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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[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.
[271.] Notæ in Propoſit. IX.
[272.] Notæ in Propoſit. X.
[273.] Notæ in Propoſit. XI.
[274.] Notæ in Propoſit. XV.
[275.] Notæ in Propoſit. XIX.
[276.] Notæ in Propoſit. XVI.
[277.] Notæ in Propoſit. XVIII.
[278.] Notæ in Propoſit. XVII.
[279.] Notæ in Propoſit. XX.
[280.] SECTIO QVARTA Continens Propoſit. Apollonij XII. XIII. XXIX. XVII. XXII. XXX. XIV. & XXV.
[281.] Notæ in Propoſit. XII.
[282.] Notæ in Propoſit. XIII.
[283.] Notæ in Propoſit. XXIX.
[284.] Notæ in Propoſit. XXX.
[285.] Notæ in Propoſit. XIV. & XXV.
[286.] Notæ in Propoſit. XXVII.
[287.] SECTIO QVINTA Continens Propoſit. XXI. XXVIII. XXXXII. XXXXIII. XXIV. & XXXVII.
[288.] PROPOSITIO XXI. & XXVIII.
[289.] PROPOSITIO XXVI
[290.] PROPOSITIO XXXXII.
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            aggregato differentiali ab-
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            ſciſſarum ramorum I L, I
              <lb/>
            M ab abſciſſa rami breuiſ-
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            ſimi.</s>
            <s xml:id="echoid-s1469" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s1470" xml:space="preserve">Pari modo in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s1471" xml:space="preserve">ellipſi quadratum I L ſu-
              <lb/>
            perat quadratum I M eodẽ
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            exceſſu, quo exemplar ap-
              <lb/>
              <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">Ex 9. 10. h.</note>
            plicatum ad H P ſuperat
              <lb/>
            exemplar applicatum ad H
              <lb/>
            L; </s>
            <s xml:id="echoid-s1472" xml:space="preserve">ſed differentia exem-
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            plarium applicatorum ad H
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            P, & </s>
            <s xml:id="echoid-s1473" xml:space="preserve">H Q æqualis eſt re-
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            ctangulo ſub P Q exceſſu
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            differentiali, & </s>
            <s xml:id="echoid-s1474" xml:space="preserve">recta linea
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            compoſita ex X m, & </s>
            <s xml:id="echoid-s1475" xml:space="preserve">u l, ad quam ſumma
              <lb/>
            differentialis P H Q eandem proportionem
              <lb/>
              <figure xlink:label="fig-0062-02" xlink:href="fig-0062-02a" number="36">
                <image file="0062-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0062-02"/>
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            habet, quam latus trãſuerſum ad ſummam
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            in hyperbola, & </s>
            <s xml:id="echoid-s1476" xml:space="preserve">ad differentiam in ellipſi
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            laterum tranſuerſi, & </s>
            <s xml:id="echoid-s1477" xml:space="preserve">recti, vt in nota
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            propoſitionis 5. </s>
            <s xml:id="echoid-s1478" xml:space="preserve">oſtenſum eſt; </s>
            <s xml:id="echoid-s1479" xml:space="preserve">igitur quadra-
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            tum I L ſuperat quadratum I M iam dicto
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            rectangulo ſub P Q, & </s>
            <s xml:id="echoid-s1480" xml:space="preserve">ſub X m, & </s>
            <s xml:id="echoid-s1481" xml:space="preserve">u l,
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            quod erat oſtendendum.</s>
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          <head xml:id="echoid-head76" xml:space="preserve">SECTIO IV.</head>
          <head xml:id="echoid-head77" xml:space="preserve">Continens Propoſit. VII.
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          & XII. Apollonij.</head>
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            <s xml:id="echoid-s1483" xml:space="preserve">SIfuerit menſura A
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            D minor com-
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              <note position="right" xlink:label="note-0062-02" xlink:href="note-0062-02a" xml:space="preserve">a</note>
            parata A E, (12.) </s>
            <s xml:id="echoid-s1484" xml:space="preserve">aut
              <lb/>
            ſit pars lineæ breuiſſi-
              <lb/>
            mæ, & </s>
            <s xml:id="echoid-s1485" xml:space="preserve">axis in ellipſi
              <lb/>
            ſit maior, erit A D
              <lb/>
            breuiſſimus ramorum
              <lb/>
            egredientium ex ori-
              <lb/>
            gine eius in omnibus
              <lb/>
            ſectionibus, vt ſunt F
              <lb/>
            D, G D, B D, C D,
              <lb/>
            & </s>
            <s xml:id="echoid-s1486" xml:space="preserve">proximior illi minor eſt remotiore, nempe F D quam G D, & </s>
            <s xml:id="echoid-s1487" xml:space="preserve">G
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            D, quàm B D.</s>
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