes æquales diuiditur à rectis lineis H C, & </s>
            <s xml:id="echoid-s13588" xml:space="preserve">G C, quarum quæli-
              <lb/>
            bet duæ quintæ partes eſt vnius recti, atque angulus E C G rurſus bifariam
              <lb/>
            diuiditur à recta C A: </s>
            <s xml:id="echoid-s13589" xml:space="preserve">non ſecus tres anguli E D A, A D G, & </s>
            <s xml:id="echoid-s13590" xml:space="preserve">G D H
              <lb/>
            æquales ſunt inter ſe, atque quilibet eorum duæ quintæ vnius recti. </s>
            <s xml:id="echoid-s13591" xml:space="preserve">Et effi-
              <lb/>
            ciuntur quatuor rectæ lineæ E A, A D, D G, D C, inter ſe, & </s>
            <s xml:id="echoid-s13592" xml:space="preserve">lateri de-
              <lb/>
            cagoni regularis circulo inſcripti æquales. </s>
            <s xml:id="echoid-s13593" xml:space="preserve">Pari modo rectæ lineæ E D, E G,
              <lb/>
            G C, H C, H A, æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s13594" xml:space="preserve">lateri hexagoni regularis circulo
              <lb/>
            inſcripti. </s>
            <s xml:id="echoid-s13595" xml:space="preserve">Tandem recta linea C B ſubtendens tres partes decimas circumfe-
              <lb/>
            rentiæ totius circuli æqualis eſt rectæ lineæ C E, ſcilicet compoſitæ ex latere
              <lb/>
            hexagoni, & </s>
            <s xml:id="echoid-s13596" xml:space="preserve">latere decagoni regularium eidem circulo incſriptorum. </s>
            <s xml:id="echoid-s13597" xml:space="preserve"/>
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