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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            <s xml:id="echoid-s13276" xml:space="preserve">
              <pb o="397" file="0435" n="436" rhead="Aſſumpt. Liber."/>
            pendicularis ad E D, & </s>
            <s xml:id="echoid-s13277" xml:space="preserve">D I eſt quoque perpendicularis ad A E, & </s>
            <s xml:id="echoid-s13278" xml:space="preserve">iam
              <lb/>
            ſe mutuo ſecuerunt in M, ergo E M O erit etiam perpendicularis, que-
              <lb/>
            madmodum oſtendimus in expoſitione, quàm confecimus de proprieta-
              <lb/>
            tibus triangulorum, & </s>
            <s xml:id="echoid-s13279" xml:space="preserve">cuius demonſtratio iam quidem præceſſit in ſupe-
              <lb/>
              <figure xlink:label="fig-0435-01" xlink:href="fig-0435-01a" number="503">
                <image file="0435-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0435-01"/>
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            riori propoſitione; </s>
            <s xml:id="echoid-s13280" xml:space="preserve">Similiter quoque erit F P perpendicularis ſuper C A,
              <lb/>
            & </s>
            <s xml:id="echoid-s13281" xml:space="preserve">quia duo anguli, qui ſunt apud L, & </s>
            <s xml:id="echoid-s13282" xml:space="preserve">B ſunt recti, erit D L parallela
              <lb/>
            ipſi A B, & </s>
            <s xml:id="echoid-s13283" xml:space="preserve">pariter D I ipſi C B, igitur proportio A D ad D C eſt vt
              <lb/>
            proportio A M ad F M, immo vt proportio A O ad O P, & </s>
            <s xml:id="echoid-s13284" xml:space="preserve">proportio
              <lb/>
            C D ad D A vt proportio C N ad N E, immo vt proportio C P ad P
              <lb/>
            O, & </s>
            <s xml:id="echoid-s13285" xml:space="preserve">erat A D ſexquialtera D C, ergo A O eſt ſexquialtera O P, & </s>
            <s xml:id="echoid-s13286" xml:space="preserve">
              <lb/>
            O P ſexquialtera C P, ergo tres lineæ A O, O P, P C ſunt proportio-
              <lb/>
            nales: </s>
            <s xml:id="echoid-s13287" xml:space="preserve">& </s>
            <s xml:id="echoid-s13288" xml:space="preserve">in eadem menſura, in qua eſt P C quatuor, erit O P ſex, & </s>
            <s xml:id="echoid-s13289" xml:space="preserve">
              <lb/>
            A O nouem, & </s>
            <s xml:id="echoid-s13290" xml:space="preserve">C A nouendecim, & </s>
            <s xml:id="echoid-s13291" xml:space="preserve">quia P O æ qualis eſt E F, erit
              <lb/>
            proportio A C ad E F vt nouendecim ad ſex, igitur reperimus dictam
              <lb/>
            proportionem. </s>
            <s xml:id="echoid-s13292" xml:space="preserve">Etiam ſi fuerit A D ad D C qualiſcumque vt ſexquiter-
              <lb/>
            tia, aut ſexquiquarta, aut alia, erit iudicium, & </s>
            <s xml:id="echoid-s13293" xml:space="preserve">ratio, vti dictum eſt.
              <lb/>
            </s>
            <s xml:id="echoid-s13294" xml:space="preserve">Et hoc eſt quod voluimus.</s>
            <s xml:id="echoid-s13295" xml:space="preserve"/>
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        <div xml:id="echoid-div1136" type="section" level="1" n="365">
          <head xml:id="echoid-head457" xml:space="preserve">Notæ in Propoſit. VI.</head>
          <p style="it">
            <s xml:id="echoid-s13296" xml:space="preserve">HAEc propoſitio nil prorſus differre videtur à 16. </s>
            <s xml:id="echoid-s13297" xml:space="preserve">propoſit. </s>
            <s xml:id="echoid-s13298" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s13299" xml:space="preserve">4. </s>
            <s xml:id="echoid-s13300" xml:space="preserve">Pappi
              <lb/>
            Alex. </s>
            <s xml:id="echoid-s13301" xml:space="preserve">eſt tamen pars illius, & </s>
            <s xml:id="echoid-s13302" xml:space="preserve">particulariter demonſtrata, quod quidem
              <lb/>
            peccatum alicui expoſitori tribui debet; </s>
            <s xml:id="echoid-s13303" xml:space="preserve">nunquam enim Archimedes propoſitionẽ
              <lb/>
            illam, quam vniuerſaltſſimè demonſtrare potuißet, exemplis numericis tam
              <lb/>
            pueriliter oſtendiſſet. </s>
            <s xml:id="echoid-s13304" xml:space="preserve">Pappus igitur quærit menſuram diametri illius circuli,
              <lb/>
            qui in loco inter tres circunferentias circulares interijcitur, quod Arbelon ap-
              <lb/>
            pellatur, & </s>
            <s xml:id="echoid-s13305" xml:space="preserve">oſtendit quidem diametrum ſemicirculi maioris A C ſecari in duo-
              <lb/>
            bus punctis O, & </s>
            <s xml:id="echoid-s13306" xml:space="preserve">P à perpendicularibus cadentibus à terminis E, & </s>
            <s xml:id="echoid-s13307" xml:space="preserve">F dia-
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            metri circuli in Arbelo inſcripti, ac diuidi in tria ſegmenta A O, O P, P C
              <lb/>
            continue proportionalia in eadem ratione, quàm habet A D ad D C, & </s>
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