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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[241.] Notæ in Propoſit. XXVIII.
[242.] LEMMAX.
[243.] SECTIO VNDECIMA Continens Propoſit. XXIX. XXX. & XXXI. PROPOSTIO XXIX.
[244.] PROPOSITIO XXX.
[245.] PROPOSITIO XXXI.
[246.] Notæ in Propoſit. XXIX.
[247.] Notæ in Propoſit. XXX.
[248.] Notæ in Propoſit. XXXI.
[249.] LIBRI SEXTI FINIS.
[250.] DEFINITIONES. I.
[251.] II.
[252.] III.
[253.] IV.
[255.] VI.
[256.] VII.
[257.] VIII.
[258.] NOTÆ.
[259.] SECTIO PRIMA Continens Propoſit. I. V. & XXIII. Apollonij. PROPOSITIO I.
[260.] PROPOSITIO V. & XXIII.
[261.] Notæ in Propoſit. I.
[262.] Notæ in Propoſit. V. & XXIII.
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
[264.] PROPOSITIO IV.
[265.] PROPOSITIO VI. & VII.
[266.] Notæ in Propoſit. II. III.
[267.] Notæ in Propoſit. IV.
[268.] Notæ in Propoſit. VI. & VII.
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
[270.] Notæ in Propoſit. VIII.
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            <s xml:id="echoid-s10898" xml:space="preserve">
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            ſummam earundem: </s>
            <s xml:id="echoid-s10899" xml:space="preserve">& </s>
            <s xml:id="echoid-s10900" xml:space="preserve">ſumma duorum quadratorum ipſarum æqualis eſt
              <lb/>
            ſummæ duorum quadratorum A C, Q R ( 22. </s>
            <s xml:id="echoid-s10901" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10902" xml:space="preserve">) ergo ſumma A C,
              <lb/>
            Q R minor eſt, quàm ſumma I L, N O, atque ſic oſtendetur, quod sũ-
              <lb/>
            ma I L, N O minor eſt, quàm ſumma S T, V X. </s>
            <s xml:id="echoid-s10903" xml:space="preserve">Quod erat propoſitũ.</s>
            <s xml:id="echoid-s10904" xml:space="preserve"/>
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        <div xml:id="echoid-div927" type="section" level="1" n="291">
          <head xml:id="echoid-head362" xml:space="preserve">PROPOSITIO XXXXIII.</head>
          <p>
            <s xml:id="echoid-s10905" xml:space="preserve">D Einde in ellipſi quadratum ſummæ A C, Q R minus eſt quadrato
              <lb/>
            ſummæ I L, N O; </s>
            <s xml:id="echoid-s10906" xml:space="preserve">& </s>
            <s xml:id="echoid-s10907" xml:space="preserve">ſumma duorum quadratorum A C, Q R
              <lb/>
              <figure xlink:label="fig-0340-01" xlink:href="fig-0340-01a" number="396">
                <image file="0340-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0340-01"/>
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            æqualis eſt ſummæ duorum quadratorum I L, N O (22. </s>
            <s xml:id="echoid-s10908" xml:space="preserve">ex 7. </s>
            <s xml:id="echoid-s10909" xml:space="preserve">) igitur
              <lb/>
            remanet A C in Q R minus quàm I L in N O, & </s>
            <s xml:id="echoid-s10910" xml:space="preserve">ſimiliter I L in N O
              <lb/>
              <note position="left" xlink:label="note-0340-01" xlink:href="note-0340-01a" xml:space="preserve">f</note>
            minus erit, quàm S T in V X.</s>
            <s xml:id="echoid-s10911" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s10912" xml:space="preserve">Sed in hyperbola, quia quilibet axium minor eſt homologa diame-
              <lb/>
            tro coniugatarum; </s>
            <s xml:id="echoid-s10913" xml:space="preserve">igitur planum rectangulum ab axibus contentum mi-
              <lb/>
            nus eſt eo quod à duabus coniugatis continetur hoc igitur in hyperbo-
              <lb/>
            le manifeſtum eſt.</s>
            <s xml:id="echoid-s10914" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s10915" xml:space="preserve">In ellipſi autem, quia A C ad Q R maiorem proportionem habet;
              <lb/>
            </s>
            <s xml:id="echoid-s10916" xml:space="preserve">
              <note position="left" xlink:label="note-0340-02" xlink:href="note-0340-02a" xml:space="preserve">g</note>
            quàm I L ad N O per conuerſionem rationis, & </s>
            <s xml:id="echoid-s10917" xml:space="preserve">permutando maior A C
              <lb/>
            ad minorem I L minorem proportionem habebit, quàm differentia ipſa-
              <lb/>
            rum A C, Q R ad differentiam ipſarum I L & </s>
            <s xml:id="echoid-s10918" xml:space="preserve">N O; </s>
            <s xml:id="echoid-s10919" xml:space="preserve">& </s>
            <s xml:id="echoid-s10920" xml:space="preserve">propterea diffe-
              <lb/>
            rentia ipſarum A C, & </s>
            <s xml:id="echoid-s10921" xml:space="preserve">Q R maior erit differentia reliquarum I L, & </s>
            <s xml:id="echoid-s10922" xml:space="preserve">N
              <lb/>
            O. </s>
            <s xml:id="echoid-s10923" xml:space="preserve">Et ſimiliter oſtendetur, quod exceſſus I L ſuper N O maior ſit, quàm
              <lb/>
            exceſſus S T ſuper V X.</s>
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