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="263" file="0301" n="301" rhead="Conicor. Lib. VI."/>
            perpendicularis eſt ad circuli diametrum C A, & </s>
            <s xml:id="echoid-s9905" xml:space="preserve">propterea A D, planorum
              <lb/>
            H A I, & </s>
            <s xml:id="echoid-s9906" xml:space="preserve">A C M communis ſectio, tanget circulum A C, & </s>
            <s xml:id="echoid-s9907" xml:space="preserve">ideo ſuperficiem
              <lb/>
            ipſam conicam, & </s>
            <s xml:id="echoid-s9908" xml:space="preserve">ſectionem in ea exiſtentem continget; </s>
            <s xml:id="echoid-s9909" xml:space="preserve">& </s>
            <s xml:id="echoid-s9910" xml:space="preserve">diameter A L non
              <lb/>
            erit perpendicularis ad tangentem, ſeu ordinatim applicatam A D per verticem
              <lb/>
            A, alias A L eſſet axis, quod non ponitur. </s>
            <s xml:id="echoid-s9911" xml:space="preserve">Deinde in plano D A B ex A du-
              <lb/>
            catur recta linea A E perpendicularis ad A D ſupra, vel infra circulum, & </s>
            <s xml:id="echoid-s9912" xml:space="preserve">
              <lb/>
            vertice quolibet puncto E ſumpto in recta linea A E, & </s>
            <s xml:id="echoid-s9913" xml:space="preserve">baſi circulo A C M fiat
              <lb/>
            alter conus E A C, in cuius ſuperficie planũ D A H I deſignet ſectionẽ F A G, & </s>
            <s xml:id="echoid-s9914" xml:space="preserve">
              <lb/>
            in ea triangulum per axim E A C efficiat diametrum A K: </s>
            <s xml:id="echoid-s9915" xml:space="preserve">Et quia eadem re-
              <lb/>
            cta linea D A perpendicularis eſt ad A C, atque ad A E ſe ſecantes in A; </s>
            <s xml:id="echoid-s9916" xml:space="preserve">ergo
              <lb/>
            D A perpendicularis eſt ad planum C E A, atque planum D A C extenſum
              <lb/>
            per perpendicularem D A, erit quoque perpendiculare ad planum trianguli per
              <lb/>
            axim C E A, quare triangulum per axim efficiet diametrum A K, quæ erit
              <lb/>
              <figure xlink:label="fig-0301-01" xlink:href="fig-0301-01a" number="348">
                <image file="0301-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0301-01"/>
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            axis ſectionis F A G, atque D A perpendicularis erit ad axim A K exiſtentem
              <lb/>
            in plano C E A, ad quod D A eſt perpendicularis, & </s>
            <s xml:id="echoid-s9917" xml:space="preserve">cum ea conuenit: </s>
            <s xml:id="echoid-s9918" xml:space="preserve">quare
              <lb/>
            D A ordinatim ad axim applicata perverticem A tanget ſectionem F A G, quæ
              <lb/>
              <note position="right" xlink:label="note-0301-01" xlink:href="note-0301-01a" xml:space="preserve">32. lib. I.</note>
            prius in eodem puncto A tangebat ſectionem H A I in eodem plano exiſtentem;
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            </s>
            <s xml:id="echoid-s9919" xml:space="preserve">& </s>
            <s xml:id="echoid-s9920" xml:space="preserve">propterea eadem recta A D vtramque ſectionem tangit in puncto A. </s>
            <s xml:id="echoid-s9921" xml:space="preserve">Poſtea
              <lb/>
            coniungatur recta linea B E, & </s>
            <s xml:id="echoid-s9922" xml:space="preserve">quia rectæ lineæ B A, A D, A E ſunt in eo-
              <lb/>
            dem plano tangente vtrumque conum (cum per vertices B, & </s>
            <s xml:id="echoid-s9923" xml:space="preserve">E, atque per D
              <lb/>
            A contingentem circulum baſis communis ducatur) & </s>
            <s xml:id="echoid-s9924" xml:space="preserve">E A, & </s>
            <s xml:id="echoid-s9925" xml:space="preserve">B A angulum
              <lb/>
            conſtituunt, cum E A poſita ſit perpendicularis ad D A, at B A ad eandem ſit
              <lb/>
            inclinata, & </s>
            <s xml:id="echoid-s9926" xml:space="preserve">exiſtunt in eodem plano; </s>
            <s xml:id="echoid-s9927" xml:space="preserve">ergo recta B E parallela eſt, aut ſecat
              <lb/>
            contingentem D A extra circulum vt in D. </s>
            <s xml:id="echoid-s9928" xml:space="preserve">Poterit igitur ex propoſ. </s>
            <s xml:id="echoid-s9929" xml:space="preserve">15. </s>
            <s xml:id="echoid-s9930" xml:space="preserve">addi-
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            tarum duci per rectam B E planum aliud B E M V vtrumq; </s>
            <s xml:id="echoid-s9931" xml:space="preserve">conum </s>
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