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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[311.] PROPOSITIO XXXIX.
Page: 363 (324)
[312.] PROPOSITIO XXXX.
Page: 364 (325)
[313.] In Sectionem VII. Propoſit: XXXVIII. XXXIX. & XXXX. LEMMA VI.
Page: 366 (327)
[314.] LEMMA VII.
Page: 366 (327)
[315.] LEMMA VIII.
Page: 367 (328)
[316.] LEMMA IX.
Page: 367 (328)
[317.] Notæ in Propoſit. XXXVIII. XXXIX.
Page: 369 (330)
[318.] Notæ in Propoſit. XXXX.
Page: 369 (330)
[319.] SECTIO OCTAVA Continens Propoſit. XXXXIIII. XXXXV. & XXXXVI.
Page: 372 (333)
[320.] PROPOSITIO XXXXVI.
Page: 374 (335)
[321.] In Sectionem VIII. Propoſit. XXXXIIII. XXXXV. & XXXXVI. LEMM A.X.
Page: 375 (336)
[322.] LEMM A XI.
Page: 375 (336)
[323.] LEMM A XII.
Page: 376 (337)
[324.] Notæ in Propoſit. XXXXIV. & XXXXV.
Page: 378 (339)
[325.] Notæ in Propoſit. XXXXVI.
Page: 378 (339)
[326.] SECTIO NONA Continens Propoſit. XXXXI. XXXXVII. & XXXXVIII.
Page: 380 (341)
[327.] PROPOSITIO XXXXI.
Page: 382 (343)
[328.] PROPOSITIO XXXXVII.
Page: 383 (344)
[329.] PROPOSITIO XXXXVIII.
Page: 386 (347)
[330.] In Sectionem IX. Propoſit. XXXXI. XXXXVII. & XXXXVIII. LEMMA. XIII.
Page: 388 (349)
[331.] LEMMA XIV.
Page: 389 (350)
[332.] LEMMA XV.
Page: 389 (350)
[333.] Notæ in Propoſit. XXXXI.
Page: 392 (353)
[334.] Notæ in Propoſit. XXXXVII.
Page: 393 (354)
[335.] Notæ in Propoſit. XXXXVIII.
Page: 394 (355)
[336.] SECTIO DECIMA Continens Propoſit. XXXXIX. XXXXX. & XXXXXI.
Page: 397 (358)
[337.] In Sectionem X. Propoſit. XXXXIX. XXXXX. & XXXXXI. LEMMA XVI.
Page: 400 (361)
[338.] LEMMA XVII.
Page: 400 (361)
[339.] LEMMA XVIII.
Page: 403 (364)
[340.] Notæ in Propoſit. XXXXIX.
Page: 404 (365)
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            producto ex G E, & </s>
            <s xml:id="echoid-s11318" xml:space="preserve">G H in E H, erit M H in H E cum E G, atquè
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            G H in H E, nempe ſumma M G, G E, quæ eſt æqualis ipſi f in E H
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            minus erit, quàm quadratum H G cum aggregato E G, G H in E H,
              <lb/>
            quæ ſunt æqualia quadrato G E; </s>
            <s xml:id="echoid-s11319" xml:space="preserve">igitur f in E H minus eſt quadrato E
              <lb/>
            G. </s>
            <s xml:id="echoid-s11320" xml:space="preserve">Poſtea vti prius dictum eſt oſtendetur, quod quadratum A C ad
              <lb/>
            quadratum P R maiorem proportionem habet, quàm ad quadratum I K:
              <lb/>
            </s>
            <s xml:id="echoid-s11321" xml:space="preserve">& </s>
            <s xml:id="echoid-s11322" xml:space="preserve">propterea P R minor eſt, quàm I K. </s>
            <s xml:id="echoid-s11323" xml:space="preserve">Non aliter oſtendetur quod I K
              <lb/>
            minor ſit, quàm A F. </s>
            <s xml:id="echoid-s11324" xml:space="preserve">Ponatur poſtea diameter S T extra locum inter
              <lb/>
            P Q, A C compræhenſum, ducaturque C X ei parallela, & </s>
            <s xml:id="echoid-s11325" xml:space="preserve">ad axim
              <lb/>
            perpendicularis X V. </s>
            <s xml:id="echoid-s11326" xml:space="preserve">Igitur V H M maius erit quàm quadratum H G,
              <lb/>
              <figure xlink:label="fig-0355-01" xlink:href="fig-0355-01a" number="421">
                <image file="0355-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0355-01"/>
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            & </s>
            <s xml:id="echoid-s11327" xml:space="preserve">eodem modo procedendo, tandem oſtendetur quod quadratum A C ad
              <lb/>
            quadratum S Z minorem proportionem habet, quàm ad quadratum P
              <lb/>
            R, & </s>
            <s xml:id="echoid-s11328" xml:space="preserve">ideo P R minor erit quàm S Z. </s>
            <s xml:id="echoid-s11329" xml:space="preserve">Non ſecus oſtendetur quod S Z
              <lb/>
            minor eſt erecto cuiuslibet inclinati cadentis ad partem S T extra illam.
              <lb/>
            </s>
            <s xml:id="echoid-s11330" xml:space="preserve">Itaque demonſtratum eſt, quod P R minor ſit erecto cuiuslibet diametri
              <lb/>
            ſectionis cadentis ad vtraſque partes ipſius P Q verſus A, & </s>
            <s xml:id="echoid-s11331" xml:space="preserve">X, & </s>
            <s xml:id="echoid-s11332" xml:space="preserve">ere-
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            cti proximiores diametro P Q minores ſunt remotioribus. </s>
            <s xml:id="echoid-s11333" xml:space="preserve">Et hoc erat
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            propoſitum.</s>
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          <head xml:id="echoid-head376" xml:space="preserve">In Sectionem VI.</head>
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            <s xml:id="echoid-s11335" xml:space="preserve">IN Expoſitione ſequentium Propoſitionum difficultas, quæ à nimia prolixitate
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            oritur, ineuitabilis eſt, niſi Methodus in textu ſeruata aliquantisper relin-
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            quatur: </s>
            <s xml:id="echoid-s11336" xml:space="preserve">propterea non nulla lemmata præmittam, ex quibus ſemel demonſtra-
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            tis caſus omnes ſequentium propoſitionum facillime, & </s>
            <s xml:id="echoid-s11337" xml:space="preserve">breuiſſime deducnntur.</s>
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