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-s4107" xml:space="preserve">
              <pb o="101" file="0139" n="139" rhead="Conicor. Lib. V."/>
            dendum, &</s>
            <s xml:id="echoid-s4108" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4109" xml:space="preserve">Quæ poſtrema verba ſic intelligi, ac corrigi debent. </s>
            <s xml:id="echoid-s4110" xml:space="preserve">Quia qui-
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Lem. 8.
                <lb/>
              huius.</note>
            libet ramus ex E ad A F ductus cadit ſupra breuiſsimam ad partes A ab eius
              <lb/>
            termino ad axim C A ductam; </s>
            <s xml:id="echoid-s4111" xml:space="preserve">igitur, vt multoties dictum eſt, conſtituit cum
              <lb/>
            ſua tangente angulum reſpicientem verticem A acutum, ſicuti angulus E A K
              <lb/>
            acutus quoque eſt, & </s>
            <s xml:id="echoid-s4112" xml:space="preserve">omnium ramorum ad peripheriam A F cadentiũ tantum-
              <lb/>
            modo angulus E F 1 eſt rectus; </s>
            <s xml:id="echoid-s4113" xml:space="preserve">igitur omnium ramorum ex E ad peripheriam
              <lb/>
              <note position="right" xlink:label="note-0139-02" xlink:href="note-0139-02a" xml:space="preserve">Coroll.
                <lb/>
              Prop. 67.
                <lb/>
              huius.</note>
            A F cadentium maximus eſt F E remotiſsimus à vertice A, eſtque ramus E G
              <lb/>
            æqualis E F, & </s>
            <s xml:id="echoid-s4114" xml:space="preserve">E G maximus eſt ramorum cadentium ex E ad peripheriam
              <lb/>
            G C; </s>
            <s xml:id="echoid-s4115" xml:space="preserve">igitur ramus E F maximus etiam eſt ramorum cadentium ad peripheriam
              <lb/>
            G C: </s>
            <s xml:id="echoid-s4116" xml:space="preserve">poſtea ducto quolibet ramo E M inter F, B, & </s>
            <s xml:id="echoid-s4117" xml:space="preserve">M N tangente ſectionem
              <lb/>
            in M, quæ conueniat cum tangente I F in N, quia E M, vt dictum eſt, cadit
              <lb/>
            infra breuiſsimam ex M ad axim B A ductam, cum qua contingens N M an-
              <lb/>
            gulum rectũ conſtituit, (ex 30. </s>
            <s xml:id="echoid-s4118" xml:space="preserve">huius) ergo angulus E M N reſpiciens verticem
              <lb/>
            A eſt obtuſus, & </s>
            <s xml:id="echoid-s4119" xml:space="preserve">angulus E F N eſt rectus, cum F O ſit breuiſsima, igitur duo
              <lb/>
            quadrata E F, F N maiora ſunt duobus quadratis E M, M N ſimul ſumptis,
              <lb/>
            & </s>
            <s xml:id="echoid-s4120" xml:space="preserve">ablatum quadratum M N ex minori ſumma maius eſt ablato quadrato N F,
              <lb/>
            cum contingens N F vertici A maioris axis propinquior ſit; </s>
            <s xml:id="echoid-s4121" xml:space="preserve">ergo quadratum
              <lb/>
              <note position="right" xlink:label="note-0139-03" xlink:href="note-0139-03a" xml:space="preserve">70. huius.</note>
            E F maius ex quadrato E M, ideoque ramus E F maior erit quolibet ramo E
              <lb/>
            M inter F, & </s>
            <s xml:id="echoid-s4122" xml:space="preserve">B poſito. </s>
            <s xml:id="echoid-s4123" xml:space="preserve">Non ſecus oſtendetur E M maior quàm E B; </s>
            <s xml:id="echoid-s4124" xml:space="preserve">quare
              <lb/>
            ramus E F maximus erit omnium cadentium ad peripheriam F B. </s>
            <s xml:id="echoid-s4125" xml:space="preserve">Eodem mo-
              <lb/>
            do ramus breuiſecans E G maximus erit omnium cadentium ad peripheriam G
              <lb/>
            B; </s>
            <s xml:id="echoid-s4126" xml:space="preserve">& </s>
            <s xml:id="echoid-s4127" xml:space="preserve">propterea ramus E F maximus erit omnium ad peripheriam F B G ca-
              <lb/>
            dentium; </s>
            <s xml:id="echoid-s4128" xml:space="preserve">Quapropter ramus breuiſecans E F æqualis erit vni tantummodo E
              <lb/>
            G æquè ab axi remoto, & </s>
            <s xml:id="echoid-s4129" xml:space="preserve">maximus omnium ramorum ex concurſu E ad ſemi-
              <lb/>
            ellipſim A B C cadentium, quod erat oſtendendum.</s>
            <s xml:id="echoid-s4130" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4131" xml:space="preserve">Sicuti in prioribus propoſitionibus factum eſt, reperientur, quotnam rami in-
              <lb/>
            ter ſe æquales à puncto concurſus ad coniſectionem duci poſſunt, qua occaſione
              <lb/>
            afferam propoſitiones aliquas non iniucundas, quarum prima erit.</s>
            <s xml:id="echoid-s4132" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4133" xml:space="preserve">Si ad coniſectionem B A à concurſu D vnicus tantum breuiſecans D
              <lb/>
              <note position="right" xlink:label="note-0139-04" xlink:href="note-0139-04a" xml:space="preserve">PROP.7.
                <lb/>
              Addit.</note>
            A duci poſsit, & </s>
            <s xml:id="echoid-s4134" xml:space="preserve">ducatur quælibet F C parallela perpendiculari D E
              <lb/>
              <figure xlink:label="fig-0139-01" xlink:href="fig-0139-01a" number="124">
                <image file="0139-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0139-01"/>
              </figure>
            inter productionem breuiſsimæ, & </s>
            <s xml:id="echoid-s4135" xml:space="preserve">axim intercepta quem ſecet in F, </s>
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