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-s12625" xml:space="preserve">
              <pb o="370" file="0408" n="409" rhead="Apollonij Pergæi"/>
            tum E H, E G in ſuum exceſſum ad aggregatum H A, E G in ſuum ex-
              <lb/>
            ceſſum æqualis exceſſui duorum quadratorum E H, E G, nempe qua-
              <lb/>
            dratum A C ad exceſſum quadratorum duorum laterum figuræ I L mi-
              <lb/>
            nor in prima ellypſi, & </s>
            <s xml:id="echoid-s12626" xml:space="preserve">maior in ſecunda, quàm quadratum A H ad ag-
              <lb/>
            gregatum H A, A G in eorum exceſſu æqualis, &</s>
            <s xml:id="echoid-s12627" xml:space="preserve">c. </s>
            <s xml:id="echoid-s12628" xml:space="preserve">Hæc omnia corrigi
              <lb/>
            debuiſſe nemo negabit, atque hinc manifeſtum eſt non pauca in textu arabico
              <lb/>
            deſiderari, cum propoſitio 51, vera non ſit abſque determinationibus ſuperius
              <lb/>
            expoſitis.</s>
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        <div xml:id="echoid-div1093" type="section" level="1" n="343">
          <head xml:id="echoid-head424" xml:space="preserve">SECTIO VNDECIMA</head>
          <head xml:id="echoid-head425" xml:space="preserve">Continens Propoſit. XXXII. & XXXI.</head>
          <head xml:id="echoid-head426" xml:space="preserve">Apollonij.</head>
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            <s xml:id="echoid-s12630" xml:space="preserve">IN ellypſi, & </s>
            <s xml:id="echoid-s12631" xml:space="preserve">ſectionibus coniugatis parallelogrammum ſub
              <lb/>
              <note position="right" xlink:label="note-0408-01" xlink:href="note-0408-01a" xml:space="preserve">a</note>
            axibus contentum æquale eſt parallelogrammo à quibuſcun-
              <lb/>
            que duabus coniugatis diametris comprehenſo, ſi eorum anguli
              <lb/>
            æquales fuerint angulis ad centrum contentis à coniugatis dia-
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            metris.</s>
            <s xml:id="echoid-s12632" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12633" xml:space="preserve">Sint duo axes A B, C D in ellipſi A C
              <lb/>
              <figure xlink:label="fig-0408-01" xlink:href="fig-0408-01a" number="482">
                <image file="0408-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0408-01"/>
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            B D, ſiue in ſectionibus coniugatis A, B,
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            C, D, & </s>
            <s xml:id="echoid-s12634" xml:space="preserve">ſint F G, I H aliæ duæ coniu-
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            gatæ diametri, & </s>
            <s xml:id="echoid-s12635" xml:space="preserve">ducantur per puncta F,
              <lb/>
            I, G, H, lìneæ tangentes coniſectiones,
              <lb/>
            quæ ſibi mutuo occurrant ad puncta K, L,
              <lb/>
            M, N: </s>
            <s xml:id="echoid-s12636" xml:space="preserve">& </s>
            <s xml:id="echoid-s12637" xml:space="preserve">producatur A B ex vtraque
              <lb/>
            parte vſque ad tangentes, eaſque ſecet in
              <lb/>
            O, P, & </s>
            <s xml:id="echoid-s12638" xml:space="preserve">ſit centrum E. </s>
            <s xml:id="echoid-s12639" xml:space="preserve">Dico quod A
              <lb/>
            B in C D æquale eſt ſpatio parallelogram-
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            mo M K: </s>
            <s xml:id="echoid-s12640" xml:space="preserve">ſit itaque F R perpendicularis
              <lb/>
            ad A B; </s>
            <s xml:id="echoid-s12641" xml:space="preserve">& </s>
            <s xml:id="echoid-s12642" xml:space="preserve">ponamus S R mediam propor-
              <lb/>
            tionalem inter O R, R E.</s>
            <s xml:id="echoid-s12643" xml:space="preserve"/>
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            <s xml:id="echoid-s12644" xml:space="preserve">Et quia quadratum A E ad quadratum
              <lb/>
            E C eandem proportionem habet, quàm
              <lb/>
              <note position="right" xlink:label="note-0408-02" xlink:href="note-0408-02a" xml:space="preserve">b</note>
            O R in R E, nempe quàm quadratum S
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            R ad quadratum F R (37. </s>
            <s xml:id="echoid-s12645" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s12646" xml:space="preserve">erit A E
              <lb/>
            ad E C nempe quadratum A E ad A E in
              <lb/>
            E C, vt S R ad F R, nempe S R in O E
              <lb/>
            ad F R in O E, & </s>
            <s xml:id="echoid-s12647" xml:space="preserve">permutando erit qua-
              <lb/>
            dratum A E, nempe R E in O E (39. </s>
            <s xml:id="echoid-s12648" xml:space="preserve">ex 1.)</s>
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