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="225" file="0263" n="263" rhead="Conicor. Lib. VI."/>
            I M ad partes O A M; </s>
            <s xml:id="echoid-s8431" xml:space="preserve">ideoque interceptæ R P, f h parallelæ erunt alicui re-
              <lb/>
            ctæ lineæ diuidenti angulum D A O ab axe interioris parabola, & </s>
            <s xml:id="echoid-s8432" xml:space="preserve">vertices
              <lb/>
            coniungente contentum, vel angulum I M L ab asymptoto interioris hyperbolæ,
              <lb/>
            & </s>
            <s xml:id="echoid-s8433" xml:space="preserve">centra coniungente contentum; </s>
            <s xml:id="echoid-s8434" xml:space="preserve">igitur R P propinquior verticibus, vel vlte-
              <lb/>
              <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">3. 4. addit.</note>
            rius tendens ad partes reliquæ asymptoti M N maior erit quàm f h; </s>
            <s xml:id="echoid-s8435" xml:space="preserve">eſtque f h
              <lb/>
              <figure xlink:label="fig-0263-01" xlink:href="fig-0263-01a" number="309">
                <image file="0263-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0263-01"/>
              </figure>
            maior f e quæ eſt productio rami breuiſſimi; </s>
            <s xml:id="echoid-s8436" xml:space="preserve">ergo diſtãtia R P propinquior maximæ
              <lb/>
              <note position="right" xlink:label="note-0263-02" xlink:href="note-0263-02a" xml:space="preserve">38. lib. 5.</note>
            E B maior erit, quàm f e. </s>
            <s xml:id="echoid-s8437" xml:space="preserve">E contra quia breuiſſimus ramus i l m cadit inter
              <lb/>
            duas parallelas E B, & </s>
            <s xml:id="echoid-s8438" xml:space="preserve">D A, & </s>
            <s xml:id="echoid-s8439" xml:space="preserve">ſecat ramũ breuiſſimum E B ad partes O i;
              <lb/>
            </s>
            <s xml:id="echoid-s8440" xml:space="preserve">
              <note position="right" xlink:label="note-0263-03" xlink:href="note-0263-03a" xml:space="preserve">28. lib. 5.</note>
            ergo l m occurrit A D, vel M I ad partes D, vel I; </s>
            <s xml:id="echoid-s8441" xml:space="preserve">ideoque intercepta m l,
              <lb/>
            & </s>
            <s xml:id="echoid-s8442" xml:space="preserve">ei parallela G S erunt æquidiſtantes alicui rectæ lineæ diuidenti angulum Y
              <lb/>
            D A, in parabolis, vel H I M in hyperbolis: </s>
            <s xml:id="echoid-s8443" xml:space="preserve">& </s>
            <s xml:id="echoid-s8444" xml:space="preserve">propterea G S propinquior ver-
              <lb/>
              <note position="right" xlink:label="note-0263-04" xlink:href="note-0263-04a" xml:space="preserve">3. 4. addit.</note>
            tici parabolæ, vel vlterius tendens ad partes reliquæ asymptoti M N minor
              <lb/>
            erit, quàm m l; </s>
            <s xml:id="echoid-s8445" xml:space="preserve">eſtque G A productio rami breuiſſimi minor quàm G S; </s>
            <s xml:id="echoid-s8446" xml:space="preserve">ergo
              <lb/>
              <note position="right" xlink:label="note-0263-05" xlink:href="note-0263-05a" xml:space="preserve">38. lib. 5.</note>
            m l maior erit, quàm G A; </s>
            <s xml:id="echoid-s8447" xml:space="preserve">& </s>
            <s xml:id="echoid-s8448" xml:space="preserve">ſic vlterius G A maior erit C F, quando oc-
              <lb/>
            curſus Z ſectionum cadit vltra interceptam F C ad partes T V; </s>
            <s xml:id="echoid-s8449" xml:space="preserve">vt in prima
              <lb/>
            parte oſtenſum eſt.</s>
            <s xml:id="echoid-s8450" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8451" xml:space="preserve">Iiſdem manentibus: </s>
            <s xml:id="echoid-s8452" xml:space="preserve">dico poſtea, quod vltra diſtantiam maximam E B ad
              <lb/>
            partes R P, diſtantiæ, licet ſemper diminuantur non efficiuntur minores inter-
              <lb/>
            uallo diametrorum æquidiſtantium D Y, A O in parabolis, vel interuallo asym-
              <lb/>
            ptotorum collateralium I H, M L in hyperbolis, vt facile deducitur ex 3. </s>
            <s xml:id="echoid-s8453" xml:space="preserve">& </s>
            <s xml:id="echoid-s8454" xml:space="preserve">4.
              <lb/>
            </s>
            <s xml:id="echoid-s8455" xml:space="preserve">additarum. </s>
            <s xml:id="echoid-s8456" xml:space="preserve">At ad partes asymptotorum congruentium hyperbolæ ad ſe ſe ipſas
              <lb/>
            propius accedunt, interuallo minori quolibet dato: </s>
            <s xml:id="echoid-s8457" xml:space="preserve">Nam in locum ab hyperbole
              <lb/>
            B A C, & </s>
            <s xml:id="echoid-s8458" xml:space="preserve">asymptoto M N contentum extenditur altera hyperbole E D F; </s>
            <s xml:id="echoid-s8459" xml:space="preserve">ſed
              <lb/>
            diſtantia hyperbolæ B A C ab asymptoto M N efficitur minor qualibet data: </s>
            <s xml:id="echoid-s8460" xml:space="preserve">igi-
              <lb/>
            tur diſtantia hyperbolæ D G F compræhenſæ ab hyperbole intercipiente minor erit
              <lb/>
            qualibet data diſtantia.</s>
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