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 O (cum C D, & </s>
            <s xml:id="echoid-s9981" xml:space="preserve">H B ſint parallelæ, atque D O ſit parallelogrammum) com-
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            ponunt verò hæ duæ proportiones rationem quadrati C A ad rectangulum F
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            A O: </s>
            <s xml:id="echoid-s9982" xml:space="preserve">ergo vt rectangulum A H C ad quadratum H B; </s>
            <s xml:id="echoid-s9983" xml:space="preserve">ita eſt quadratum C A
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            ad rectangulum F A O, & </s>
            <s xml:id="echoid-s9984" xml:space="preserve">pro-
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            pterea vt X ad A F, ita erit qua-
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            dratum A C ad rectangulum F A
              <lb/>
            O, ſed vt F A ad A D (ſum-
              <lb/>
            ptis æqualibus altitudinibus A O,
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            C D) ita eſt rectangulum F A O
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            ad rectangulum A D C; </s>
            <s xml:id="echoid-s9985" xml:space="preserve">quare ex
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            æquali X ad A D erit vt quadra-
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            tum A C ad rectangulum A D C;
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            </s>
            <s xml:id="echoid-s9986" xml:space="preserve">tandem vt Z latus rectum para-
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            boles A M ad D A ita eſt quadra-
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              <note position="left" xlink:label="note-0304-01" xlink:href="note-0304-01a" xml:space="preserve">II. lib. I.</note>
            tum A C ad rectangulum A D C;
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            </s>
            <s xml:id="echoid-s9987" xml:space="preserve">igitur X, & </s>
            <s xml:id="echoid-s9988" xml:space="preserve">Z ad eandem D A
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            habent eandem proportionem quàm
              <lb/>
            quadr atum A C ad rectangulum
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            A D C, & </s>
            <s xml:id="echoid-s9989" xml:space="preserve">propterea latera recta
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            X, & </s>
            <s xml:id="echoid-s9990" xml:space="preserve">Z æqualia ſunt inter ſe. </s>
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            Et quoniam in quolibet caſu ſectio-
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            nis conicæ A N latus rectum X
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            ſemper æquale eſt Z lateri recto
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            vnius eiuſdemq; </s>
            <s xml:id="echoid-s9992" xml:space="preserve">paraboles A M; </s>
            <s xml:id="echoid-s9993" xml:space="preserve">
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            ergo latera recta X reliquarum
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            omnium ſectionum æqualia ſunt
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            inter ſe, licet ſectiones illæ ſint
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            inæquales, & </s>
            <s xml:id="echoid-s9994" xml:space="preserve">habeant latera trã-
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            ſuerſa inæqualia, imò neque eiuſ-
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            dem ſpeciei ſint. </s>
            <s xml:id="echoid-s9995" xml:space="preserve">Quod erat pro-
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            poſitum.</s>
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            <s xml:id="echoid-s9997" xml:space="preserve">Admiratione dignum præcipuè
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            eſt in hac propoſitione, quod ſi ſe-
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            ctio A N fuerit circulus, vnicus
              <lb/>
            tantummodò erit; </s>
            <s xml:id="echoid-s9998" xml:space="preserve">nam circuli la-
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            tus rectum X æquale erit eius dia-
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            metro, ſeu axi tranſuerſo A F; </s>
            <s xml:id="echoid-s9999" xml:space="preserve">eſt-
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            que ſemper latus rectum eiuſdem
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            menſuræ, vt aſtenſum eſt; </s>
            <s xml:id="echoid-s10000" xml:space="preserve">igitur
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            circuli diameter F A idem ſemper erit; </s>
            <s xml:id="echoid-s10001" xml:space="preserve">& </s>
            <s xml:id="echoid-s10002" xml:space="preserve">propterea circulus, qui à tali plano
              <lb/>
            generari poteſt ſingularis erit, nimirum ille, qui in vnico cono A B C efficit
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            triangula per axim ſimilia, & </s>
            <s xml:id="echoid-s10003" xml:space="preserve">ſubcontraria B A C, & </s>
            <s xml:id="echoid-s10004" xml:space="preserve">B F A. </s>
            <s xml:id="echoid-s10005" xml:space="preserve">Manifeſtum
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            quoq; </s>
            <s xml:id="echoid-s10006" xml:space="preserve">eſt parabolem A M ſingularem eße, nam ſupponitur idem circulus baſis A
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            C, & </s>
            <s xml:id="echoid-s10007" xml:space="preserve">in plano per axim coni cõmune latus A D B ſemper eoſdẽ angulos D A E,
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            & </s>
            <s xml:id="echoid-s10008" xml:space="preserve">D A C efficere conceditur; </s>
            <s xml:id="echoid-s10009" xml:space="preserve">igitur vt ſectio A M ſit parabole neceßariò recta à
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            puncto C duci debet parallela diametro par aboles A E; </s>
            <s xml:id="echoid-s10010" xml:space="preserve">cum ergo in triangulo per
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            axim D A C detur baſis A C inuariabilis quia circulus vnicus ſupponitur </s>
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