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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          <p style="it">
            <s xml:id="echoid-s9621" xml:space="preserve">
              <pb o="256" file="0294" n="294" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0294-01" xlink:href="fig-0294-01a" number="342">
                <image file="0294-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0294-01"/>
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            V æqualis eſt V H, quod eſt abſurdum.</s>
            <s xml:id="echoid-s9622" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9623" xml:space="preserve">Patet quadratum L P nempe N E, ſeu O N in N L ad quadratum E P,
              <lb/>
              <note position="left" xlink:label="note-0294-01" xlink:href="note-0294-01a" xml:space="preserve">f</note>
            nempe ad quadratum N L, ſcilicet O N ad N L habere minorem pro-
              <lb/>
            portionem, quàm H E ad E I: </s>
            <s xml:id="echoid-s9624" xml:space="preserve">ponamus iam O N ad Z X, vt H E ad E
              <lb/>
            I; </s>
            <s xml:id="echoid-s9625" xml:space="preserve">& </s>
            <s xml:id="echoid-s9626" xml:space="preserve">per X ducamus X R, & </s>
            <s xml:id="echoid-s9627" xml:space="preserve">iungamus E R, &</s>
            <s xml:id="echoid-s9628" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9629" xml:space="preserve">Suppoſita conſtructione
              <lb/>
            prioris caſus, quandò conus rectus E L K factus eſt ſimilis cono A B C quadra-
              <lb/>
            tum L P ad quadratum E P habebat eandem proportionem, quàm O N ad N L,
              <lb/>
            ſeu quàm quadratum B Q ad quadratum Q A: </s>
            <s xml:id="echoid-s9630" xml:space="preserve">modò in hac altera ſuppoſitione
              <lb/>
            conceditur quadratum B Q ad quadratum Q A habere minorem proportionem,
              <lb/>
            quàm E H ad E I; </s>
            <s xml:id="echoid-s9631" xml:space="preserve">igitur O N ad N L minorem proportionem habebit, quàm,
              <lb/>
            H E ad E I; </s>
            <s xml:id="echoid-s9632" xml:space="preserve">& </s>
            <s xml:id="echoid-s9633" xml:space="preserve">fiat O N ad N X vt H E ad E I, erit N X minor quàm N L,
              <lb/>
            & </s>
            <s xml:id="echoid-s9634" xml:space="preserve">ideo punctum X intra circulum cadet, & </s>
            <s xml:id="echoid-s9635" xml:space="preserve">per X ducta R X Y parallelæ H E;
              <lb/>
            </s>
            <s xml:id="echoid-s9636" xml:space="preserve">vtique ſecabit circulum in duobus punctis, vt in R, & </s>
            <s xml:id="echoid-s9637" xml:space="preserve">Y. </s>
            <s xml:id="echoid-s9638" xml:space="preserve">Quod verò recta,
              <lb/>
            R X Y duci debeat parallela ipſi H E, non quomodocunque, patet ex contextu
              <lb/>
            ſequenti, nam debent O X, O R ſecari in N, & </s>
            <s xml:id="echoid-s9639" xml:space="preserve">V proportionaliter, quarè tex-
              <lb/>
            tus debuit omnino corrigi.</s>
            <s xml:id="echoid-s9640" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9641" xml:space="preserve">Oſtendetur, quemadmodum dictum eſt, quod E T R, & </s>
            <s xml:id="echoid-s9642" xml:space="preserve">A B C ſunt
              <lb/>
              <note position="right" xlink:label="note-0294-02" xlink:href="note-0294-02a" xml:space="preserve">g</note>
            iſoſcelia, & </s>
            <s xml:id="echoid-s9643" xml:space="preserve">ſimilia, &</s>
            <s xml:id="echoid-s9644" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9645" xml:space="preserve">Quoniam arcus circuli E O, & </s>
            <s xml:id="echoid-s9646" xml:space="preserve">O H æquales ſunt
              <lb/>
            inter ſe ex conſtructione, erunt anguli E R O, & </s>
            <s xml:id="echoid-s9647" xml:space="preserve">O R H æquales inter ſe, & </s>
            <s xml:id="echoid-s9648" xml:space="preserve">
              <lb/>
            propter parallelas O R, & </s>
            <s xml:id="echoid-s9649" xml:space="preserve">E T eſt angulus O R E æqualis alterno T E R; </s>
            <s xml:id="echoid-s9650" xml:space="preserve">at-
              <lb/>
            què externus H R O æqualis eſt interno, & </s>
            <s xml:id="echoid-s9651" xml:space="preserve">oppoſito R T E; </s>
            <s xml:id="echoid-s9652" xml:space="preserve">igitur duo anguli
              <lb/>
            R E T, & </s>
            <s xml:id="echoid-s9653" xml:space="preserve">R T E æquales ſunt inter ſe; </s>
            <s xml:id="echoid-s9654" xml:space="preserve">& </s>
            <s xml:id="echoid-s9655" xml:space="preserve">propterea triangulum E R T erit
              <lb/>
            iſoſcelium. </s>
            <s xml:id="echoid-s9656" xml:space="preserve">Rurſus quia duo anguli E L H, E R H in eodem circuli ſegmento
              <lb/>
            couſtituti æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s9657" xml:space="preserve">erat ex conſtructione angulus M B C æqualis
              <lb/>
            angulo H L E; </s>
            <s xml:id="echoid-s9658" xml:space="preserve">igitur anguli H R E, & </s>
            <s xml:id="echoid-s9659" xml:space="preserve">M B C æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s9660" xml:space="preserve">ideo
              <lb/>
            conſequentes anguli verticales E R T, & </s>
            <s xml:id="echoid-s9661" xml:space="preserve">A B C æquales erunt inter ſe, eſt quo-
              <lb/>
            que triangulum A B C per axim coni recti iſoſcelium igitur duo triangula,
              <lb/>
            E R T, & </s>
            <s xml:id="echoid-s9662" xml:space="preserve">A B C ſimilia ſunt inter ſe. </s>
            <s xml:id="echoid-s9663" xml:space="preserve">Et quia vt dictum eſt O N ad N X
              <lb/>
            eandem proportionem habet, quàm H E ad E I, atque propter parallelas V N,
              <lb/>
            & </s>
            <s xml:id="echoid-s9664" xml:space="preserve">R X eſt O V ad V R vt O N ad N X, & </s>
            <s xml:id="echoid-s9665" xml:space="preserve">ſumpta cõmuni altitudine V R </s>
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