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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[261.] Notæ in Propoſit. I.
Page: 312 (274)
[262.] Notæ in Propoſit. V. & XXIII.
Page: 313 (275)
[263.] SECTIO SECVNDA Continens Propoſit. II. III. IV. VI. & VII. Apollonij. PROPOSITIO II. & III.
Page: 314 (276)
[264.] PROPOSITIO IV.
Page: 315 (277)
[265.] PROPOSITIO VI. & VII.
Page: 316 (278)
[266.] Notæ in Propoſit. II. III.
Page: 317 (279)
[267.] Notæ in Propoſit. IV.
Page: 318 (280)
[268.] Notæ in Propoſit. VI. & VII.
Page: 319 (281)
[269.] SECTIO TERTIA Continens Propoſit. Apollonij VIII. IX. X. XI. XV. XIX. XVI. XVIII. XVII. & XX.
Page: 320 (282)
[270.] Notæ in Propoſit. VIII.
Page: 323 (285)
[271.] Notæ in Propoſit. IX.
Page: 324 (286)
[272.] Notæ in Propoſit. X.
Page: 325 (287)
[273.] Notæ in Propoſit. XI.
Page: 325 (287)
[274.] Notæ in Propoſit. XV.
Page: 326 (288)
[275.] Notæ in Propoſit. XIX.
Page: 326 (288)
[276.] Notæ in Propoſit. XVI.
Page: 327 (289)
[277.] Notæ in Propoſit. XVIII.
Page: 327 (289)
[278.] Notæ in Propoſit. XVII.
Page: 328 (290)
[279.] Notæ in Propoſit. XX.
Page: 328 (290)
[280.] SECTIO QVARTA Continens Propoſit. Apollonij XII. XIII. XXIX. XVII. XXII. XXX. XIV. & XXV.
Page: 329 (291)
[281.] Notæ in Propoſit. XII.
Page: 332 (293)
[282.] Notæ in Propoſit. XIII.
Page: 333 (294)
[283.] Notæ in Propoſit. XXIX.
Page: 334 (295)
[284.] Notæ in Propoſit. XXX.
Page: 334 (295)
[285.] Notæ in Propoſit. XIV. & XXV.
Page: 335 (296)
[286.] Notæ in Propoſit. XXVII.
Page: 335 (296)
[287.] SECTIO QVINTA Continens Propoſit. XXI. XXVIII. XXXXII. XXXXIII. XXIV. & XXXVII.
Page: 337 (298)
[288.] PROPOSITIO XXI. & XXVIII.
Page: 338 (299)
[289.] PROPOSITIO XXVI
Page: 339 (300)
[290.] PROPOSITIO XXXXII.
Page: 340 (301)
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          <head xml:id="echoid-head166" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <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
              <lb/>
            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
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            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.
                <lb/>
              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-
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            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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