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="105" file="0143" n="143" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div395" type="section" level="1" n="123">
          <head xml:id="echoid-head166" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s4248" xml:space="preserve">HInc conſtat, ſupremam circuli peripheriam A Z cadere in locum à tan-
              <lb/>
            gente X A, & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">coniſectionem B A contentum, infimam vero circuferen-
              <lb/>
            tiam A γ cadere ne dum infra tangentem, ſed etiam infra coniſectionem A G;
              <lb/>
            </s>
            <s xml:id="echoid-s4250" xml:space="preserve">eoquod recta A X cadit extra circuli peripheriam A Z, quàm contingit in A,
              <lb/>
            & </s>
            <s xml:id="echoid-s4251" xml:space="preserve">eadem circumferentia A Z cadit extra ſectionem A B, quàm ſecat in A, vt
              <lb/>
            dictum eſt.</s>
            <s xml:id="echoid-s4252" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4253" xml:space="preserve">Mirabile quidem hoc videri poterit aliquibus, qui contingentiæ angulos, quos
              <lb/>
            vocant, verè angulos eſſe cenſent; </s>
            <s xml:id="echoid-s4254" xml:space="preserve">nam hic duæ circumſerentiæ curuæ, conica
              <lb/>
            nimirum B A G, & </s>
            <s xml:id="echoid-s4255" xml:space="preserve">circularis Z A γ ſe mutuo ſecant in A, & </s>
            <s xml:id="echoid-s4256" xml:space="preserve">tamen ambo
              <lb/>
            tanguntur ab eadẽ recta linea A X in eodem puncto A, in quo illæ ſe mutuò ſecant.
              <lb/>
            </s>
            <s xml:id="echoid-s4257" xml:space="preserve">Vnde colligent etiam, quod anguli contingentiæ facti à coniſectione B A G, & </s>
            <s xml:id="echoid-s4258" xml:space="preserve">
              <lb/>
            recta linea X A non ſunt æquales inter ſe, quando punctum A in vertice axis
              <lb/>
            non exiſtit; </s>
            <s xml:id="echoid-s4259" xml:space="preserve">nam duo anguli contingentiæ circumſerentiæ circularis, & </s>
            <s xml:id="echoid-s4260" xml:space="preserve">rectæ
              <lb/>
            tangentis X A æquales ſunt inter ſe: </s>
            <s xml:id="echoid-s4261" xml:space="preserve">at angulus contingentiæ ſectionis conicæ ſu-
              <lb/>
            premus reſpiciens verticem B maior eſt angulo contingentiæ circularis, vt dictũ
              <lb/>
            eſt: </s>
            <s xml:id="echoid-s4262" xml:space="preserve">infimus vero angulus contingentiæ à ſectione conica, & </s>
            <s xml:id="echoid-s4263" xml:space="preserve">eadem tangente
              <lb/>
            contentus minor eſt eodem angulo contingentiæ circularis, & </s>
            <s xml:id="echoid-s4264" xml:space="preserve">propterea ſupremus
              <lb/>
            angnlus contingentiæ ſectionis conicæ maior erit inferiori.</s>
            <s xml:id="echoid-s4265" xml:space="preserve"/>
          </p>
          <figure number="129">
            <image file="0143-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0143-01"/>
          </figure>
          <p style="it">
            <s xml:id="echoid-s4266" xml:space="preserve">Sit perpendicularis D E
              <lb/>
              <note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">PROP.
                <lb/>
              II.
                <lb/>
              Addit.
                <lb/>
              Ex 51. 52.
                <lb/>
              53. huius.</note>
            minor trutina L, ſintque D
              <lb/>
            A, & </s>
            <s xml:id="echoid-s4267" xml:space="preserve">D C duo illi rami,
              <lb/>
            qui tantummodo breuiſecantes
              <lb/>
            eſſe poſſunt omnium ramorum
              <lb/>
            ex concurſu D ad ſectionem
              <lb/>
            B C cadentium; </s>
            <s xml:id="echoid-s4268" xml:space="preserve">atque cen-
              <lb/>
            tro D, interuallo D A deſcri-
              <lb/>
            batur circulus Z A γ; </s>
            <s xml:id="echoid-s4269" xml:space="preserve">pari-
              <lb/>
            terque centro D, interuallo D
              <lb/>
            C deſcribatur circulus O C Q;
              <lb/>
            </s>
            <s xml:id="echoid-s4270" xml:space="preserve">ducanturque rectæ X P, M
              <lb/>
            P contingentes coniſectionem
              <lb/>
            in A, & </s>
            <s xml:id="echoid-s4271" xml:space="preserve">C. </s>
            <s xml:id="echoid-s4272" xml:space="preserve">Dico, circulũ
              <lb/>
            Z A γ contingere coniſectio-
              <lb/>
            nem in A, & </s>
            <s xml:id="echoid-s4273" xml:space="preserve">extra ipſam
              <lb/>
            cadere, at circulum O C Q contingere eandem coniſectionem in C, & </s>
            <s xml:id="echoid-s4274" xml:space="preserve">
              <lb/>
            intra ipſam cadere.</s>
            <s xml:id="echoid-s4275" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4276" xml:space="preserve">Ducantur quilibet rami D F, D G ſupra, & </s>
            <s xml:id="echoid-s4277" xml:space="preserve">infra breuiſecantem D A, ſe-
              <lb/>
            cantes circulum Z A γ in Z, & </s>
            <s xml:id="echoid-s4278" xml:space="preserve">γ; </s>
            <s xml:id="echoid-s4279" xml:space="preserve">pariterque ducantur quilibet rami D </s>
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