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-div362" type="section" level="1" n="118">
          <p>
            <s xml:id="echoid-s3819" xml:space="preserve">
              <pb o="94" file="0132" n="132" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0132-01" xlink:href="fig-0132-01a" number="117">
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            concur ſu E non exiſtente ſuper axim rectum minorem ellipſis A B C ducatur ad
              <lb/>
            ſectionem A B vnicus ramus vtrumque axim ſecans, cuius portio G I inter ſe-
              <lb/>
            ctionem, & </s>
            <s xml:id="echoid-s3820" xml:space="preserve">axim maiorem A C intercepta ſit linea breuiſsima; </s>
            <s xml:id="echoid-s3821" xml:space="preserve">vel ducatur præ-
              <lb/>
            ter E G alius ramus breuiſecans, menſuram tantummodo abſcindens; </s>
            <s xml:id="echoid-s3822" xml:space="preserve">vtique,
              <lb/>
            ramorum ſecantium, ex illo concurſu egredientium, maximus erit ille, qui axim
              <lb/>
            rectum ſectionis diuidit, &</s>
            <s xml:id="echoid-s3823" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3824" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3825" xml:space="preserve">Erigamus itaque ſuper D perpendicularem, &</s>
            <s xml:id="echoid-s3826" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">Scilicet ex centro ſectio-
              <lb/>
              <note position="right" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">b</note>
            nis D eleuetur D B perpendicularis ad axim maiorem A C, occurrens ſectioni
              <lb/>
            in B, & </s>
            <s xml:id="echoid-s3828" xml:space="preserve">ipſi E G in L, & </s>
            <s xml:id="echoid-s3829" xml:space="preserve">propterea D B erit ſemiſsis recti axis, & </s>
            <s xml:id="echoid-s3830" xml:space="preserve">punctum
              <lb/>
            E in axi B D non exiſtit ex hypotheſi, &</s>
            <s xml:id="echoid-s3831" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3832" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3833" xml:space="preserve">Quoniam non egreditur ex E niſi vnus breuiſecans, ergo lineæ breuiſsi-
              <lb/>
              <note position="right" xlink:label="note-0132-02" xlink:href="note-0132-02a" xml:space="preserve">c</note>
            mæ egredientes ab extremitatibus reliquorum ramorum, abſcindunt ab axi
              <lb/>
            cum A C, L A lineam maiorem, quàm ſecent illorum rami (51. </s>
            <s xml:id="echoid-s3834" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3835" xml:space="preserve">ex
              <lb/>
            5.) </s>
            <s xml:id="echoid-s3836" xml:space="preserve">& </s>
            <s xml:id="echoid-s3837" xml:space="preserve">iam patet, quod ſi ita ſe res habet L E C eſt acutus; </s>
            <s xml:id="echoid-s3838" xml:space="preserve">quia E C
              <lb/>
            breuiſsima eſt linearum egredientium ex E ad quadrantem A B, & </s>
            <s xml:id="echoid-s3839" xml:space="preserve">pro-
              <lb/>
            pinquior illi, minor eſt remotiore, &</s>
            <s xml:id="echoid-s3840" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3841" xml:space="preserve">Sic legendum puto; </s>
            <s xml:id="echoid-s3842" xml:space="preserve">Luia præter E
              <lb/>
            G, vtrumque axim ſecantem nullus alius breuiſecans duci poſſe à concurſu E ad
              <lb/>
            ſectionem ſupponitur, ergo lineæ breniſsimæ egredientes ab axtremitatibus reli-
              <lb/>
            quorum ramorum in quadrante C B abſcindunt ab axi A C cum vertice C li-
              <lb/>
            neas maiores, quàm ſecent rami (51 52. </s>
            <s xml:id="echoid-s3843" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3844" xml:space="preserve">pariterque conſtat, quod an-
              <lb/>
            gulus E C F ſit acutus, atque ramus E C eſt minimus egredientium ex E ad qua-
              <lb/>
              <note position="left" xlink:label="note-0132-03" xlink:href="note-0132-03a" xml:space="preserve">64. 65,
                <lb/>
              huius.</note>
            drantem C B, & </s>
            <s xml:id="echoid-s3845" xml:space="preserve">propinquior minimæ, minor eſt remotiore. </s>
            <s xml:id="echoid-s3846" xml:space="preserve">Demonſtrandum,
              <lb/>
            modo eſt, quod K E maior quoque eſt, quàm E B, &</s>
            <s xml:id="echoid-s3847" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3848" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3849" xml:space="preserve">Producamus itaque M B, M K tangentes; </s>
            <s xml:id="echoid-s3850" xml:space="preserve">ergo M B E eſt obtuſus, & </s>
            <s xml:id="echoid-s3851" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0132-04" xlink:href="note-0132-04a" xml:space="preserve">d</note>
            M K E eſt acutus (29. </s>
            <s xml:id="echoid-s3852" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3853" xml:space="preserve">quia breuiſsima egrediens ex K abſcindit A
              <lb/>
            lineam minorem, quàm A E (57. </s>
            <s xml:id="echoid-s3854" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3855" xml:space="preserve">eo quod K eſt inter duo ſegmen-
              <lb/>
            ta L B, L G: </s>
            <s xml:id="echoid-s3856" xml:space="preserve">& </s>
            <s xml:id="echoid-s3857" xml:space="preserve">iungamus M E; </s>
            <s xml:id="echoid-s3858" xml:space="preserve">ergo duo quadrata M B, B E minora,
              <lb/>
            ſunt, quàm quadratum M E, quæ minora ſunt duobus quadratis M K,
              <lb/>
            K E, &</s>
            <s xml:id="echoid-s3859" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3860" xml:space="preserve">Ideſt: </s>
            <s xml:id="echoid-s3861" xml:space="preserve">ex punctis B, K ducantur duæ tangentes ſectionem M B, K </s>
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