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-div614" type="section" level="1" n="205">
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            <s xml:id="echoid-s6482" xml:space="preserve">
              <pb o="168" file="0206" n="206" rhead="Apollonij Pergæi"/>
            natim ad axium applicatæ, numero pares, quæ ad abſciſſas ſint proportionales,
              <lb/>
            tum abſcißæ inter ſe: </s>
            <s xml:id="echoid-s6483" xml:space="preserve">V nde ſequitur poſtrema concluſio, quæ in textu habetur,
              <lb/>
            quod nimirum rectangulum a L B ad rectangulum a K B eandem proportionem
              <lb/>
            habeat, quàm abſciſſa, L B ad abſciſſam K B: </s>
            <s xml:id="echoid-s6484" xml:space="preserve">ſed quotieſcunque duo rectangu-
              <lb/>
            la eandem proportionem habent, quàm baſes, illa ſunt æque alta: </s>
            <s xml:id="echoid-s6485" xml:space="preserve">igitur altitu-
              <lb/>
            dines a L, & </s>
            <s xml:id="echoid-s6486" xml:space="preserve">a K æquales ſunt inter ſe, pars, & </s>
            <s xml:id="echoid-s6487" xml:space="preserve">totum: </s>
            <s xml:id="echoid-s6488" xml:space="preserve">quod eſt absurdum.</s>
            <s xml:id="echoid-s6489" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div617" type="section" level="1" n="206">
          <head xml:id="echoid-head260" xml:space="preserve">Notæ in Propoſit. XIV.</head>
          <p style="it">
            <s xml:id="echoid-s6490" xml:space="preserve">ALioquin ſequitur, quod quadratum R L ad quadratum K P, &</s>
            <s xml:id="echoid-s6491" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6492" xml:space="preserve">In
              <lb/>
              <note position="right" xlink:label="note-0206-01" xlink:href="note-0206-01a" xml:space="preserve">a</note>
            propoſitione deficit expoſitio, quæ talis eſt. </s>
            <s xml:id="echoid-s6493" xml:space="preserve">Sit A B quælibet hyperbolc,
              <lb/>
            & </s>
            <s xml:id="echoid-s6494" xml:space="preserve">E F quælibet ellipſis. </s>
            <s xml:id="echoid-s6495" xml:space="preserve">Dico A B ipſi E
              <lb/>
              <figure xlink:label="fig-0206-01" xlink:href="fig-0206-01a" number="226">
                <image file="0206-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0206-01"/>
              </figure>
            F ſimilem non eße. </s>
            <s xml:id="echoid-s6496" xml:space="preserve">Sint eorum axes late-
              <lb/>
            ra tranſuerſa, & </s>
            <s xml:id="echoid-s6497" xml:space="preserve">recta eadem, quæ in præ-
              <lb/>
            cedenti propoſitione poſita ſunt. </s>
            <s xml:id="echoid-s6498" xml:space="preserve">Et ſiqui-
              <lb/>
            dem ſectiones A B, & </s>
            <s xml:id="echoid-s6499" xml:space="preserve">E F ſimiles credan-
              <lb/>
            tur, neceßario ex definitione ſecunda, duci
              <lb/>
            poterunt ad axes ordinatim applicatæ nu-
              <lb/>
            mero pares proportionales abſciſſis, tum
              <lb/>
            abſciſſæ inter ſe proportionales: </s>
            <s xml:id="echoid-s6500" xml:space="preserve">& </s>
            <s xml:id="echoid-s6501" xml:space="preserve">vt in
              <lb/>
            præcedenti propoſitione oſtenſum eſt, qua-
              <lb/>
            dratum R L ad quadratum P K, ſcilicet
              <lb/>
            rectangulum a L B ad rectangulum a K B in hyperbola eandem proportionem
              <lb/>
              <note position="left" xlink:label="note-0206-02" xlink:href="note-0206-02a" xml:space="preserve">21. lib. 1.</note>
            habebit, quàm quadratum γ N ad quadratum V M, ſeu quàm rectangulum b
              <lb/>
              <note position="left" xlink:label="note-0206-03" xlink:href="note-0206-03a" xml:space="preserve">Ibidem.</note>
            N F ad rectangulum b M F in ellipſi, ergo rectangulum a L B ad rectangulum
              <lb/>
            a K B eandem proportionem habet, quàm rectangulum b N F ad rectangulum
              <lb/>
            b M F: </s>
            <s xml:id="echoid-s6502" xml:space="preserve">ſed eorundem rectangulorum baſes proportionales ſunt, eo quod L B ad
              <lb/>
            B K erat vt N F ad F M; </s>
            <s xml:id="echoid-s6503" xml:space="preserve">igitur eorundem altitudines proportionales erunt,
              <lb/>
            ſcilicet a L ad a K eandem proportionem habebit, quàm b N ad b M, ſed in
              <lb/>
            hyperqola a L maior eſt, quàm a K; </s>
            <s xml:id="echoid-s6504" xml:space="preserve">in ellipſi verò contra b N minor eſt, quã
              <lb/>
            b M; </s>
            <s xml:id="echoid-s6505" xml:space="preserve">igitur maior a L ad minorem a K eandem proportionem habebit, quàm
              <lb/>
            minor b N ad maiorem b M. </s>
            <s xml:id="echoid-s6506" xml:space="preserve">Luod erat abſurdum.</s>
            <s xml:id="echoid-s6507" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div619" type="section" level="1" n="207">
          <head xml:id="echoid-head261" xml:space="preserve">SECTIO QVINTA</head>
          <head xml:id="echoid-head262" xml:space="preserve">Continens ſex Propoſitiones Præmiſſas,
            <lb/>
          PROPOSITIO I. II. III. IV. & V.</head>
          <p>
            <s xml:id="echoid-s6508" xml:space="preserve">SI in triangulis A B C, D E F in duobus circulorum ſeg-
              <lb/>
              <note position="right" xlink:label="note-0206-04" xlink:href="note-0206-04a" xml:space="preserve">I</note>
            mentis A T C, D G F deſcriptis, à duobus angulis B,
              <lb/>
            E, educantur duæ rectæ lineæ B T H, E G I efficientes cum
              <lb/>
            baſibus A C, D F duos angulos H, I æquales (incidentes </s>
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