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="108" file="0146" n="146" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s4335" xml:space="preserve">Sumpto
              <unsure/>
            in eadem ſi-
              <lb/>
              <figure xlink:label="fig-0146-01" xlink:href="fig-0146-01a" number="133">
                <image file="0146-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0146-01"/>
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            gura quolibet puncto g
              <lb/>
              <note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">11. Addit.</note>
            infra punctum D, quo-
              <lb/>
            niam circulus radio g A
              <lb/>
            deſcriptus contingit ex-
              <lb/>
            trinſecus coniſectionem
              <lb/>
            in A, nec vnquam ceſ-
              <lb/>
            ſabit prædictus cõtactus
              <lb/>
            extrinſecus, licet magis,
              <lb/>
            ac magis in infinitum,
              <lb/>
            punctum g ipſi D pro-
              <lb/>
            pinquior fiat, & </s>
            <s xml:id="echoid-s4336" xml:space="preserve">tunc de-
              <lb/>
            mu
              <unsure/>
            m ceſſat huiuſmodi
              <lb/>
            extrinſecus contactus,
              <lb/>
            quando deſcribitur cir-
              <lb/>
            culus radio D A, qui
              <lb/>
            quidem ſectionem ſecat
              <lb/>
            in A, vt dictũ eſt; </s>
            <s xml:id="echoid-s4337" xml:space="preserve">qua-
              <lb/>
            propter minimus omniũ
              <lb/>
            extrinſecus ſectionem,
              <lb/>
            tangentium in A aſsignari nequit. </s>
            <s xml:id="echoid-s4338" xml:space="preserve">Quodvero extrinſecus tangentium eandem
              <lb/>
            ſectionem in vertice axis B non poſsit aſsignari minimus, patet; </s>
            <s xml:id="echoid-s4339" xml:space="preserve">nam omnes
              <lb/>
            circuli, quorum radij maiores ſunt ſemierecto ſectionis, eam extrinſecus tan-
              <lb/>
              <note position="left" xlink:label="note-0146-02" xlink:href="note-0146-02a" xml:space="preserve">Maurol. 4.
                <lb/>
              7. & 10.
                <lb/>
              lib. 5.
                <lb/>
              Conic.</note>
            gunt; </s>
            <s xml:id="echoid-s4340" xml:space="preserve">& </s>
            <s xml:id="echoid-s4341" xml:space="preserve">tunc demum eiuſmodi contactus extrinſecus ceſſat, quando radius cir-
              <lb/>
            culi æqualis efſicitur ſemierecto: </s>
            <s xml:id="echoid-s4342" xml:space="preserve">at tunc intrinſecus ſectionem tangit; </s>
            <s xml:id="echoid-s4343" xml:space="preserve">quapro-
              <lb/>
            pter reperiri non poteſt minimus circulorum coniſectionem extrinſecus tangenti-
              <lb/>
            um: </s>
            <s xml:id="echoid-s4344" xml:space="preserve">quod erat oſtendendum.</s>
            <s xml:id="echoid-s4345" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4346" xml:space="preserve">Ex dictis colligitur, quod ex concurſu ad quamlibet coniſectionem poßunt du-
              <lb/>
            ci tres, vel quatuor ramiſecantes inter ſe æquales: </s>
            <s xml:id="echoid-s4347" xml:space="preserve">in ellipſi vero, & </s>
            <s xml:id="echoid-s4348" xml:space="preserve">in reliquis
              <lb/>
            ſectionibus ſi rami ſecantes non fuerint, duci poteſt vnus, vel duo rami inter
              <lb/>
            ſe æquales.</s>
            <s xml:id="echoid-s4349" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4350" xml:space="preserve">Nam circulus radio alicuius breuiſecantis deſcriptus tangit, vel ſecat coni-
              <lb/>
            ſectionem, & </s>
            <s xml:id="echoid-s4351" xml:space="preserve">ſiquidem eam extrinſecus tangit, neceſſario eandem bis ſecat, ſi
              <lb/>
            fuerit parabole, aut hyperbole, quæ infinitè augẽtur, & </s>
            <s xml:id="echoid-s4352" xml:space="preserve">dilatãtur; </s>
            <s xml:id="echoid-s4353" xml:space="preserve">& </s>
            <s xml:id="echoid-s4354" xml:space="preserve">propterea
              <lb/>
            radij circuli ad occurſus, & </s>
            <s xml:id="echoid-s4355" xml:space="preserve">contactum ducti æquales ſunt interſe; </s>
            <s xml:id="echoid-s4356" xml:space="preserve">& </s>
            <s xml:id="echoid-s4357" xml:space="preserve">ideo tres
              <lb/>
            rami tantum erunt æquales: </s>
            <s xml:id="echoid-s4358" xml:space="preserve">ſi vero deſcribatur circulus, cuius centrum eſt con-
              <lb/>
            curſus, radius vero minor eſt maximo, & </s>
            <s xml:id="echoid-s4359" xml:space="preserve">maior minimo duorum breuiſecan-
              <lb/>
            tium: </s>
            <s xml:id="echoid-s4360" xml:space="preserve">tunc quidem neceſſario circulus quatuor in punctis ſectioni conicæ occur-
              <lb/>
            ret: </s>
            <s xml:id="echoid-s4361" xml:space="preserve">& </s>
            <s xml:id="echoid-s4362" xml:space="preserve">propterea quatuor radij ad occurſus ducti erunt inter ſe æquales.</s>
            <s xml:id="echoid-s4363" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4364" xml:space="preserve">At in ellipſi ſi concurſus ſiat circuli centrum, radius vero breuiſecans maxi-
              <lb/>
            mus trium, qui in ea duci puſſunt, circulus prædicto radio deſcriptus continget
              <lb/>
            quidem exterius ellipſim, neque deinceps vnquam ei occurret: </s>
            <s xml:id="echoid-s4365" xml:space="preserve">& </s>
            <s xml:id="echoid-s4366" xml:space="preserve">propterea ra-
              <lb/>
            mus ille maximus erit vnicus, cum nullus alius ei æqualis duci poſsit in eadem
              <lb/>
            ellipſi: </s>
            <s xml:id="echoid-s4367" xml:space="preserve">ſi verò à concurſu in productione axis ellipſis poſito deſcribatur circulus,
              <lb/>
            cuius radius minor ſit maximo ramo, ſed maior vtroque terminato; </s>
            <s xml:id="echoid-s4368" xml:space="preserve">tunc qui-
              <lb/>
            dem circulus duobus in locis ellipſi occurret; </s>
            <s xml:id="echoid-s4369" xml:space="preserve">& </s>
            <s xml:id="echoid-s4370" xml:space="preserve">propterea duo tantum rami inter
              <lb/>
            ſe æquales erunt; </s>
            <s xml:id="echoid-s4371" xml:space="preserve">pari modo, quando à concurſu tres breuiſecantes ad </s>
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