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-div814" type="section" level="1" n="248">
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            <s xml:id="echoid-s9931" xml:space="preserve">
              <pb o="264" file="0302" n="302" rhead="Apollonij Pergæi"/>
            & </s>
            <s xml:id="echoid-s9932" xml:space="preserve">per rectam B E extendatur aliud planum E N O B inter duo plana contin-
              <lb/>
            gentia prope verticem A vbicumq; </s>
            <s xml:id="echoid-s9933" xml:space="preserve">cadens, quod ſecet vtrumque conum, & </s>
            <s xml:id="echoid-s9934" xml:space="preserve">cir-
              <lb/>
            culum baſis in recta linea N O, & </s>
            <s xml:id="echoid-s9935" xml:space="preserve">ſuperficies duorum conorum in lateribus B
              <lb/>
            N Q, E N, B O, E O R, quarum B N occurret ſemiſectioni A H in quolibet
              <lb/>
            eius puncto Q prope verticem A, eo quod portio A H, & </s>
            <s xml:id="echoid-s9936" xml:space="preserve">peripheria A N C ex
              <lb/>
            cepto puncto eius A totæ inter duo plana conos tangentia intercipiuntur; </s>
            <s xml:id="echoid-s9937" xml:space="preserve">& </s>
            <s xml:id="echoid-s9938" xml:space="preserve">eadem
              <lb/>
            ratione E O occurret ſemiſectioni A G in quolibet eius puncto R vltra verticem
              <lb/>
            A ad partes G. </s>
            <s xml:id="echoid-s9939" xml:space="preserve">Et quoniam in eo-
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              <figure xlink:label="fig-0302-01" xlink:href="fig-0302-01a" number="349">
                <image file="0302-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0302-01"/>
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            dem plano trianguli E N B (ſcili-
              <lb/>
            cet plani B N O E ſecantis vtrum-
              <lb/>
            que conum) à puncto E ducitur re-
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            cta linea E O intra angulum N E B;
              <lb/>
            </s>
            <s xml:id="echoid-s9940" xml:space="preserve">ergo vlterius producta ſecabit latus
              <lb/>
            B N ſubtendentem angulum N E B
              <lb/>
            inter puncta N, & </s>
            <s xml:id="echoid-s9941" xml:space="preserve">B, vt in X, & </s>
            <s xml:id="echoid-s9942" xml:space="preserve">
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            propterearecta linea N X intra triã-
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            gulum E N O, & </s>
            <s xml:id="echoid-s9943" xml:space="preserve">ideo intra conum
              <lb/>
            E A C intercepta erit; </s>
            <s xml:id="echoid-s9944" xml:space="preserve">ſimiliter re-
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            cta linea O X intra triangulum B N
              <lb/>
            O, & </s>
            <s xml:id="echoid-s9945" xml:space="preserve">intra conum B A C interclu-
              <lb/>
            ſa erit: </s>
            <s xml:id="echoid-s9946" xml:space="preserve">quare quodlibet aliud punctũ
              <lb/>
            Qlateris conici B N citra, vel vltra
              <lb/>
            interclusã portionẽ N X cadet neceſ-
              <lb/>
            ario extra ſuperficiem coni E A C,
              <lb/>
            & </s>
            <s xml:id="echoid-s9947" xml:space="preserve">ideo quodlibet punctum Q in pro-
              <lb/>
            ductione lateris coni B N ſumptum
              <lb/>
            & </s>
            <s xml:id="echoid-s9948" xml:space="preserve">in ſemiſſe ſectionis conicæ H A
              <lb/>
            prope verticem A cadet extra ſemiſ-
              <lb/>
            ſem ſectionis F A, quæ in ſuperfi-
              <lb/>
            cie coni E A C exiſtit, & </s>
            <s xml:id="echoid-s9949" xml:space="preserve">ad eaſ-
              <lb/>
            dem partes vergit. </s>
            <s xml:id="echoid-s9950" xml:space="preserve">Pari modo quod-
              <lb/>
            libet aliud punctum R lateris conici
              <lb/>
            E O citra, vel vltra intercluſam
              <lb/>
            portionẽ X O cadet extra ſuperſiciem
              <lb/>
            coni B A C, & </s>
            <s xml:id="echoid-s9951" xml:space="preserve">ideo quodlibet punctũ
              <lb/>
            R ſumptum in medietate ſectionis
              <lb/>
            conicæ A G prope verticem A cadet
              <lb/>
            extra medietatem ſectionis A I, quæ
              <lb/>
            in ſuperficie coni B A C exiſtit, & </s>
            <s xml:id="echoid-s9952" xml:space="preserve">
              <lb/>
            ad eaſdem partes vergit. </s>
            <s xml:id="echoid-s9953" xml:space="preserve">Igitur ſe-
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            ctio H A I abſcindit coniſectionem
              <lb/>
            F A G in vertice communi A, vbi
              <lb/>
            ambo tanguntur ab eadem recta li-
              <lb/>
            nea A D. </s>
            <s xml:id="echoid-s9954" xml:space="preserve">Quod erat faciendum.</s>
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