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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[291.] PROPOSITIO XXXXIII.
Page: 341 (302)
[292.] PROPOSITIO XXIV.
Page: 342 (303)
[293.] PROPOSITIO XXXVII.
Page: 343 (304)
[294.] Notę in Propoſit. XXVIII.
Page: 344 (305)
[295.] LEMMA. I.
Page: 345 (306)
[296.] Notę in Propoſit. XXI.
Page: 347 (308)
[297.] Notę in Propoſit. XXXXII.
Page: 349 (310)
[298.] Notæ in Propoſit. XXXXIII.
Page: 350 (311)
[299.] Notæ in Propoſit. XXIV.
Page: 352 (313)
[300.] SECTIO SEXTA Continens Propoſit. XXXIII. XXXIV. XXXV. & XXXVI. PROPOSITIO XXXIII.
Page: 353 (314)
[301.] PROPOSITIO XXXIV.
Page: 354 (315)
[302.] PROPOSITIO XXXV. & XXXVI.
Page: 355 (316)
[303.] In Sectionem VI.
Page: 356 (317)
[304.] LEMMA II.
Page: 357 (318)
[305.] LEMMA III.
Page: 357 (318)
[306.] LEMMA IV.
Page: 357 (318)
[307.] LEMMA V.
Page: 358 (319)
[308.] Notæ in Propof. XXXIII. & XXXIV.
Page: 359 (320)
[309.] Notæ in Propoſit. XXXV.
Page: 360 (321)
[310.] SECTIO SEPTIMA Continens Propoſit. XXXVIII. XXXIX. & XXXX. PROPOSITIO XXXVIII.
Page: 362 (323)
[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)
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            quadratum Q A; </s>
            <s xml:id="echoid-s9719" xml:space="preserve">ſed in hac poſtrema ſuppoſitione conceditur quadratum B Q
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            ad quadratum Q A habere maiorem proportionem, quàm H E ad E I; </s>
            <s xml:id="echoid-s9720" xml:space="preserve">igitur
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            O N ad N L maiorem proportionem habebit, quàm H E ad E I; </s>
            <s xml:id="echoid-s9721" xml:space="preserve">ſed quia co-
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            nus E R T ponitur continere ſectionem D E F: </s>
            <s xml:id="echoid-s9722" xml:space="preserve">habebit O V ad V R eandem
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            proportionem, quàm H E ad E I (vt ex 53. </s>
            <s xml:id="echoid-s9723" xml:space="preserve">primi deducitur, & </s>
            <s xml:id="echoid-s9724" xml:space="preserve">in hac pro-
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            poſitione denuò factum eſt): </s>
            <s xml:id="echoid-s9725" xml:space="preserve">igitur O N ad N L maiorem proportionem habebit
              <lb/>
            quàm O V ad V R; </s>
            <s xml:id="echoid-s9726" xml:space="preserve">oſtenſa autem fuit O N ad N X, vt O V ad V R; </s>
            <s xml:id="echoid-s9727" xml:space="preserve">ergo O
              <lb/>
            N ad N L maiorem proportionem habebit, quàm O N ad N X: </s>
            <s xml:id="echoid-s9728" xml:space="preserve">quod eſt abſur-
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            dum, nam N X minor eſt, quàm N L.</s>
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          <head xml:id="echoid-head311" xml:space="preserve">Notæ in Propoſit. XXXI.</head>
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            <s xml:id="echoid-s9730" xml:space="preserve">DEinde ſit ſectio elliptica A B C, & </s>
            <s xml:id="echoid-s9731" xml:space="preserve">tranſuerſa illius A C, & </s>
            <s xml:id="echoid-s9732" xml:space="preserve">erectus
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            A D, & </s>
            <s xml:id="echoid-s9733" xml:space="preserve">circunducamus ſuper A C in plano erecto ad ſectionis
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            planum A B C ſegmentum circuli, quod capiat angulum æqualem an-
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            gulo F: </s>
            <s xml:id="echoid-s9734" xml:space="preserve">&</s>
            <s xml:id="echoid-s9735" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9736" xml:space="preserve">Rurſus conus exhiberi debet ſimilis cono dato E F G, qui datam
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            ellipſim A B C contineat, ſitque axis tranſuerſus ellipſis C A, eiuſque latus
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            rectum A D.</s>
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            <s xml:id="echoid-s9738" xml:space="preserve">Quia H I in I K, quod eſt æquale ipſi C I in I A, ad quadratum I A
              <lb/>
              <note position="right" xlink:label="note-0296-02" xlink:href="note-0296-02a" xml:space="preserve">b</note>
            eſt, vt A C ad A D, & </s>
            <s xml:id="echoid-s9739" xml:space="preserve">C I in A I ad quadratum I K nempe K N ad
              <lb/>
            N O propter ſimilitudinem duorum triangulorum, & </s>
            <s xml:id="echoid-s9740" xml:space="preserve">ex A I, nempe N
              <lb/>
            K ad I K nempe A N vt parallelas conſtituamus lineas, & </s>
            <s xml:id="echoid-s9741" xml:space="preserve">ex his dua-
              <lb/>
            bus proportionibus componitur proportio quadrati N K ad A N in N O,
              <lb/>
            &</s>
            <s xml:id="echoid-s9742" xml:space="preserve">c. </s>
            <s xml:id="echoid-s9743" xml:space="preserve">Senſus huius textus valdè corrupti hic eſt. </s>
            <s xml:id="echoid-s9744" xml:space="preserve">Quia ex conſtructione H I ad
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            I K erat vt C A ad A D, & </s>
            <s xml:id="echoid-s9745" xml:space="preserve">ſumpta communi altitudine I K, erit </s>
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