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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          <pb o="43" file="0081" n="81" rhead="Conicor. Lib. V."/>
          <figure number="58">
            <image file="0081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081-01"/>
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          <p style="it">
            <s xml:id="echoid-s2104" xml:space="preserve">Et ſimili modo conſtat, quod breuiſſima egrediens ex puncto L cadit
              <lb/>
              <note position="left" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">f</note>
            extra S L, &</s>
            <s xml:id="echoid-s2105" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2106" xml:space="preserve">Ad vitandam confuſionem figuræ, & </s>
            <s xml:id="echoid-s2107" xml:space="preserve">prolixitatem demonſtrationis
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            appoſui duas figuras, in quibus duo caſus ijſdem caracteribus notantur, itaque abſq;
              <lb/>
            </s>
            <s xml:id="echoid-s2108" xml:space="preserve">nouo labore, ſi inſpiciatur ſecunda figura, ijſdem verbis prioris caſus, oſtendetur ca-
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            ſus ſecundus.</s>
            <s xml:id="echoid-s2109" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s2110" xml:space="preserve">Pariter demonſtrabitur, quemadmodum iam oſtenſumeſt, &</s>
            <s xml:id="echoid-s2111" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2112" xml:space="preserve">Pars ſecun-
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              <note position="left" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve">g</note>
            da huius propoſitionis innuitur tantummodo pauciſsimis verbis; </s>
            <s xml:id="echoid-s2113" xml:space="preserve">quare maioris cla-
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            ritatis gratia integram demonſtrationem hìc afferre libuit.</s>
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        <div xml:id="echoid-div179" type="section" level="1" n="71">
          <head xml:id="echoid-head103" xml:space="preserve">Demonſtratio ſecundæ partis.</head>
          <head xml:id="echoid-head104" xml:space="preserve">PROPOSITIONIS LI.</head>
          <p style="it">
            <s xml:id="echoid-s2115" xml:space="preserve">Eſto E D æqualis trutinæ H: </s>
            <s xml:id="echoid-s2116" xml:space="preserve">Dico ex concurſu E vnicum tantùm breui-
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            ſecantem ramum duci poſſe.</s>
            <s xml:id="echoid-s2117" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s2118" xml:space="preserve">In eadem ſigura, quia ex conſtructione H ad B G eſt, vt G F ad F D, ponitur verò
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            E D æqualis H; </s>
            <s xml:id="echoid-s2119" xml:space="preserve">ergo E D ad B G, ſeu D I ad I G (propter ſimilitudinem triangulo-
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            rum E D I, B G I) eſt, vt G F ad F D, & </s>
            <s xml:id="echoid-s2120" xml:space="preserve">componendo D G ad G I eſt, vt eadem G D
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            ad D F; </s>
            <s xml:id="echoid-s2121" xml:space="preserve">ideoque I G æqualis eſt D F, ſeu A C ſemierecto; </s>
            <s xml:id="echoid-s2122" xml:space="preserve">igitur B I eſt breuiſsima.</s>
            <s xml:id="echoid-s2123" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">8. huius.</note>
          <p style="it">
            <s xml:id="echoid-s2124" xml:space="preserve">Poſte a ducto quolibet ramo E K ſupra breuiſecantem E B (in prima figura, & </s>
            <s xml:id="echoid-s2125" xml:space="preserve">in-
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            fra in ſecunda) occurrente axi in R, & </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ducta K M perpendiculari ad axim, quæ eum
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            ſecet in M, & </s>
            <s xml:id="echoid-s2127" xml:space="preserve">tangentem O B in P. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">Quoniam (vt dictum eſt) O F ſecatur </s>
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