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">
          <pb o="96" file="0134" n="134" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div371" type="section" level="1" n="119">
          <head xml:id="echoid-head162" xml:space="preserve">Notæ in Propoſ. LXXIV.</head>
          <p>
            <s xml:id="echoid-s3926" xml:space="preserve">ERgo E F per centrum non tranſit, cadat ſuper C D, & </s>
            <s xml:id="echoid-s3927" xml:space="preserve">quia produ-
              <lb/>
              <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">a</note>
            cti ſunt ex E duo breuiſecantes; </s>
            <s xml:id="echoid-s3928" xml:space="preserve">ergo C F excedit dimidium erecti,
              <lb/>
            & </s>
            <s xml:id="echoid-s3929" xml:space="preserve">E F æqualis eſt Trutinæ (52. </s>
            <s xml:id="echoid-s3930" xml:space="preserve">ex 5.) </s>
            <s xml:id="echoid-s3931" xml:space="preserve">patet itaque, vt antea demonſtra-
              <lb/>
            uimus, quod E G ſit maximus ramorum, & </s>
            <s xml:id="echoid-s3932" xml:space="preserve">E C minimus, &</s>
            <s xml:id="echoid-s3933" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s3934" xml:space="preserve">
              <figure xlink:label="fig-0134-01" xlink:href="fig-0134-01a" number="118">
                <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0134-01"/>
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            Quoniam in 11. </s>
            <s xml:id="echoid-s3935" xml:space="preserve">huius oſtenſum eſt, quod ſemiaxis minor ellipſis eſt ramus bre-
              <lb/>
            uiſsimus, ergo ſi incidentia perpendicularis E F ſuper axim A C, ideſt punctum
              <lb/>
            F eſt centrum ellipſis educerentur ex concurſu E tres breuiſecantes, nimirum
              <lb/>
            E H, E G, & </s>
            <s xml:id="echoid-s3936" xml:space="preserve">E F producta, quæ eſſet axis minor ellipſis: </s>
            <s xml:id="echoid-s3937" xml:space="preserve">hoc autem eſt con-
              <lb/>
            tra hypotheſim, cum ducti ſint ex E duo breuiſecantes: </s>
            <s xml:id="echoid-s3938" xml:space="preserve">ergo eorum vnus E H
              <lb/>
            menſuram C F ſecat, quæ minor eſſe debet ſemiſſe axis maioris C D; </s>
            <s xml:id="echoid-s3939" xml:space="preserve">igitur
              <lb/>
            ex conuerſa propoſitione 50. </s>
            <s xml:id="echoid-s3940" xml:space="preserve">huius, menſura C F maior erit ſemiſſe lateris re-
              <lb/>
            cti, & </s>
            <s xml:id="echoid-s3941" xml:space="preserve">(ex conuerſa propoſ. </s>
            <s xml:id="echoid-s3942" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3943" xml:space="preserve">huius) erit perpendicularis E F æqualis Tru-
              <lb/>
            tinæ. </s>
            <s xml:id="echoid-s3944" xml:space="preserve">Demonſtratio huius propoſitionis neglecta ab Apollonio, propterea quod
              <lb/>
            eodem ferè modo, ac præcedens oſtendi poteſt, breuiſsimè perficietur in hunc
              <lb/>
            modum.</s>
            <s xml:id="echoid-s3945" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3946" xml:space="preserve">Quoniam à concurſu E vnicus tantum breuiſecans E H ad quadrantem C B
              <lb/>
              <note position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">Propoſ.
                <lb/>
              67. huius.</note>
            ducitur; </s>
            <s xml:id="echoid-s3947" xml:space="preserve">igitur C E minimus eſt omnium ramorum cadentium ad ſectionis pe-
              <lb/>
            ripheriam C B, & </s>
            <s xml:id="echoid-s3948" xml:space="preserve">E C vertici B propinquior minor eſt remotiore E H, & </s>
            <s xml:id="echoid-s3949" xml:space="preserve">E
              <lb/>
            H minor, quàm E B: </s>
            <s xml:id="echoid-s3950" xml:space="preserve">rurſus, quia ramorum cadentium ex E ad peripheriam
              <lb/>
              <note position="left" xlink:label="note-0134-03" xlink:href="note-0134-03a" xml:space="preserve">Ex 29. 30.
                <lb/>
              huius.</note>
            B G vnus tantummodo breuiſecans E G conſtituit cum tangente N G </s>
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