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-div378" type="section" level="1" n="121">
          <p style="it">
            <s xml:id="echoid-s4067" xml:space="preserve">
              <pb o="100" file="0138" n="138" rhead="Apollonij Pergæi"/>
            miaxim minorem B D habet eandem, aut
              <lb/>
              <figure xlink:label="fig-0138-01" xlink:href="fig-0138-01a" number="122">
                <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0138-01"/>
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            maiorem proportionem, quàm latus tran-
              <lb/>
            ſuerſum A C ad eius latus rectum; </s>
            <s xml:id="echoid-s4068" xml:space="preserve">tunc
              <lb/>
            nullus alius ramus ad ſectionem A B C
              <lb/>
            breuiſecans duci poteſt, & </s>
            <s xml:id="echoid-s4069" xml:space="preserve">quælibet linea,
              <lb/>
            breuiſsima vt F H ducta ex puncto F ad
              <lb/>
            axim A C cadit infra ramum E F adpar-
              <lb/>
            tes centri, & </s>
            <s xml:id="echoid-s4070" xml:space="preserve">propterea ſi per F ducatur
              <lb/>
            F I contingens ellipſin quilibet ramus E
              <lb/>
              <note position="left" xlink:label="note-0138-01" xlink:href="note-0138-01a" xml:space="preserve">ex 29. 30.
                <lb/>
              huius.</note>
            F efficiet cum tangente angulum E F I reſ-
              <lb/>
            picientem verticem A acutum: </s>
            <s xml:id="echoid-s4071" xml:space="preserve">Similiter ſi
              <lb/>
            ducatur A K contingens ſectionem in A co-
              <lb/>
              <note position="left" xlink:label="note-0138-02" xlink:href="note-0138-02a" xml:space="preserve">ex 32.
                <lb/>
              lib. 1.</note>
            niungaturque E A, erit quoque angulus E A K acutus, & </s>
            <s xml:id="echoid-s4072" xml:space="preserve">ducta B L contingente
              <lb/>
            ſectionem in B erit angulus E B L rectus; </s>
            <s xml:id="echoid-s4073" xml:space="preserve">quapropter omnes rami ex concurſu
              <lb/>
            E ad quadrantem A B ducti efficiunt cum ſuis tangentibus angulos reſpicientes
              <lb/>
            verticem A acutos, & </s>
            <s xml:id="echoid-s4074" xml:space="preserve">vnus tantummodo E B L eſt rectus; </s>
            <s xml:id="echoid-s4075" xml:space="preserve">igitur ramorum ca-
              <lb/>
              <note position="left" xlink:label="note-0138-03" xlink:href="note-0138-03a" xml:space="preserve">Coroll.
                <lb/>
              67. huius.</note>
            dentium ex E ad quadrantem B A minimus eſt E A, & </s>
            <s xml:id="echoid-s4076" xml:space="preserve">quilibet ramus E F
              <lb/>
            propinquior vertici A minor eſt quolibet remotiore; </s>
            <s xml:id="echoid-s4077" xml:space="preserve">& </s>
            <s xml:id="echoid-s4078" xml:space="preserve">propterea E B erit ma-
              <lb/>
            ximus: </s>
            <s xml:id="echoid-s4079" xml:space="preserve">ſimili modo E B maior erit quolibet ramo E G in quadrante B C exiſten-
              <lb/>
            te; </s>
            <s xml:id="echoid-s4080" xml:space="preserve">Et hic eſt ſenſus, ni fallor illorum verborum; </s>
            <s xml:id="echoid-s4081" xml:space="preserve">demonſtrabitur in lineis
              <lb/>
            tangentibus, quemadmodum antea oſtenſum eſt, &</s>
            <s xml:id="echoid-s4082" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4083" xml:space="preserve"/>
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        <div xml:id="echoid-div382" type="section" level="1" n="122">
          <head xml:id="echoid-head165" xml:space="preserve">Notæ in Propoſit. LXXVII.</head>
          <p style="it">
            <s xml:id="echoid-s4084" xml:space="preserve">POſtea educatur E F, qui eſt maxi-
              <lb/>
              <figure xlink:label="fig-0138-02" xlink:href="fig-0138-02a" number="123">
                <image file="0138-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0138-02"/>
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            musramorum, &</s>
            <s xml:id="echoid-s4085" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4086" xml:space="preserve">Repono hic ſimi-
              <lb/>
            liter verba, quæ in textu deſiderantur; </s>
            <s xml:id="echoid-s4087" xml:space="preserve">Po-
              <lb/>
            ſtea educatur alius breuiſecans E F; </s>
            <s xml:id="echoid-s4088" xml:space="preserve">Dico,
              <lb/>
            quod eſt æqualis vni breuiſecanti E G æquè
              <lb/>
            remoto à recto D B, & </s>
            <s xml:id="echoid-s4089" xml:space="preserve">eſt maximus reli-
              <lb/>
            quorum omnium.</s>
            <s xml:id="echoid-s4090" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4091" xml:space="preserve">Quia B D, F H ſunt duæ breuiſſimæ;
              <lb/>
            </s>
            <s xml:id="echoid-s4092" xml:space="preserve">ergo rami egredientes ad ſectionem B F
              <lb/>
            abſcindunt cum A lineas maiores, quàm
              <lb/>
            ſecent breuiſſimæ egredientes ab eorum extremitatibus, & </s>
            <s xml:id="echoid-s4093" xml:space="preserve">rami egredien-
              <lb/>
            tes ad duas peripherias C B, F A abſcindunt cum A, vel C lineas mino-
              <lb/>
            res (52. </s>
            <s xml:id="echoid-s4094" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s4095" xml:space="preserve">&</s>
            <s xml:id="echoid-s4096" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4097" xml:space="preserve">Quia in ellipſi ſemiaxis minor B D, & </s>
            <s xml:id="echoid-s4098" xml:space="preserve">breuiſsima F H
              <lb/>
            concurrunt in E; </s>
            <s xml:id="echoid-s4099" xml:space="preserve">ergo quilibet ramus ex E ad peripheriam F B ductus cadit
              <lb/>
              <note position="left" xlink:label="note-0138-04" xlink:href="note-0138-04a" xml:space="preserve">Lem. 8.
                <lb/>
              huius.</note>
            infra breuiſsimam ab eius termino ad axim A C ductam: </s>
            <s xml:id="echoid-s4100" xml:space="preserve">ſimiliter, quia ramus
              <lb/>
            E G æquè recedit ab axi D B, ac ramus E F; </s>
            <s xml:id="echoid-s4101" xml:space="preserve">propterea, ne dum ramus F E
              <lb/>
            æqualis erit ramo E G, ſed ſimiliter quilibet alius ramus incidens inter E B,
              <lb/>
            & </s>
            <s xml:id="echoid-s4102" xml:space="preserve">E G eadet infra breuiſsimam ab eius termino ad axim A C ductam verſus
              <lb/>
              <note position="left" xlink:label="note-0138-05" xlink:href="note-0138-05a" xml:space="preserve">Ibidem.</note>
            D, & </s>
            <s xml:id="echoid-s4103" xml:space="preserve">rami cadentes ad peripherias A F, & </s>
            <s xml:id="echoid-s4104" xml:space="preserve">C G cadunt ſupra breuiſsimas ab
              <lb/>
              <note position="left" xlink:label="note-0138-06" xlink:href="note-0138-06a" xml:space="preserve">Ibidem.</note>
            eorum terminis ad axim C A ductas ad partes A, & </s>
            <s xml:id="echoid-s4105" xml:space="preserve">C.</s>
            <s xml:id="echoid-s4106" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4107" xml:space="preserve">Conſtat itaque, vt dictum eſt de lineis tangentibus, quod E F ſit ma-
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            ximus ramorum ſecantium egredientium ex E ad A B C, quod erat </s>
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