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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[81.] PROPOSITIO LX.
Page: 100 (62)
[82.] PROPOSITIO LXI.
Page: 100 (62)
[83.] Notæ in Propoſit. LVIII.
Page: 101 (63)
[84.] Notæ in Propoſit. LIX. LXII. & LXIII.
Page: 102 (64)
[85.] Notæ in Propoſit. LX.
Page: 103 (65)
[86.] Notæ in Propoſit. LXI.
Page: 103 (65)
[87.] SECTIO DECIMA Continens Propof. XXXXIV. XXXXV. Apollonij.
Page: 105 (67)
[88.] PROPOSITIO XXXXIV.
Page: 105 (67)
[89.] PROPOSITIO XXXXV.
Page: 106 (68)
[90.] Notæ in Propoſ. XXXXIV.
Page: 106 (68)
[91.] Notæ in Propoſ. XLV.
Page: 107 (69)
[92.] SECTIO VNDECIMA Continens Propoſ. LXVIII. LXIX. LXX. & LXXI. Apollonij. PROPOSITIO LXVIII. LXIX.
Page: 108 (70)
[93.] PROPOSITIO LXX.
Page: 109 (71)
[94.] PROPOSITIO LXXI.
Page: 109 (71)
[95.] Notæ in Propoſit. LXVIII. LXIX. LXX. & LXXI.
Page: 109 (71)
[96.] SECTIO DVODECIMA Continens XXIX. XXX. XXXI. Propoſ. Appollonij.
Page: 110 (72)
[97.] Notæ in Propoſit. XXIX. XXX. & XXXI.
Page: 111 (73)
[98.] SECTIO DECIMATERTIA Continens Propoſ. LXIV. LXV. LXVI. LXVII. & LXXII. Apollonij. PROPOSITIO LXIV. LXV.
Page: 112 (74)
[99.] PROPOSITIO LXVI.
Page: 113 (75)
[100.] PROPOSITIO LXVII.
Page: 114 (76)
[101.] PROPOSITIO LXXII.
Page: 115 (77)
[102.] MONITVM.
Page: 116 (78)
[103.] LEMMA IX.
Page: 116 (78)
[104.] LEMMA X.
Page: 116 (78)
[105.] LEMMA XI.
Page: 117 (79)
[106.] Notæ in Propoſ. LXIV. & LXV.
Page: 117 (79)
[107.] Notæ in Propoſ. LXVI.
Page: 120 (82)
[108.] Ex demonſtratione præmiſſa propoſitionum 64. & 65. deduci poteſt conſectarium, à quo notæ ſubſe-quentes breuiores reddantur. COROLLARIVM PROPOSIT. LXIV. & LXV.
Page: 120 (82)
[109.] Notæ in Propoſ. LXVII.
Page: 121 (83)
[110.] COROLLARIVM PROPOSIT. LXVII.
Page: 122 (84)
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            perpendicularis eſt ad circuli diametrum C A, & </s>
            <s xml:id="echoid-s9905" xml:space="preserve">propterea A D, planorum
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            H A I, & </s>
            <s xml:id="echoid-s9906" xml:space="preserve">A C M communis ſectio, tanget circulum A C, & </s>
            <s xml:id="echoid-s9907" xml:space="preserve">ideo ſuperficiem
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            ipſam conicam, & </s>
            <s xml:id="echoid-s9908" xml:space="preserve">ſectionem in ea exiſtentem continget; </s>
            <s xml:id="echoid-s9909" xml:space="preserve">& </s>
            <s xml:id="echoid-s9910" xml:space="preserve">diameter A L non
              <lb/>
            erit perpendicularis ad tangentem, ſeu ordinatim applicatam A D per verticem
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            A, alias A L eſſet axis, quod non ponitur. </s>
            <s xml:id="echoid-s9911" xml:space="preserve">Deinde in plano D A B ex A du-
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            catur recta linea A E perpendicularis ad A D ſupra, vel infra circulum, & </s>
            <s xml:id="echoid-s9912" xml:space="preserve">
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            vertice quolibet puncto E ſumpto in recta linea A E, & </s>
            <s xml:id="echoid-s9913" xml:space="preserve">baſi circulo A C M fiat
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            alter conus E A C, in cuius ſuperficie planũ D A H I deſignet ſectionẽ F A G, & </s>
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            in ea triangulum per axim E A C efficiat diametrum A K: </s>
            <s xml:id="echoid-s9915" xml:space="preserve">Et quia eadem re-
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            cta linea D A perpendicularis eſt ad A C, atque ad A E ſe ſecantes in A; </s>
            <s xml:id="echoid-s9916" xml:space="preserve">ergo
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            D A perpendicularis eſt ad planum C E A, atque planum D A C extenſum
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            per perpendicularem D A, erit quoque perpendiculare ad planum trianguli per
              <lb/>
            axim C E A, quare triangulum per axim efficiet diametrum A K, quæ erit
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            axis ſectionis F A G, atque D A perpendicularis erit ad axim A K exiſtentem
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            in plano C E A, ad quod D A eſt perpendicularis, & </s>
            <s xml:id="echoid-s9917" xml:space="preserve">cum ea conuenit: </s>
            <s xml:id="echoid-s9918" xml:space="preserve">quare
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            D A ordinatim ad axim applicata perverticem A tanget ſectionem F A G, quæ
              <lb/>
              <note position="right" xlink:label="note-0301-01" xlink:href="note-0301-01a" xml:space="preserve">32. lib. I.</note>
            prius in eodem puncto A tangebat ſectionem H A I in eodem plano exiſtentem;
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            <s xml:id="echoid-s9919" xml:space="preserve">& </s>
            <s xml:id="echoid-s9920" xml:space="preserve">propterea eadem recta A D vtramque ſectionem tangit in puncto A. </s>
            <s xml:id="echoid-s9921" xml:space="preserve">Poſtea
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            coniungatur recta linea B E, & </s>
            <s xml:id="echoid-s9922" xml:space="preserve">quia rectæ lineæ B A, A D, A E ſunt in eo-
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            dem plano tangente vtrumque conum (cum per vertices B, & </s>
            <s xml:id="echoid-s9923" xml:space="preserve">E, atque per D
              <lb/>
            A contingentem circulum baſis communis ducatur) & </s>
            <s xml:id="echoid-s9924" xml:space="preserve">E A, & </s>
            <s xml:id="echoid-s9925" xml:space="preserve">B A angulum
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            conſtituunt, cum E A poſita ſit perpendicularis ad D A, at B A ad eandem ſit
              <lb/>
            inclinata, & </s>
            <s xml:id="echoid-s9926" xml:space="preserve">exiſtunt in eodem plano; </s>
            <s xml:id="echoid-s9927" xml:space="preserve">ergo recta B E parallela eſt, aut ſecat
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            contingentem D A extra circulum vt in D. </s>
            <s xml:id="echoid-s9928" xml:space="preserve">Poterit igitur ex propoſ. </s>
            <s xml:id="echoid-s9929" xml:space="preserve">15. </s>
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            tarum duci per rectam B E planum aliud B E M V vtrumq; </s>
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