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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[111.] Notæ in Propoſit. LXXII.
Page: 123 (85)
[112.] SECTIO DECIMAQVARTA Continens Propoſ. LXXIII. LXXIV. LXXV. LXXVI. & LXXVII. PROPOSITIO LXXIII.
Page: 126 (88)
[113.] PROPOSITO LXXIV.
Page: 128 (90)
[114.] PROPOSITO LXXV.
Page: 128 (90)
[115.] PROPOSITIO LXXVI.
Page: 129 (91)
[116.] PROPOSITIO LXXVII.
Page: 130 (92)
[117.] Notæ in Propoſit. LXXIII.
Page: 130 (92)
[118.] LEMMA XII.
Page: 130 (92)
[119.] Notæ in Propoſ. LXXIV.
Page: 134 (96)
[120.] Notæ in Propoſit. LXXV.
Page: 135 (97)
[121.] Notæ in Propoſ. LXXVI.
Page: 137 (99)
[122.] Notæ in Propoſit. LXXVII.
Page: 138 (100)
[123.] COROLLARIVM.
Page: 143 (105)
[124.] SECTIO DECIMAQVINTA Continens Propoſ. XXXXI. XXXXII. XXXXIII. Apollonij. PROPOSITIO XXXXI.
Page: 147 (109)
[125.] PROPOSITO XXXXII.
Page: 147 (109)
[126.] PROPOSITIO XXXXIII.
Page: 148 (110)
[127.] Notæ in Propoſ. XXXXI.
Page: 148 (110)
[128.] Notæ in Propoſ. XXXXII.
Page: 149 (111)
[129.] Notæ in Propoſit. XXXXIII.
Page: 149 (111)
[130.] SECTIO DECIMASEXTA Continens XVI. XVII. XVIII. Propoſ. Apollonij.
Page: 150 (112)
[131.] Notæ in Propoſit. XVI. XVII. XVIII.
Page: 152 (114)
[132.] SECTIO DECIMASEPTIMA Continens XIX. XX. XXI. XXII. XXIII. XXIV. & XXV. Propoſ. Apollonij. PROPOSITIO XIX.
Page: 154 (116)
[133.] PROPOSITIO XX. XXI. & XXII.
Page: 155 (117)
[134.] PROPOSITIO XXIII. & XXIV.
Page: 156 (118)
[135.] PROPOSITIO XXV.
Page: 157 (119)
[136.] Notæ in Propoſit. XIX.
Page: 157 (119)
[137.] Notæ in Propoſit. XX. XXI. XXII.
Page: 158 (120)
[138.] Notæ in Propoſ. XXIII. XXIV.
Page: 161 (123)
[139.] Notæ in Propoſ. XXXV.
Page: 161 (123)
[140.] SECTIO DECIMAOCTAVA Continens XXXII. XXXIII. XXXIV. XXXV. XXXVI. XXXVII. XXXVIII. XXXIX. XXXX. XXXXVII. XXXXVIII. Propoſit. Apollonij. PROPOSITIO XXXII.
Page: 162 (124)
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          <head xml:id="echoid-head166" xml:space="preserve">COROLLARIVM.</head>
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            <s xml:id="echoid-s4248" xml:space="preserve">HInc conſtat, ſupremam circuli peripheriam A Z cadere in locum à tan-
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            gente X A, & </s>
            <s xml:id="echoid-s4249" xml:space="preserve">coniſectionem B A contentum, infimam vero circuferen-
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            tiam A γ cadere ne dum infra tangentem, ſed etiam infra coniſectionem A G;
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            <s xml:id="echoid-s4250" xml:space="preserve">eoquod recta A X cadit extra circuli peripheriam A Z, quàm contingit in A,
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            & </s>
            <s xml:id="echoid-s4251" xml:space="preserve">eadem circumferentia A Z cadit extra ſectionem A B, quàm ſecat in A, vt
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            dictum eſt.</s>
            <s xml:id="echoid-s4252" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s4253" xml:space="preserve">Mirabile quidem hoc videri poterit aliquibus, qui contingentiæ angulos, quos
              <lb/>
            vocant, verè angulos eſſe cenſent; </s>
            <s xml:id="echoid-s4254" xml:space="preserve">nam hic duæ circumſerentiæ curuæ, conica
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            nimirum B A G, & </s>
            <s xml:id="echoid-s4255" xml:space="preserve">circularis Z A γ ſe mutuo ſecant in A, & </s>
            <s xml:id="echoid-s4256" xml:space="preserve">tamen ambo
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            tanguntur ab eadẽ recta linea A X in eodem puncto A, in quo illæ ſe mutuò ſecant.
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            </s>
            <s xml:id="echoid-s4257" xml:space="preserve">Vnde colligent etiam, quod anguli contingentiæ facti à coniſectione B A G, & </s>
            <s xml:id="echoid-s4258" xml:space="preserve">
              <lb/>
            recta linea X A non ſunt æquales inter ſe, quando punctum A in vertice axis
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            non exiſtit; </s>
            <s xml:id="echoid-s4259" xml:space="preserve">nam duo anguli contingentiæ circumſerentiæ circularis, & </s>
            <s xml:id="echoid-s4260" xml:space="preserve">rectæ
              <lb/>
            tangentis X A æquales ſunt inter ſe: </s>
            <s xml:id="echoid-s4261" xml:space="preserve">at angulus contingentiæ ſectionis conicæ ſu-
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            premus reſpiciens verticem B maior eſt angulo contingentiæ circularis, vt dictũ
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            eſt: </s>
            <s xml:id="echoid-s4262" xml:space="preserve">infimus vero angulus contingentiæ à ſectione conica, & </s>
            <s xml:id="echoid-s4263" xml:space="preserve">eadem tangente
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            contentus minor eſt eodem angulo contingentiæ circularis, & </s>
            <s xml:id="echoid-s4264" xml:space="preserve">propterea ſupremus
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            angnlus contingentiæ ſectionis conicæ maior erit inferiori.</s>
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            <s xml:id="echoid-s4266" xml:space="preserve">Sit perpendicularis D E
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              <note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">PROP.
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              II.
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              Addit.
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              Ex 51. 52.
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              53. huius.</note>
            minor trutina L, ſintque D
              <lb/>
            A, & </s>
            <s xml:id="echoid-s4267" xml:space="preserve">D C duo illi rami,
              <lb/>
            qui tantummodo breuiſecantes
              <lb/>
            eſſe poſſunt omnium ramorum
              <lb/>
            ex concurſu D ad ſectionem
              <lb/>
            B C cadentium; </s>
            <s xml:id="echoid-s4268" xml:space="preserve">atque cen-
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            tro D, interuallo D A deſcri-
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            batur circulus Z A γ; </s>
            <s xml:id="echoid-s4269" xml:space="preserve">pari-
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            terque centro D, interuallo D
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            C deſcribatur circulus O C Q;
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            <s xml:id="echoid-s4270" xml:space="preserve">ducanturque rectæ X P, M
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            P contingentes coniſectionem
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            in A, & </s>
            <s xml:id="echoid-s4271" xml:space="preserve">C. </s>
            <s xml:id="echoid-s4272" xml:space="preserve">Dico, circulũ
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            Z A γ contingere coniſectio-
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            nem in A, & </s>
            <s xml:id="echoid-s4273" xml:space="preserve">extra ipſam
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            cadere, at circulum O C Q contingere eandem coniſectionem in C, & </s>
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            intra ipſam cadere.</s>
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            <s xml:id="echoid-s4276" xml:space="preserve">Ducantur quilibet rami D F, D G ſupra, & </s>
            <s xml:id="echoid-s4277" xml:space="preserve">infra breuiſecantem D A, ſe-
              <lb/>
            cantes circulum Z A γ in Z, & </s>
            <s xml:id="echoid-s4278" xml:space="preserve">γ; </s>
            <s xml:id="echoid-s4279" xml:space="preserve">pariterque ducantur quilibet rami D </s>
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