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-div814" type="section" level="1" n="248">
          <p style="it">
            <s xml:id="echoid-s9823" xml:space="preserve">
              <pb o="261" file="0299" n="299" rhead="Conicor. Lib. VI."/>
            recta linea H R parallela eſt ipſi A S; </s>
            <s xml:id="echoid-s9824" xml:space="preserve">& </s>
            <s xml:id="echoid-s9825" xml:space="preserve">erat prius Q S parallela ipſi C R,
              <lb/>
            & </s>
            <s xml:id="echoid-s9826" xml:space="preserve">recta linea C P Q eſt communis; </s>
            <s xml:id="echoid-s9827" xml:space="preserve">igitur triangula C R Q, & </s>
            <s xml:id="echoid-s9828" xml:space="preserve">Q S P ſimi-
              <lb/>
            lia ſunt, & </s>
            <s xml:id="echoid-s9829" xml:space="preserve">ſpatium R S parallelogrammum eſt; </s>
            <s xml:id="echoid-s9830" xml:space="preserve">eritque vt prius dictum eſt
              <lb/>
            proportio quadrati Q S ad rectangulum A S P eadem proportioni rectangnli C
              <lb/>
            R A ad quadratum R Q; </s>
            <s xml:id="echoid-s9831" xml:space="preserve">eſt vero quadratum Q S ad rectangulum A S P, vt
              <lb/>
            ellipſis axis tranſuerſus C A ad eius latus rectùm A D, propterea quod conus
              <lb/>
            A Q P ſupponitur continere ellipſim A B C; </s>
            <s xml:id="echoid-s9832" xml:space="preserve">igitur rectangulum C R A ad qua-
              <lb/>
            dratum R Q eandem proportionem habet, quàm C A ad A D; </s>
            <s xml:id="echoid-s9833" xml:space="preserve">eſt verò rectan-
              <lb/>
            gulum H R Q æquale rectangulo C R A; </s>
            <s xml:id="echoid-s9834" xml:space="preserve">igitur rectangulum H R Q ad qua-
              <lb/>
            dratum R Q ſeu H R ad R Q eandem proportionem habebit, quàm C A ad A
              <lb/>
            D; </s>
            <s xml:id="echoid-s9835" xml:space="preserve">ſed in priori caſu facta eſt H I ad I K in eadem proportione, quàm C A
              <lb/>
            ad A D; </s>
            <s xml:id="echoid-s9836" xml:space="preserve">igitur H R ad R Q eandem proportionem habebit quàm H I ad I K.</s>
            <s xml:id="echoid-s9837" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9838" xml:space="preserve">Ergo diuidendo H K maior ad minorem K I erit vt minor H Q ad ma-
              <lb/>
              <note position="left" xlink:label="note-0299-01" xlink:href="note-0299-01a" xml:space="preserve">e</note>
            iorem Q R, &</s>
            <s xml:id="echoid-s9839" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9840" xml:space="preserve">Ideſt quia H R ad R Q eſt vt H I ad I K, & </s>
            <s xml:id="echoid-s9841" xml:space="preserve">diuiden-
              <lb/>
            do H Q ad Q R eandem proportionem habebit quàm H K ad K I, & </s>
            <s xml:id="echoid-s9842" xml:space="preserve">permu-
              <lb/>
            tando H Q ad H K erit vt Q R ad K I: </s>
            <s xml:id="echoid-s9843" xml:space="preserve">quod eſt abſurdum; </s>
            <s xml:id="echoid-s9844" xml:space="preserve">quandoquidem
              <lb/>
            in circulo ſubtenſa H Q à centro remotior minor eſt, quàm H K, at exterius
              <lb/>
            comprehenſa Q R maior eſt, quàm K I. </s>
            <s xml:id="echoid-s9845" xml:space="preserve">Quapropter fieri non poteſt, vt ali-
              <lb/>
            quis alius conus A Q P præter iam dictos contineat ellipſim A B C, & </s>
            <s xml:id="echoid-s9846" xml:space="preserve">ſit ſi-
              <lb/>
            milis dato cono E F G. </s>
            <s xml:id="echoid-s9847" xml:space="preserve">Textus ergo confuſus corrigi debebat.</s>
            <s xml:id="echoid-s9848" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9849" xml:space="preserve">Ad propoſitionem 77. </s>
            <s xml:id="echoid-s9850" xml:space="preserve">libri quinti egi de
              <lb/>
              <figure xlink:label="fig-0299-01" xlink:href="fig-0299-01a" number="346">
                <image file="0299-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0299-01"/>
              </figure>
            contactibus circulorum, & </s>
            <s xml:id="echoid-s9851" xml:space="preserve">ſectionum coni-
              <lb/>
            carum, eorumque admirabilia ſymptomata à
              <lb/>
            nemine adhuc quod ſciam excogitata patefeci,
              <lb/>
            non tamen prædicta diſceptatio omnino perfe-
              <lb/>
            cta, & </s>
            <s xml:id="echoid-s9852" xml:space="preserve">abſoluta fuit: </s>
            <s xml:id="echoid-s9853" xml:space="preserve">itaque iuxta loci exigen-
              <lb/>
            tiam hic afferam coronidis loco eiuſdem doctri-
              <lb/>
            næ complementum.</s>
            <s xml:id="echoid-s9854" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9855" xml:space="preserve">Per rectam lineam coniungentem ver-
              <lb/>
              <note position="right" xlink:label="note-0299-02" xlink:href="note-0299-02a" xml:space="preserve">PROP.
                <lb/>
              15.
                <lb/>
              Addit.</note>
            tices duorum conorum eandem baſim ha-
              <lb/>
            bentium ducere duo plana vtrumque co-
              <lb/>
            num tangentia: </s>
            <s xml:id="echoid-s9856" xml:space="preserve">oportet autem rectam li-
              <lb/>
            neam vertices coniungentem extra peri-
              <lb/>
            pheriam circuli communis baſis cadere.</s>
            <s xml:id="echoid-s9857" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s9858" xml:space="preserve">Circulus A M C ſit communis baſis duorum
              <lb/>
            conorum, quorum vertices B, & </s>
            <s xml:id="echoid-s9859" xml:space="preserve">E, & </s>
            <s xml:id="echoid-s9860" xml:space="preserve">co-
              <lb/>
            niuncta recta linea B E extra peripheriam
              <lb/>
            circuli A M C cadat: </s>
            <s xml:id="echoid-s9861" xml:space="preserve">duci debent duo plana
              <lb/>
            tangentia vtroſque conos per eandem rectam
              <lb/>
            lineam B E extenſa. </s>
            <s xml:id="echoid-s9862" xml:space="preserve">Et primo recta linea
              <lb/>
            E B plano circuli A M C æquidiſtet, & </s>
            <s xml:id="echoid-s9863" xml:space="preserve">ducto
              <lb/>
            quolibet plano per E B circulum ſecante in
              <lb/>
            recta linea N O erit ipſa N O pirallela E B;
              <lb/>
            </s>
            <s xml:id="echoid-s9864" xml:space="preserve">tunc ducatur diameter A M perpendicularis
              <lb/>
            ad N O, & </s>
            <s xml:id="echoid-s9865" xml:space="preserve">per A, & </s>
            <s xml:id="echoid-s9866" xml:space="preserve">M ducantur A D, M
              <lb/>
            V tangentes circulum, ſiue perpendiculares </s>
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