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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            A F ad A C, & </s>
            <s xml:id="echoid-s10275" xml:space="preserve">vt A G ad G C; </s>
            <s xml:id="echoid-s10276" xml:space="preserve">ergo H E ad E C eſt vt A G ad G
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            C; </s>
            <s xml:id="echoid-s10277" xml:space="preserve">& </s>
            <s xml:id="echoid-s10278" xml:space="preserve">componendo in hyperbolis, & </s>
            <s xml:id="echoid-s10279" xml:space="preserve">diuidendo in ellipſibus, deinde
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            comparando homologorum differentias in duabus figuris prioribus, & </s>
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            ſummas homologorum in reliquis, fiet A H ad G E, vt C A ad C G;
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            </s>
            <s xml:id="echoid-s10281" xml:space="preserve">ergo A H in A E; </s>
            <s xml:id="echoid-s10282" xml:space="preserve">nempe quadratum A B ad G E in A E eſt vt C A
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            inclinatus, ſiue tranſuerſus ad C G præſectam. </s>
            <s xml:id="echoid-s10283" xml:space="preserve">Quod fuerat propoſi-
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            tum.</s>
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          <head xml:id="echoid-head332" xml:space="preserve">PROPOSITIO IV.</head>
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            <s xml:id="echoid-s10285" xml:space="preserve">SI hyperbolen, aut ellipſin A B tangat recta linea I M in I,
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            & </s>
            <s xml:id="echoid-s10286" xml:space="preserve">occurrat axi A C in M; </s>
            <s xml:id="echoid-s10287" xml:space="preserve">vtique ipſius I M quadratum
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            ad quadratum ſemidiametri ND coniugatæ ipſi I L habebit eã-
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            dem proportionem, quàm axis contenta M S ad eius inuerſam
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            S D.</s>
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            <s xml:id="echoid-s10289" xml:space="preserve">Educantur A Q, M R perpendiculares ad axim vſque ad I L, ponatur-
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            que linea P, quæ ad I M eandem proportionem habeat, quàm K I ad
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            Q I, ſeu eandem, quàm habet M I ad I R; </s>
            <s xml:id="echoid-s10290" xml:space="preserve">Ergo P eſt ſemiſſis erecti
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            diametri I L (52. </s>
            <s xml:id="echoid-s10291" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s10292" xml:space="preserve">atque D N dimidium coniugatæ diametri N O
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            poterit P in I D, atque I M poterit P in I R; </s>
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            <s xml:id="echoid-s10294" xml:space="preserve">ideo I R ad I D,
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            nempe M S contenta ad S D inuerſam eandem proportionem habet, quã
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            quadratum tangentis I M ad quadratum N D ſemiſſis coniugatæ ipſius I
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            L. </s>
            <s xml:id="echoid-s10295" xml:space="preserve">Et hoc erat propoſitum.</s>
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