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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[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)
[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)
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              <pb o="394" file="0432" n="433" rhead="Archimedis"/>
            & </s>
            <s xml:id="echoid-s13187" xml:space="preserve">circulus I H L tangat circulum A B C in H, & </s>
            <s xml:id="echoid-s13188" xml:space="preserve">circulum A D E in
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            L, & </s>
            <s xml:id="echoid-s13189" xml:space="preserve">perpendicularem in I. </s>
            <s xml:id="echoid-s13190" xml:space="preserve">Dico eſſe æqualem circulo, qui eſt in al-
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            tera parte. </s>
            <s xml:id="echoid-s13191" xml:space="preserve">Hoc modo, Educamus I M parallelam ipſi A C, & </s>
            <s xml:id="echoid-s13192" xml:space="preserve">iungamus
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            A H, quæ tranſibit per M, quemadmodum demonſtrauit Archimedes,
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              <note position="left" xlink:label="note-0432-01" xlink:href="note-0432-01a" xml:space="preserve">Prop. I.
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              huius.</note>
              <figure xlink:label="fig-0432-01" xlink:href="fig-0432-01a" number="500">
                <image file="0432-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0432-01"/>
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            & </s>
            <s xml:id="echoid-s13193" xml:space="preserve">producamus eam quouſque occurrat perpendiculari N G in N, & </s>
            <s xml:id="echoid-s13194" xml:space="preserve">
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            iungamus I A, quæ tranſibit per L, & </s>
            <s xml:id="echoid-s13195" xml:space="preserve">producamus illam ad O, & </s>
            <s xml:id="echoid-s13196" xml:space="preserve">iun-
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            gamus C O, O N, quæ erit linea recta, & </s>
            <s xml:id="echoid-s13197" xml:space="preserve">iungamus M E, quæ tranſi-
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            bit per L, & </s>
            <s xml:id="echoid-s13198" xml:space="preserve">iungamus C H, quæ tranſibit per I; </s>
            <s xml:id="echoid-s13199" xml:space="preserve">& </s>
            <s xml:id="echoid-s13200" xml:space="preserve">linea C O N pa-
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            a eſt lineæ E M, & </s>
            <s xml:id="echoid-s13201" xml:space="preserve">proportio A N ad N M, nempe proportio A
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            G ad I M eſt vt C A ad C E, ergo rectangulum A G in C E æquale
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            eſt rectangulo C A in I M; </s>
            <s xml:id="echoid-s13202" xml:space="preserve">& </s>
            <s xml:id="echoid-s13203" xml:space="preserve">quia G D eſt perpendicularis in duobus
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            circulis C D F, E D A ſuper duas diametros C F, E A, erit rectangu-
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            lum C G in G F æquale quadrato G D, & </s>
            <s xml:id="echoid-s13204" xml:space="preserve">rectangulum A G in G E
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            æquale etiam eſt illi, ergo rectangulum C G in G F æquale eſt rectan-
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            lo A G in G E, & </s>
            <s xml:id="echoid-s13205" xml:space="preserve">proportio C G ad G A eſt vt proportio E G ad G
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            F, immo vt proportio C E ad F A reſiduam; </s>
            <s xml:id="echoid-s13206" xml:space="preserve">ergo rectangulum C G in
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            F A, eſt æquale rectangulo C A in I M cui æquale eſt rectangulum G
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            A in C E. </s>
            <s xml:id="echoid-s13207" xml:space="preserve">Et ſi fuerit in altera parte circulus modo præfato eadem ra-
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            tione oſtendemus, quod reſtangulum C A in diametrum illius circuli
              <lb/>
            æquale ſit rectangulo C G in A F, & </s>
            <s xml:id="echoid-s13208" xml:space="preserve">oſtendetur quod duæ diametri duo-
              <lb/>
            rum circulorum ſint æquales.</s>
            <s xml:id="echoid-s13209" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div1130" type="section" level="1" n="362">
          <head xml:id="echoid-head454" xml:space="preserve">SCHOLIVM SECVNDVM ALKAVHI.</head>
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            <s xml:id="echoid-s13210" xml:space="preserve">POrrò ſecunda eſt hæc. </s>
            <s xml:id="echoid-s13211" xml:space="preserve">Dicit quod ſi duo ſemicirculi non
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            ſint tangentes, nec ſe mutuo ſecantes, ſed ſeparati, & </s>
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            perpendicularis tranſeat per concurſum duarum linearum </s>
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