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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            <s xml:id="echoid-s8844" xml:space="preserve">
              <pb o="236" file="0274" n="274" rhead="Apollonij Pergæi"/>
            nuuntur quidem; </s>
            <s xml:id="echoid-s8845" xml:space="preserve">ſed non efficiuntur minora interuallo quo parallelæ asymptoti
              <lb/>
            diſtant inter ſe; </s>
            <s xml:id="echoid-s8846" xml:space="preserve">ex altera verò parte perueniri poteſt ad interuallum minus
              <lb/>
            quolibet dato. </s>
            <s xml:id="echoid-s8847" xml:space="preserve">Et hoc erat faciendum.</s>
            <s xml:id="echoid-s8848" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8849" xml:space="preserve">Data hyperbola eadem X præcedentis propoſitionis deſcribere duos ſi-
              <lb/>
              <note position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">PROP.
                <lb/>
              14. Add.</note>
            miles conos, vt idem planum in eis efficiat duas hyperbolas ſimiles da-
              <lb/>
            tæ ſectioni, quæ asymptoticæ ſint, & </s>
            <s xml:id="echoid-s8850" xml:space="preserve">ex vtraque parte ſibi ipſis vici-
              <lb/>
            niores fiant interuallo minori quolibet dato.</s>
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          <figure number="320">
            <image file="0274-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0274-01"/>
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            <s xml:id="echoid-s8852" xml:space="preserve">In quolibet plano fiat angulus A d G æqualis angulo inclinationis diametri,
              <lb/>
            & </s>
            <s xml:id="echoid-s8853" xml:space="preserve">baſis hyperbolæ datæ X, & </s>
            <s xml:id="echoid-s8854" xml:space="preserve">per G d extenſo quolibet alio plano, ducatur in
              <lb/>
            eo recta linea B d C perpendicularis ad G d O, & </s>
            <s xml:id="echoid-s8855" xml:space="preserve">ſumpto quolibet alio puncto
              <lb/>
            b in recta linea B C in plano per B G O extenſo, centris d, & </s>
            <s xml:id="echoid-s8856" xml:space="preserve">b, deſcribãtur
              <lb/>
            duo circuli inter ſe æquales G C O B, & </s>
            <s xml:id="echoid-s8857" xml:space="preserve">S Q P L ſe ſe ſecantes in duobus punctis
              <lb/>
            R, a: </s>
            <s xml:id="echoid-s8858" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s8859" xml:space="preserve">vt latus rectum ad tranſuerſum ſectionis datæ X, ita fiat quadratũ
              <lb/>
            G d ad quadratũ d A, & </s>
            <s xml:id="echoid-s8860" xml:space="preserve">ducatur recta linea A N M parallela ipſi B C, quæ ſecet
              <lb/>
            b N æquidiſtantẽ d A in N, & </s>
            <s xml:id="echoid-s8861" xml:space="preserve">coniungantur rectæ lineæ A B, A C, N L, N Q,
              <lb/>
            & </s>
            <s xml:id="echoid-s8862" xml:space="preserve">fiant A, & </s>
            <s xml:id="echoid-s8863" xml:space="preserve">N vertices duorũ conorũ A B C, N L Q, & </s>
            <s xml:id="echoid-s8864" xml:space="preserve">in eorũ ſuper ficiebus
              <lb/>
            planum M c T æquidiſtans planis A G O, & </s>
            <s xml:id="echoid-s8865" xml:space="preserve">N S P efficiat ſectiones H I K,
              <lb/>
            & </s>
            <s xml:id="echoid-s8866" xml:space="preserve">T V c, quarum diametri D V I genitæ à triangulis A B C, & </s>
            <s xml:id="echoid-s8867" xml:space="preserve">N L Q per
              <lb/>
            axes in eodem plano exiſbentibus ſunt æquidiſtantes axibus conorum A d, N b,
              <lb/>
            propter planorum æquidiſtantiam: </s>
            <s xml:id="echoid-s8868" xml:space="preserve">Dico, eas eſſe hyperbolas quæſitas. </s>
            <s xml:id="echoid-s8869" xml:space="preserve">Qnoniam
              <lb/>
            (propter æquidiſtantiam oppoſitarum linearum) eſt ſpatium A b parallelogram-
              <lb/>
            mum; </s>
            <s xml:id="echoid-s8870" xml:space="preserve">igitur conorum axes A d, N b æquales ſunt inter ſe, & </s>
            <s xml:id="echoid-s8871" xml:space="preserve">æquè inclinan-
              <lb/>
            tur ad communem rectam lineam B C Q (propter æquidiſtantiam earundem
              <lb/>
            A d, N b); </s>
            <s xml:id="echoid-s8872" xml:space="preserve">ſuntque æqualium circulorum radij d B, d C, b L, b Q æqua-
              <lb/>
            les inter ſe; </s>
            <s xml:id="echoid-s8873" xml:space="preserve">igitur triangula A B C, N L Q ſimilia ſunt inter ſe, & </s>
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