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="221" file="0259" n="259" rhead="Conicor. Lib. VI."/>
            Manifeſtum eſt interceptas I H, F B, G D eſſe minimas linearum rectarum,
              <lb/>
            quæ à punctis I, F, G ad ſectionem B D duci poßunt; </s>
            <s xml:id="echoid-s8317" xml:space="preserve">& </s>
            <s xml:id="echoid-s8318" xml:space="preserve">ideo eædem interce-
              <lb/>
              <note position="right" xlink:label="note-0259-01" xlink:href="note-0259-01a" xml:space="preserve">38. lib. 5.</note>
            ptæ erunt diſtantiæ quorunlibet punctorum ſectionis I F G à ſectione B D: </s>
            <s xml:id="echoid-s8319" xml:space="preserve">& </s>
            <s xml:id="echoid-s8320" xml:space="preserve">
              <lb/>
            propterea erunt diſtantiæ prædictarum curuarum. </s>
            <s xml:id="echoid-s8321" xml:space="preserve">Oſtendendum modo eſt H I
              <lb/>
            maiorem eſſe, quàm B F, & </s>
            <s xml:id="echoid-s8322" xml:space="preserve">B F maiorem, quàm D G, & </s>
            <s xml:id="echoid-s8323" xml:space="preserve">ſic ſemper. </s>
            <s xml:id="echoid-s8324" xml:space="preserve">Duca-
              <lb/>
            tur à puncto F intercepta recta linea F M parallela axi I H, atque à puncto G
              <lb/>
            ducatur recta linea G N parallela ipſi F B, quæ occurrant ſectioni B D in M,
              <lb/>
            N. </s>
            <s xml:id="echoid-s8325" xml:space="preserve">Et quoniam F M æquidiſtat vertices coniungenti I H, erit intercepta F M
              <lb/>
              <note position="right" xlink:label="note-0259-02" xlink:href="note-0259-02a" xml:space="preserve">5. aiddit.
                <lb/>
              huus.
                <lb/>
              38. lib. 5.</note>
            æqualis I H, ſed cum ramus B A ſit breuiſſimus, & </s>
            <s xml:id="echoid-s8326" xml:space="preserve">eius portio F B erit quoque
              <lb/>
            breuiſſima omnium, quæ ex puncto F ad eandem ſectionem B H duci poſſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s8327" xml:space="preserve">quare B F minor erit quàm F M, & </s>
            <s xml:id="echoid-s8328" xml:space="preserve">F M oſtenſa fuit æqualis I H; </s>
            <s xml:id="echoid-s8329" xml:space="preserve">igitur di-
              <lb/>
            ſtantia intercepta F B minor erit quàm I H.</s>
            <s xml:id="echoid-s8330" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8331" xml:space="preserve">Secundò quia duæ interceptæ B F, N G parallelæ inter ſe productæ occurrunt
              <lb/>
            axi intra ſectiones ad partes A C, & </s>
            <s xml:id="echoid-s8332" xml:space="preserve">in parabola, quàm ſecabunt in binis pun-
              <lb/>
              <note position="right" xlink:label="note-0259-03" xlink:href="note-0259-03a" xml:space="preserve">27. lib. 1.</note>
            ctis, erunt ſaltem ordinatim applicatæ ad aliquàm diametrum: </s>
            <s xml:id="echoid-s8333" xml:space="preserve">in byperbolis verò
              <lb/>
              <figure xlink:label="fig-0259-01" xlink:href="fig-0259-01a" number="303">
                <image file="0259-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0259-01"/>
              </figure>
            parallelæ erunt rectæ lineæ diuidenti angulum P E K à recta linea E K centra
              <lb/>
            coniungente, & </s>
            <s xml:id="echoid-s8334" xml:space="preserve">E P interiore asymptoto contentum; </s>
            <s xml:id="echoid-s8335" xml:space="preserve">propterea tam in parabo-
              <lb/>
              <note position="right" xlink:label="note-0259-04" xlink:href="note-0259-04a" xml:space="preserve">3. & 4.
                <lb/>
              addit.</note>
            lis, quàm in hyperbolis intercepta B F, quæ vlterius tendit ad partes reliquæ
              <lb/>
            asymptoti E O maior erit intercepta N G; </s>
            <s xml:id="echoid-s8336" xml:space="preserve">ſed quia G D eſt linea breuiſſima om-
              <lb/>
              <note position="right" xlink:label="note-0259-05" xlink:href="note-0259-05a" xml:space="preserve">38. lib. 5.</note>
            nium, quæ ad ſectienem H D duci poſſunt, cum ſit portio breuiſſimæ D C, quæ
              <lb/>
            perpendicularis eſt ad rectam contingentem in D, igitur G D minor erit,
              <lb/>
            quàm G N; </s>
            <s xml:id="echoid-s8337" xml:space="preserve">eſtque G N oſtenſa minor, quàm F B; </s>
            <s xml:id="echoid-s8338" xml:space="preserve">ergo G D minor erit, quàm
              <lb/>
            F B.</s>
            <s xml:id="echoid-s8339" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8340" xml:space="preserve">In parabolis autem, quia duci poteſt aliqua recta linea, vt N G parallela
              <lb/>
            cuilibet interceptæ B F; </s>
            <s xml:id="echoid-s8341" xml:space="preserve">itaut ſit N G minor quacunque recta linea data (quan-
              <lb/>
              <note position="right" xlink:label="note-0259-06" xlink:href="note-0259-06a" xml:space="preserve">Prop. 4.
                <lb/>
              addit.</note>
            do nimirum ad aliquam diametrum ordinatim ſunt applicatæ, ſcilicet, quando
              <lb/>
            vna ipſarum, puta B F occurrat axi intra ſectiones; </s>
            <s xml:id="echoid-s8342" xml:space="preserve">quod quidem neceſſario
              <lb/>
              <note position="right" xlink:label="note-0259-07" xlink:href="note-0259-07a" xml:space="preserve">27. lib. 1.</note>
            eueniet, quando B A eſt ramus breuiſſimus) eſtque ramus breuiſſimus D G </s>
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