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-div770" type="section" level="1" n="239">
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              <pb o="242" file="0280" n="280" rhead="Apollonij Pergæi"/>
            contentum, habet eandẽ rationem, quam
              <lb/>
              <figure xlink:label="fig-0280-01" xlink:href="fig-0280-01a" number="326">
                <image file="0280-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0280-01"/>
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            G E ad H B, ſufficienter deducitur, quod
              <lb/>
            G E ſit latus rectum tàm parabolæ L H
              <lb/>
              <note position="left" xlink:label="note-0280-01" xlink:href="note-0280-01a" xml:space="preserve">11. lib. 1.</note>
            K, quàm D E; </s>
            <s xml:id="echoid-s9061" xml:space="preserve">& </s>
            <s xml:id="echoid-s9062" xml:space="preserve">ideo erit parabole L
              <lb/>
              <note position="left" xlink:label="note-0280-02" xlink:href="note-0280-02a" xml:space="preserve">Propoſ. 1.
                <lb/>
              huius.</note>
            H æqualis D E. </s>
            <s xml:id="echoid-s9063" xml:space="preserve">Non igitur neceſſe eſt,
              <lb/>
            vt rectangula ſub abſciſſis, & </s>
            <s xml:id="echoid-s9064" xml:space="preserve">lateribus
              <lb/>
            rectis æqualibus oſtendãtur æqualia inter
              <lb/>
            ſe, & </s>
            <s xml:id="echoid-s9065" xml:space="preserve">inde eliciatur æqualitas, & </s>
            <s xml:id="echoid-s9066" xml:space="preserve">con-
              <lb/>
            gruentia ſectionum. </s>
            <s xml:id="echoid-s9067" xml:space="preserve">Quapropter caſu il-
              <lb/>
            la verba in Codice Arabico irrepſiße.
              <lb/>
            </s>
            <s xml:id="echoid-s9068" xml:space="preserve">puto.</s>
            <s xml:id="echoid-s9069" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9070" xml:space="preserve">Et dico, quod non reperiatur in.
              <lb/>
            </s>
            <s xml:id="echoid-s9071" xml:space="preserve">ſectione A B C alia ſectio parabolica; </s>
            <s xml:id="echoid-s9072" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0280-03" xlink:href="note-0280-03a" xml:space="preserve">b</note>
            quia ſi reperiretur, &</s>
            <s xml:id="echoid-s9073" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9074" xml:space="preserve">Verba, quæ in hoc textu addidi ex ſerie demonſtra-
              <lb/>
            tionis facile colliguntur: </s>
            <s xml:id="echoid-s9075" xml:space="preserve">Sed animaduertendum eſt, quod ne dum in cono recto,
              <lb/>
            ſed in quolibet cono ſcaleno quomodolibet per axim ſecetur triangulo A B C, de-
              <lb/>
            ſignari poteſt in eius ſuper ficie parabole æqualis datæ D E.</s>
            <s xml:id="echoid-s9076" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9077" xml:space="preserve">Ducatur C P contingens circulum baſis in C, & </s>
            <s xml:id="echoid-s9078" xml:space="preserve">in parabola D E ducatur
              <lb/>
            diameter E F, & </s>
            <s xml:id="echoid-s9079" xml:space="preserve">contingens verticalis, quæ contineat angulum F E G æqua-
              <lb/>
              <note position="left" xlink:label="note-0280-04" xlink:href="note-0280-04a" xml:space="preserve">51. lib. 2.</note>
            lem angulo B C P; </s>
            <s xml:id="echoid-s9080" xml:space="preserve">ſitque G E latus rectum diametri F E; </s>
            <s xml:id="echoid-s9081" xml:space="preserve">atque vt quadratum
              <lb/>
            C A ad rectangulum C B A, ita fiat G E ad H B, & </s>
            <s xml:id="echoid-s9082" xml:space="preserve">per H extendatur pla-
              <lb/>
            num L H K æquidiſtans plano per B C P ducto. </s>
            <s xml:id="echoid-s9083" xml:space="preserve">Dico ſectionem L H K eße pa-
              <lb/>
            rabolen quæſitam. </s>
            <s xml:id="echoid-s9084" xml:space="preserve">Quia plana æquidiſtantia L H K, & </s>
            <s xml:id="echoid-s9085" xml:space="preserve">B C P efficiunt in cir-
              <lb/>
            culo baſis rectas P C, L K inter ſe parallelas, & </s>
            <s xml:id="echoid-s9086" xml:space="preserve">in plano A B C efficiunt re-
              <lb/>
            ctas H I, B C inter ſe parallelas; </s>
            <s xml:id="echoid-s9087" xml:space="preserve">ergo anguli B C P, & </s>
            <s xml:id="echoid-s9088" xml:space="preserve">H I L æquales ſunt,
              <lb/>
            ſed in parabola D E diameter E F eſſicit cum ordinatis ad eam applicatis angulos
              <lb/>
            æquales F E G, ſcilicet ei, qui cum tangente verticali conſtituit, ſeu angulo B C
              <lb/>
              <note position="left" xlink:label="note-0280-05" xlink:href="note-0280-05a" xml:space="preserve">Conu. 46.
                <lb/>
              lib. 1.</note>
            P; </s>
            <s xml:id="echoid-s9089" xml:space="preserve">ergo duarum ſectionum L H K, & </s>
            <s xml:id="echoid-s9090" xml:space="preserve">D E, diametri H I, & </s>
            <s xml:id="echoid-s9091" xml:space="preserve">E F æque ſunt
              <lb/>
            inclinatæ ad ſuas baſes, cumquè latus rectum parabolæ L H K ad H B ſit, vt
              <lb/>
            quadratum C A ad rectangulum C B A, ſeu vt G E ad H B; </s>
            <s xml:id="echoid-s9092" xml:space="preserve">igitur duo late-
              <lb/>
            ra recta ſimilium diametrorum I H, & </s>
            <s xml:id="echoid-s9093" xml:space="preserve">F E ad H B eandem proportionem ha-
              <lb/>
            bent; </s>
            <s xml:id="echoid-s9094" xml:space="preserve">& </s>
            <s xml:id="echoid-s9095" xml:space="preserve">ideo æqualia ſunt inter ſe; </s>
            <s xml:id="echoid-s9096" xml:space="preserve">quare ſectiones ipſæ æquales, & </s>
            <s xml:id="echoid-s9097" xml:space="preserve">congruen-
              <lb/>
            tes erunt. </s>
            <s xml:id="echoid-s9098" xml:space="preserve">Quod erat oſtendendum.</s>
            <s xml:id="echoid-s9099" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">10. huius.</note>
          <p style="it">
            <s xml:id="echoid-s9100" xml:space="preserve">Multoties in eodem cono duæ parabolæ æquales ſnbcontrariæ duci poßunt,
              <lb/>
            vt Mydorgius demonſtrauit.</s>
            <s xml:id="echoid-s9101" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div774" type="section" level="1" n="240">
          <head xml:id="echoid-head301" xml:space="preserve">Notæ in Propoſit. XXVII.</head>
          <p style="it">
            <s xml:id="echoid-s9102" xml:space="preserve">DEinde ſit hyperbole, vt A B, & </s>
            <s xml:id="echoid-s9103" xml:space="preserve">axis illius C D, & </s>
            <s xml:id="echoid-s9104" xml:space="preserve">inclinatus B
              <lb/>
              <note position="right" xlink:label="note-0280-07" xlink:href="note-0280-07a" xml:space="preserve">a</note>
            D, & </s>
            <s xml:id="echoid-s9105" xml:space="preserve">erectus B E, ita vt non ſit proportio quadrati axis coni ad
              <lb/>
            quadratum dimidij diametri illius baſis, vt quadratum F G ad quadratum
              <lb/>
            G H, maior, quàm proportio figuræ ſectionis: </s>
            <s xml:id="echoid-s9106" xml:space="preserve">&</s>
            <s xml:id="echoid-s9107" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9108" xml:space="preserve">Senſus huius propoſi-
              <lb/>
            tionis hic erit. </s>
            <s xml:id="echoid-s9109" xml:space="preserve">In cono recto F H I, cuius triangulum per axim H F I repe-
              <lb/>
            rire ſectionem æqualem hyperbole datæ A B, cuius tranſuerſus axis D B, & </s>
            <s xml:id="echoid-s9110" xml:space="preserve">
              <lb/>
            latus rectum B E. </s>
            <s xml:id="echoid-s9111" xml:space="preserve">Oportet autem, vt quadratum F G axis dati coni ad qua-
              <lb/>
            dratum radij G H circuli baſis non habeant maiorem proportionem, quàm </s>
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