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-div306" type="section" level="1" n="101">
          <pb o="78" file="0116" n="116" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div310" type="section" level="1" n="102">
          <head xml:id="echoid-head142" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s3275" xml:space="preserve">ANtequam huius Decimætertiæ Sectionis explicationes, atque
              <lb/>
            emendationes aggrediamur, vt Notæ breuiores, clarioreſque
              <lb/>
            reddentatur, & </s>
            <s xml:id="echoid-s3276" xml:space="preserve">teſtus Arabici menda facilius corrigi poſſent, operæ
              <lb/>
            pretium duximus (amice lector) Lemmata ſequentia præmittere.</s>
            <s xml:id="echoid-s3277" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div311" type="section" level="1" n="103">
          <head xml:id="echoid-head143" xml:space="preserve">LEMMA IX.</head>
          <p style="it">
            <s xml:id="echoid-s3278" xml:space="preserve">Si ad coniſectionem, atque ad vnum quadrantem ellipſis A B C à
              <lb/>
            concurſu D nullus ramus duci poſsit, qui ſit breuiſecans; </s>
            <s xml:id="echoid-s3279" xml:space="preserve">Dico, quod
              <lb/>
            quilibet ſecans ramus D B cum tangente H B G per eius terminum B
              <lb/>
            ducta efficit angulum D B H ad partes verticis A acutum, & </s>
            <s xml:id="echoid-s3280" xml:space="preserve">D B
              <lb/>
            G, qui deinceps eſt, obtuſum.</s>
            <s xml:id="echoid-s3281" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3282" xml:space="preserve">Quoniam nullus ramus ex concurſu
              <lb/>
              <figure xlink:label="fig-0116-01" xlink:href="fig-0116-01a" number="98">
                <image file="0116-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0116-01"/>
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            D ad ſectionem A C ductus eſt breui-
              <lb/>
            ſecans, erit (ex conuerſa propoſitionis
              <lb/>
            49. </s>
            <s xml:id="echoid-s3283" xml:space="preserve">50. </s>
            <s xml:id="echoid-s3284" xml:space="preserve">51. </s>
            <s xml:id="echoid-s3285" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3286" xml:space="preserve">huius) menſura A E
              <lb/>
            aut non maior ſemiſſe lateris recti, aut
              <lb/>
            perpendicularis D E maior Trutina,
              <lb/>
            quæ ſit F, & </s>
            <s xml:id="echoid-s3287" xml:space="preserve">ideo quilibet ramus ſe-
              <lb/>
            cans D B cadit ſupra breuiſsimam ex
              <lb/>
            puncto B ad axim ductam, eſt verò
              <lb/>
            breuiſsima ex puncto B ad axim ducta
              <lb/>
            perpendicularis ad G B H tangentem
              <lb/>
              <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">29. 30.
                <lb/>
              huius.</note>
            ſectionem in B; </s>
            <s xml:id="echoid-s3288" xml:space="preserve">ergo angulus D B H,
              <lb/>
            verticem A reſpiciens eſt acutus, & </s>
            <s xml:id="echoid-s3289" xml:space="preserve">qui deinceps eſt D B G erit obtuſus.</s>
            <s xml:id="echoid-s3290" xml:space="preserve"/>
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        <div xml:id="echoid-div313" type="section" level="1" n="104">
          <head xml:id="echoid-head144" xml:space="preserve">LEMMA X.</head>
          <p style="it">
            <s xml:id="echoid-s3291" xml:space="preserve">Iiſdem poſitis, ſi à concurſu D vnicus tantum ramus D B breuiſe-
              <lb/>
            cans ad ſectionem A B duci poteſt; </s>
            <s xml:id="echoid-s3292" xml:space="preserve">Dico, quod quilibet alius ramus
              <lb/>
            ſecans D 1 ſupra, vel infra breuiſecantem D B poſitus efficit cum recta
              <lb/>
            L I H tangente ſectionem in I angulum D I L, verticem reſpicien-
              <lb/>
            tem, acutum, & </s>
            <s xml:id="echoid-s3293" xml:space="preserve">D I H, qui deinceps eſt, obtuſum.</s>
            <s xml:id="echoid-s3294" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s3295" xml:space="preserve">Nam ex conuerſa propoſitione 51. </s>
            <s xml:id="echoid-s3296" xml:space="preserve">& </s>
            <s xml:id="echoid-s3297" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3298" xml:space="preserve">huius perpendicularis D E æqualis
              <lb/>
            c
              <unsure/>
            rit Trutinæ F, & </s>
            <s xml:id="echoid-s3299" xml:space="preserve">ideo quilibet ramus D I poſitus ſupra, velinſra </s>
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