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

Table of contents

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[321.] In Sectionem VIII. Propoſit. XXXXIIII. XXXXV. & XXXXVI. LEMM A.X.
[322.] LEMM A XI.
[323.] LEMM A XII.
[324.] Notæ in Propoſit. XXXXIV. & XXXXV.
[325.] Notæ in Propoſit. XXXXVI.
[326.] SECTIO NONA Continens Propoſit. XXXXI. XXXXVII. & XXXXVIII.
[327.] PROPOSITIO XXXXI.
[328.] PROPOSITIO XXXXVII.
[329.] PROPOSITIO XXXXVIII.
[330.] In Sectionem IX. Propoſit. XXXXI. XXXXVII. & XXXXVIII. LEMMA. XIII.
[331.] LEMMA XIV.
[332.] LEMMA XV.
[333.] Notæ in Propoſit. XXXXI.
[334.] Notæ in Propoſit. XXXXVII.
[335.] Notæ in Propoſit. XXXXVIII.
[336.] SECTIO DECIMA Continens Propoſit. XXXXIX. XXXXX. & XXXXXI.
[337.] In Sectionem X. Propoſit. XXXXIX. XXXXX. & XXXXXI. LEMMA XVI.
[338.] LEMMA XVII.
[339.] LEMMA XVIII.
[340.] Notæ in Propoſit. XXXXIX.
[341.] Notæ in Propoſit. XXXXX.
[342.] Notæ in Propoſit. XXXXXI.
[343.] SECTIO VNDECIMA Continens Propoſit. XXXII. & XXXI. Apollonij.
[344.] Notæ in Propoſit. XXXI. & XXXII.
[345.] LIBRI SEPTIMI FINIS.
[346.] LIBER ASSVMPTORVM INTERPRETE THEBIT BEN-KORA EXPONENTE AL MOCHT ASSO Ex Codice Arabico manuſcripto SERENISS. MAGNI DV CIS ETRVRIÆ, ABRAHAMVS ECCHELLENSIS Latinè vertit. IO: ALFONSVS BORELLVS Notis Illuſtrauit.
[347.] Præfatio ad Lectorem.
[348.] MISERICORDIS MISERATORIS CVIVS OPEM IMPLORAMVS. LIBER ASSVMPTORVM ARCHIMEDIS, INTERPRETE THEBIT BEN-KORA, Et exponente Doctore ALMOCHTASSO ABILHASAN, Halì Ben-Ahmad Noſuenſi. PROPOSITIONES SEXDECIM.
[349.] PROPOSITIO I.
[350.] SCHOLIVM ALMOCHTASSO.
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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
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            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,
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            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>
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          <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/>
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                <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"/>
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          <p>
            <s xml:id="echoid-s10915" xml:space="preserve">In ellipſi autem, quia A C ad Q R maiorem proportionem habet;
              <lb/>
            </s>
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              <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-
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            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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