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

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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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            <s xml:id="echoid-s2104" xml:space="preserve">Et ſimili modo conſtat, quod breuiſſima egrediens ex puncto L cadit
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            extra S L, &</s>
            <s xml:id="echoid-s2105" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2106" xml:space="preserve">Ad vitandam confuſionem figuræ, & </s>
            <s xml:id="echoid-s2107" xml:space="preserve">prolixitatem demonſtrationis
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            appoſui duas figuras, in quibus duo caſus ijſdem caracteribus notantur, itaque abſq;
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            <s xml:id="echoid-s2108" xml:space="preserve">nouo labore, ſi inſpiciatur ſecunda figura, ijſdem verbis prioris caſus, oſtendetur ca-
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            ſus ſecundus.</s>
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            <s xml:id="echoid-s2110" xml:space="preserve">Pariter demonſtrabitur, quemadmodum iam oſtenſumeſt, &</s>
            <s xml:id="echoid-s2111" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2112" xml:space="preserve">Pars ſecun-
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            da huius propoſitionis innuitur tantummodo pauciſsimis verbis; </s>
            <s xml:id="echoid-s2113" xml:space="preserve">quare maioris cla-
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            ritatis gratia integram demonſtrationem hìc afferre libuit.</s>
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          <head xml:id="echoid-head103" xml:space="preserve">Demonſtratio ſecundæ partis.</head>
          <head xml:id="echoid-head104" xml:space="preserve">PROPOSITIONIS LI.</head>
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            <s xml:id="echoid-s2115" xml:space="preserve">Eſto E D æqualis trutinæ H: </s>
            <s xml:id="echoid-s2116" xml:space="preserve">Dico ex concurſu E vnicum tantùm breui-
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            ſecantem ramum duci poſſe.</s>
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            <s xml:id="echoid-s2118" xml:space="preserve">In eadem ſigura, quia ex conſtructione H ad B G eſt, vt G F ad F D, ponitur verò
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            E D æqualis H; </s>
            <s xml:id="echoid-s2119" xml:space="preserve">ergo E D ad B G, ſeu D I ad I G (propter ſimilitudinem triangulo-
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            rum E D I, B G I) eſt, vt G F ad F D, & </s>
            <s xml:id="echoid-s2120" xml:space="preserve">componendo D G ad G I eſt, vt eadem G D
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            ad D F; </s>
            <s xml:id="echoid-s2121" xml:space="preserve">ideoque I G æqualis eſt D F, ſeu A C ſemierecto; </s>
            <s xml:id="echoid-s2122" xml:space="preserve">igitur B I eſt breuiſsima.</s>
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          <note position="right" xml:space="preserve">8. huius.</note>
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            <s xml:id="echoid-s2124" xml:space="preserve">Poſte a ducto quolibet ramo E K ſupra breuiſecantem E B (in prima figura, & </s>
            <s xml:id="echoid-s2125" xml:space="preserve">in-
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            fra in ſecunda) occurrente axi in R, & </s>
            <s xml:id="echoid-s2126" xml:space="preserve">ducta K M perpendiculari ad axim, quæ eum
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            ſecet in M, & </s>
            <s xml:id="echoid-s2127" xml:space="preserve">tangentem O B in P. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">Quoniam (vt dictum eſt) O F ſecatur </s>
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