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-div382" type="section" level="1" n="122">
          <p style="it">
            <s xml:id="echoid-s4202" xml:space="preserve">
              <pb o="104" file="0142" n="142" rhead="104 Apollonij Pergæi"/>
            nem: </s>
            <s xml:id="echoid-s4203" xml:space="preserve">Dico, quod circumpherentia Z γ ſecat tangentem rectam lineam
              <lb/>
            x A, & </s>
            <s xml:id="echoid-s4204" xml:space="preserve">coniſectionem B G in puncto A.</s>
            <s xml:id="echoid-s4205" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4206" xml:space="preserve">Quoniam perpendicularis D E ponitur ma-
              <lb/>
              <figure xlink:label="fig-0142-01" xlink:href="fig-0142-01a" number="127">
                <image file="0142-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-01"/>
              </figure>
            ior trutina L; </s>
            <s xml:id="echoid-s4207" xml:space="preserve">ergo quilibet ramus D A cadit
              <lb/>
              <note position="left" xlink:label="note-0142-01" xlink:href="note-0142-01a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            ſupra breuiſsimam ex puncto A ad axim B E
              <lb/>
            ductam: </s>
            <s xml:id="echoid-s4208" xml:space="preserve">efficit vero breuiſsima cum tangente
              <lb/>
            A x angulum rectum; </s>
            <s xml:id="echoid-s4209" xml:space="preserve">ergo angulus D A x eſt
              <lb/>
              <note position="left" xlink:label="note-0142-02" xlink:href="note-0142-02a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            acutus; </s>
            <s xml:id="echoid-s4210" xml:space="preserve">& </s>
            <s xml:id="echoid-s4211" xml:space="preserve">propterea recta A x cadit intracir-
              <lb/>
            culum A Z; </s>
            <s xml:id="echoid-s4212" xml:space="preserve">ſed A x cadit extra coniſectio-
              <lb/>
              <note position="left" xlink:label="note-0142-03" xlink:href="note-0142-03a" xml:space="preserve">35. 36.
                <lb/>
              Lib. 1.</note>
            nem B A, quàm contingit; </s>
            <s xml:id="echoid-s4213" xml:space="preserve">ergo circumferen-
              <lb/>
            tia Z A cadit extra ſectionem B A, & </s>
            <s xml:id="echoid-s4214" xml:space="preserve">extra
              <lb/>
            tangentem A x: </s>
            <s xml:id="echoid-s4215" xml:space="preserve">poſtea ducatur quilibet ramus
              <lb/>
            D G infra ramum D A ſecans circumferentiã
              <lb/>
            circuli in r: </s>
            <s xml:id="echoid-s4216" xml:space="preserve">& </s>
            <s xml:id="echoid-s4217" xml:space="preserve">quia ramus D A propinquior
              <lb/>
            eſt vertici B, quàm D G, erit D A minor,
              <lb/>
              <note position="left" xlink:label="note-0142-04" xlink:href="note-0142-04a" xml:space="preserve">64. 65.
                <lb/>
              huius.</note>
            quàm D G; </s>
            <s xml:id="echoid-s4218" xml:space="preserve">eſtque D γ æqualis D A (cum ſint ambo radij eiuſdem circuli) ergo
              <lb/>
            D γ minor erit, quàm D G: </s>
            <s xml:id="echoid-s4219" xml:space="preserve">& </s>
            <s xml:id="echoid-s4220" xml:space="preserve">propterea quodlibet punctum γ peripheriæ cir-
              <lb/>
            cularis infra punctum A poſitum cadet intra coniſectionem B G; </s>
            <s xml:id="echoid-s4221" xml:space="preserve">& </s>
            <s xml:id="echoid-s4222" xml:space="preserve">ideo cir-
              <lb/>
            cumferentia Z A γ ſecat tangentẽ, & </s>
            <s xml:id="echoid-s4223" xml:space="preserve">coniſectionẽ in A, quod erat propoſitum.</s>
            <s xml:id="echoid-s4224" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4225" xml:space="preserve">Iſdem poſitis, ſit perpendicularis D E æqualis Trutinæ L, & </s>
            <s xml:id="echoid-s4226" xml:space="preserve">ſit D
              <lb/>
              <note position="left" xlink:label="note-0142-05" xlink:href="note-0142-05a" xml:space="preserve">PR. 10.
                <lb/>
              Addit.</note>
            A ſingularis ille ramus breuiſecans, qui ex concurſu D ad ſectionem
              <lb/>
            B G duci poteſt; </s>
            <s xml:id="echoid-s4227" xml:space="preserve">perficiaturque conſtructio, vt antea factum eſt; </s>
            <s xml:id="echoid-s4228" xml:space="preserve">Dico,
              <lb/>
              <note position="left" xlink:label="note-0142-06" xlink:href="note-0142-06a" xml:space="preserve">51. 52.
                <lb/>
              huius.</note>
            circulum Z A γ ſecare coniſectionem in A, & </s>
            <s xml:id="echoid-s4229" xml:space="preserve">contingere rectam Ax.</s>
            <s xml:id="echoid-s4230" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4231" xml:space="preserve">Ducatur quilibet ramus D F ſupra breuiſe-
              <lb/>
              <figure xlink:label="fig-0142-02" xlink:href="fig-0142-02a" number="128">
                <image file="0142-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0142-02"/>
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            cantem D A, ſecans circuli peripheriam in Z,
              <lb/>
            & </s>
            <s xml:id="echoid-s4232" xml:space="preserve">quilibet alius ramus D G infra D A ſecans
              <lb/>
            eandem peripheriam in γ. </s>
            <s xml:id="echoid-s4233" xml:space="preserve">Et quia ex con-
              <lb/>
            curſu D ad ſectionem B G vnicus tantum bre-
              <lb/>
              <note position="left" xlink:label="note-0142-07" xlink:href="note-0142-07a" xml:space="preserve">Ibidem.</note>
            uiſecans D A duci poteſt; </s>
            <s xml:id="echoid-s4234" xml:space="preserve">igitur ramus D F
              <lb/>
            propinquio
              <unsure/>
            r vertici B minor eſt remotiore D
              <lb/>
              <note position="left" xlink:label="note-0142-08" xlink:href="note-0142-08a" xml:space="preserve">67. huius.</note>
            A, & </s>
            <s xml:id="echoid-s4235" xml:space="preserve">D A propinquior vertici B minor eſt
              <lb/>
            remotiore D G: </s>
            <s xml:id="echoid-s4236" xml:space="preserve">ſuntque rectæ D Z, D γ æ-
              <lb/>
            quales eidem D A (cum ſint radij eiuſdem,
              <lb/>
            circuli) ergo D Z maior eſt, quàm D F, & </s>
            <s xml:id="echoid-s4237" xml:space="preserve">
              <lb/>
            D γ minor, quàm D G; </s>
            <s xml:id="echoid-s4238" xml:space="preserve">& </s>
            <s xml:id="echoid-s4239" xml:space="preserve">propterea quodli-
              <lb/>
            bet punctum Z circuli ſupra A ſumptum ca-
              <lb/>
            dit extra coniſectionem B F A, & </s>
            <s xml:id="echoid-s4240" xml:space="preserve">quodlibet
              <lb/>
            infimum punctum γ eiuſdem circuli cadit intra eandem coniſectionem A G;
              <lb/>
            </s>
            <s xml:id="echoid-s4241" xml:space="preserve">quapropter circumferentia circuli Z A γ ſecat coniſectionem B A G in A. </s>
            <s xml:id="echoid-s4242" xml:space="preserve">Po-
              <lb/>
            ſtea quia recta A x contingens ſectionem in A perpendicularis eſt ad breuiſe-
              <lb/>
            cantem D A, cum I A ſit breuiſsima; </s>
            <s xml:id="echoid-s4243" xml:space="preserve">igitur recta linea x A, quæ perpendicu-
              <lb/>
              <note position="left" xlink:label="note-0142-09" xlink:href="note-0142-09a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            laris eſt ad radium D A, continget circulum Z Y γ. </s>
            <s xml:id="echoid-s4244" xml:space="preserve">Quapropter circulus Z
              <lb/>
            A γ ſecant coniſectionem B A G in A, & </s>
            <s xml:id="echoid-s4245" xml:space="preserve">tangit eandem rectam lineam A x,
              <lb/>
            quàm contingit ſectio conica B A G, & </s>
            <s xml:id="echoid-s4246" xml:space="preserve">in eodem puncto A, quod erat oſtendendũ.</s>
            <s xml:id="echoid-s4247" xml:space="preserve"/>
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