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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            huius) atque A N pa-
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                <image file="0230-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0230-01"/>
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            rallela erit L O. </s>
            <s xml:id="echoid-s7275" xml:space="preserve">Edu-
              <lb/>
            catur iam R Q bifariã
              <lb/>
            diuidens A E, L M in
              <lb/>
            P, Q: </s>
            <s xml:id="echoid-s7276" xml:space="preserve">quare erit diame
              <lb/>
              <note position="left" xlink:label="note-0230-01" xlink:href="note-0230-01a" xml:space="preserve">28. lib. 2.</note>
            ter ſectionis (32. </s>
            <s xml:id="echoid-s7277" xml:space="preserve">ex 2.)
              <lb/>
            </s>
            <s xml:id="echoid-s7278" xml:space="preserve">& </s>
            <s xml:id="echoid-s7279" xml:space="preserve">educatur R V paral-
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            lela A N, quæ ſectionẽ
              <lb/>
              <note position="left" xlink:label="note-0230-02" xlink:href="note-0230-02a" xml:space="preserve">17. lib. 1.</note>
            continget (18. </s>
            <s xml:id="echoid-s7280" xml:space="preserve">ex 1.)</s>
            <s xml:id="echoid-s7281" xml:space="preserve">.
              <lb/>
            </s>
            <s xml:id="echoid-s7282" xml:space="preserve">Et quia duo ſegmen-
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            ta L M, A E ſunt ſi-
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            milia habebit maior
              <lb/>
              <note position="left" xlink:label="note-0230-03" xlink:href="note-0230-03a" xml:space="preserve">16. 17.
                <lb/>
              huius.</note>
            Q R ad eandem R V
              <lb/>
            eandem proportionẽ,
              <lb/>
            quàm habet minor R
              <lb/>
            P; </s>
            <s xml:id="echoid-s7283" xml:space="preserve">quod eſt abſurdum.
              <lb/>
            </s>
            <s xml:id="echoid-s7284" xml:space="preserve">Quare non ſunt ſimilia
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            duo ſegmenta A E, C
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            F alteri ſegmento. </s>
            <s xml:id="echoid-s7285" xml:space="preserve">
              <lb/>
            Quod erat oſtenden-
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            dum.</s>
            <s xml:id="echoid-s7286" xml:space="preserve"/>
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        <div xml:id="echoid-div668" type="section" level="1" n="222">
          <head xml:id="echoid-head280" xml:space="preserve">Notæ in Propoſit. XVIII. & XIX.</head>
          <p style="it">
            <s xml:id="echoid-s7287" xml:space="preserve">QVuoniam vnumquodque corum alteri congruit, nec non congruunt
              <lb/>
            duo ſegmenta G I, K H in ellipſi (7. </s>
            <s xml:id="echoid-s7288" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7289" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7290" xml:space="preserve">at non ſunt ſimilia
              <lb/>
              <note position="right" xlink:label="note-0230-04" xlink:href="note-0230-04a" xml:space="preserve">a</note>
            alteri ſegmento, &</s>
            <s xml:id="echoid-s7291" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7292" xml:space="preserve">Ideſt. </s>
            <s xml:id="echoid-s7293" xml:space="preserve">Sit prius ſectio A B C parabole, vel
              <lb/>
            hyperbole. </s>
            <s xml:id="echoid-s7294" xml:space="preserve">Quoniam duæ A C, & </s>
            <s xml:id="echoid-s7295" xml:space="preserve">E F ordinatim ad axim B D applicatæ ab-
              <lb/>
              <note position="left" xlink:label="note-0230-05" xlink:href="note-0230-05a" xml:space="preserve">7. huius.</note>
            ſcindunt ex vtraque parte axis duo ſegmen-
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                <image file="0230-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0230-02"/>
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            ta A E, & </s>
            <s xml:id="echoid-s7296" xml:space="preserve">C F congruentia, propterea ſi-
              <lb/>
            milia erunt, atque ſimiliter poſita. </s>
            <s xml:id="echoid-s7297" xml:space="preserve">Secundo,
              <lb/>
            in ellipſi ductæ ſint ad axim quatuor ordina-
              <lb/>
            tim applicatæ, quarum binæ extremæ E F,
              <lb/>
            & </s>
            <s xml:id="echoid-s7298" xml:space="preserve">I K æqualiter à centro D diſtent; </s>
            <s xml:id="echoid-s7299" xml:space="preserve">pari-
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            terque binæ intermediæ A C, & </s>
            <s xml:id="echoid-s7300" xml:space="preserve">G H æqua-
              <lb/>
              <note position="left" xlink:label="note-0230-06" xlink:href="note-0230-06a" xml:space="preserve">8. huius.</note>
            liter diſtent ab eodem centro: </s>
            <s xml:id="echoid-s7301" xml:space="preserve">quare quatuor
              <lb/>
            ſegmenta G I, H K, C F, & </s>
            <s xml:id="echoid-s7302" xml:space="preserve">A E æqualia
              <lb/>
            erunt, & </s>
            <s xml:id="echoid-s7303" xml:space="preserve">ſibi mutuo congruent, & </s>
            <s xml:id="echoid-s7304" xml:space="preserve">propterea
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            ſimilid quoque inter ſe erunt.</s>
            <s xml:id="echoid-s7305" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s7306" xml:space="preserve">Erit angulus N æqualis O, vti demõ-
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              <note position="right" xlink:label="note-0230-07" xlink:href="note-0230-07a" xml:space="preserve">b</note>
            ſtrauimus, &</s>
            <s xml:id="echoid-s7307" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7308" xml:space="preserve">Quoniam duo ſegmenta L
              <lb/>
            M, & </s>
            <s xml:id="echoid-s7309" xml:space="preserve">A E, ponuntur ſimilia, atque eorum
              <lb/>
            baſes L M, & </s>
            <s xml:id="echoid-s7310" xml:space="preserve">A E productæ occurrunt axi
              <lb/>
            in O, & </s>
            <s xml:id="echoid-s7311" xml:space="preserve">N: </s>
            <s xml:id="echoid-s7312" xml:space="preserve">igitur vt demonſtratum eſt,
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              <note position="left" xlink:label="note-0230-08" xlink:href="note-0230-08a" xml:space="preserve">Prop 16.
                <lb/>
              17. huius.</note>
            anguli à contingentibus verticalibus ſegmen-
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            torum ſimilium L M, & </s>
            <s xml:id="echoid-s7313" xml:space="preserve">A E cum axi com-
              <lb/>
            muni B D eiuſdem ſectionis continebunt </s>
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