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; </s>
            <s xml:id="echoid-s10232" xml:space="preserve">igitur rectangulum F D A æquale eſt
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            rectangulo D A E vna cum quadrato D A;
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            <s xml:id="echoid-s10233" xml:space="preserve">ſed quadratum ordinatim ad axim applicatæ
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              <note position="right" xlink:label="note-0313-01" xlink:href="note-0313-01a" xml:space="preserve">2 1. lib. 1.</note>
            B D æquale eſt rectangulo D A E ſub abſciſ-
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            ſa & </s>
            <s xml:id="echoid-s10234" xml:space="preserve">latere recto contento; </s>
            <s xml:id="echoid-s10235" xml:space="preserve">igitur rectangu-
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            lum F D A æquale eſt duobus quadratis B D,
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            & </s>
            <s xml:id="echoid-s10236" xml:space="preserve">D A: </s>
            <s xml:id="echoid-s10237" xml:space="preserve">eſtquè quadratum A B ſubtenden-
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            tis rectum angulum D æquale duobus quadra-
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            tis B D, & </s>
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            <s xml:id="echoid-s10239" xml:space="preserve">igitur quadratum ſubten-
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            ſæ A B æquale eſt rectangulo A D E ſub ab-
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            ſciſſa D A, & </s>
            <s xml:id="echoid-s10240" xml:space="preserve">ſub D F, quæ æqualis eſt ei-
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            dem abſciſſæ cum latere recto.</s>
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          <head xml:id="echoid-head328" xml:space="preserve">Notæ in Propoſit. V. & XXIII.</head>
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            <s xml:id="echoid-s10242" xml:space="preserve">ET diametri G C remotioris ab axe erectus C I maior eſt erecto B H
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              <note position="left" xlink:label="note-0313-02" xlink:href="note-0313-02a" xml:space="preserve">a</note>
            diametri propinquioris B F, &</s>
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            <s xml:id="echoid-s10244" xml:space="preserve">Videtur hæc 23. </s>
            <s xml:id="echoid-s10245" xml:space="preserve">propoſitio deficiens;
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            <s xml:id="echoid-s10246" xml:space="preserve">cum omnino inueriſimile ſit Apollonium non animaduertiſſe rem adeo facilem; </s>
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            quod nimirum diametri G C remotioris ab axe erectus C I maior ſit erecto B
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            H diametri B F proximioris quadruplo differentiæ axis abſciſſarum potentium
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            à terminis diametrorum ad axim ductorum.</s>
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            <s xml:id="echoid-s10249" xml:space="preserve">Quare A E cum duplo K D, nempe cum quadruplo A D eſt æqualis
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            duplo K N, nempe dimidio B H, &</s>
            <s xml:id="echoid-s10250" xml:space="preserve">c. </s>
            <s xml:id="echoid-s10251" xml:space="preserve">Zuoniam B H latus rectum diame-
              <lb/>
              <note position="right" xlink:label="note-0313-04" xlink:href="note-0313-04a" xml:space="preserve">49. lib. 1.</note>
            tri B F ad duplum contingentis B K eſt vt M B ad B L, ſed (propter æqui-
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            diſtantes, & </s>
            <s xml:id="echoid-s10252" xml:space="preserve">ſimilitudinem triangulorum L B M, & </s>
            <s xml:id="echoid-s10253" xml:space="preserve">K N B) vt M B ad B
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            L, ita eſt duplum N K ad duplum R B; </s>
            <s xml:id="echoid-s10254" xml:space="preserve">ergo latus rectum B H æquale eſt du-
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            plo K N; </s>
            <s xml:id="echoid-s10255" xml:space="preserve">ſed prius oſtenſum eſt quod D A æqualis eſt medietati ipſius D K, & </s>
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              <note position="right" xlink:label="note-0313-05" xlink:href="note-0313-05a" xml:space="preserve">35. .lib. 1.</note>
            D N æqualis medietati ipſius A E; </s>
            <s xml:id="echoid-s10257" xml:space="preserve">igitur duplum K N æquale eſt duplo K D,
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            ſeu quadruplo A D cum duplo D N, ſeu cum A E.</s>
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            <s xml:id="echoid-s10259" xml:space="preserve">Et A O maior eſt, quàm A D; </s>
            <s xml:id="echoid-s10260" xml:space="preserve">ergo erectus diametri C G remotioris
              <lb/>
              <note position="left" xlink:label="note-0313-06" xlink:href="note-0313-06a" xml:space="preserve">c</note>
            maior eſt quàm erectus B F proximioris, &</s>
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            <s xml:id="echoid-s10262" xml:space="preserve">Addidi in bac concluſione
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            verba bæc (quadruplo D O differētiæ abſciſſarum) quæ videntur deficere. </s>
            <s xml:id="echoid-s10263" xml:space="preserve">Ma-
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            nifeſtum enim eſt, quod C I latus rectum diametri C G ab axe remotioris ſu-
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            perat latus rectum B H diametri F B axi propinguioris quadruplo D O diffe-
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            rentiæ abſeiſſarum axis ab ordinatis à verticibus earũdem diametrorum ductis;
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            <s xml:id="echoid-s10264" xml:space="preserve">nam B H æqualis oſtenſa eſt E A vna cum quadruplo A D, eademque ratione
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            C I æqualis eſt eidem axis lateri recto E A cum quadruplo A O; </s>
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            C I ſupra B H erit æqualis quadruplo differentiæ D O.</s>
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