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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            <s xml:id="echoid-s4171" xml:space="preserve">
              <pb o="103" file="0141" n="141" rhead="Conicor. Lib. V."/>
            non ergo perpendicularis C F æqualis erit Trutinæ K, ſed priùs, neque maior
              <lb/>
            illa erat; </s>
            <s xml:id="echoid-s4172" xml:space="preserve">igitur perpendicularis C F neceſſario minor erit Trutina K; </s>
            <s xml:id="echoid-s4173" xml:space="preserve">quod
              <lb/>
            erat oſtendendum.</s>
            <s xml:id="echoid-s4174" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4175" xml:space="preserve">Iiſdem poſitis, ſi in productione breuiſsimæ A I ſumatur quodlibet
              <lb/>
              <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">PROP. 8.
                <lb/>
              Addit.</note>
            punctum C citra terminum D perpendicularis D E, à puncto C duci
              <lb/>
            poterit alter ramus breuiſecans ſupra C A incedens; </s>
            <s xml:id="echoid-s4176" xml:space="preserve">& </s>
            <s xml:id="echoid-s4177" xml:space="preserve">ſi punctum C
              <lb/>
            ſumatur vltra punctum D poterit ex C duci alter ramus breuiſecans
              <lb/>
            infra ipſum C A.</s>
            <s xml:id="echoid-s4178" xml:space="preserve"/>
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          <figure number="126">
            <image file="0141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0141-01"/>
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            <s xml:id="echoid-s4179" xml:space="preserve">Quoniam quælibet recta C F parallela perpendiculari D E interpoſita inter
              <lb/>
            productionem breuiſsimæ A I, & </s>
            <s xml:id="echoid-s4180" xml:space="preserve">axim minor eſt Trutina K nouæ menſuræ B
              <lb/>
            F (ex præcedenti propoſ.) </s>
            <s xml:id="echoid-s4181" xml:space="preserve">propterea ramus principalis C O cadit ſupra ipſum
              <lb/>
            C A, quando B F minor eſt, quàm B E, & </s>
            <s xml:id="echoid-s4182" xml:space="preserve">tunc quidem duci poteſt hyperbola
              <lb/>
            ex puncto A circa aſymptotos (vt in propoſitione 51. </s>
            <s xml:id="echoid-s4183" xml:space="preserve">& </s>
            <s xml:id="echoid-s4184" xml:space="preserve">52. </s>
            <s xml:id="echoid-s4185" xml:space="preserve">factum eſt) quæ pro-
              <lb/>
            ducta occurret ſectioni B A inter B, & </s>
            <s xml:id="echoid-s4186" xml:space="preserve">O, vt in P, & </s>
            <s xml:id="echoid-s4187" xml:space="preserve">coniuncto radio C P,
              <lb/>
              <note position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">51. 52. 53.
                <lb/>
              huius.</note>
            erunt duo rami C A, & </s>
            <s xml:id="echoid-s4188" xml:space="preserve">C P breuiſecantes, quorum infimus eſt C A. </s>
            <s xml:id="echoid-s4189" xml:space="preserve">Si vero
              <lb/>
            punctum C ſumatur vltra punctum D, tunc quidem menſura B F maior erit,
              <lb/>
            quàm B E, & </s>
            <s xml:id="echoid-s4190" xml:space="preserve">propterea abſciſſa N B maior, quàm H B, & </s>
            <s xml:id="echoid-s4191" xml:space="preserve">ideo principalis
              <lb/>
            ramus C O cadet infra ramum C A; </s>
            <s xml:id="echoid-s4192" xml:space="preserve">& </s>
            <s xml:id="echoid-s4193" xml:space="preserve">denuo facta eadem conſtructione propo-
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s4194" xml:space="preserve">51. </s>
            <s xml:id="echoid-s4195" xml:space="preserve">& </s>
            <s xml:id="echoid-s4196" xml:space="preserve">52. </s>
            <s xml:id="echoid-s4197" xml:space="preserve">huius, erunt duo rami C P, & </s>
            <s xml:id="echoid-s4198" xml:space="preserve">C A breuiſecantes, quorũ ſupre-
              <lb/>
            mus verſus B erit C A, quod erat probandum.</s>
            <s xml:id="echoid-s4199" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4200" xml:space="preserve">Sit coniſectio, vel ellipſis portio quadrantis B A G, cuius axis B
              <lb/>
              <note position="right" xlink:label="note-0141-03" xlink:href="note-0141-03a" xml:space="preserve">PROP. 9.
                <lb/>
              Addit.</note>
            E, perpendicularis E D, euiuſque Trutina L ſit minor perpendiculari
              <lb/>
            D E, & </s>
            <s xml:id="echoid-s4201" xml:space="preserve">centro D, interuallo cuiuslibet rami ſecantis D A circulus Z
              <lb/>
            A γ deſcribatur, & </s>
            <s xml:id="echoid-s4202" xml:space="preserve">ex puncto A ducatur recta A x contingens </s>
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