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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            D H minorem proportionem habet quàm A C, & </s>
            <s xml:id="echoid-s1188" xml:space="preserve">propterea B C ad E H minorem
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            proportionem habebit quàm A C ad D H.</s>
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            <s xml:id="echoid-s1190" xml:space="preserve">Tertiò ijſdem poſitis in ſexta fi-
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            gura, dico quod comparando homolo-
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            gorum differentias prima A B ad ſe-
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            cundam D E minorem proportionem
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            habet quàm differentia A C ad diffe-
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            rentiam D H.</s>
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            <s xml:id="echoid-s1192" xml:space="preserve">Fiat B F ad E H, vt A B ad D
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            E, ergo A F ad D H eſt vt A B ad
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              <note position="left" xlink:label="note-0054-01" xlink:href="note-0054-01a" xml:space="preserve">Lem.3.</note>
            D E, ſed A F minor eſt quam A C,
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            ergo A F ad eandem D H minorem
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            proportionem habet quàm A C: </s>
            <s xml:id="echoid-s1193" xml:space="preserve">& </s>
            <s xml:id="echoid-s1194" xml:space="preserve">
              <lb/>
            propterea A B ad D E minorem pro-
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            portionem habet quàm A C ad D H.</s>
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            <s xml:id="echoid-s1196" xml:space="preserve">Quartò, dico, quod tertia C B ad quartam H E minorem proportionem habet
              <lb/>
              <note position="left" xlink:label="note-0054-02" xlink:href="note-0054-02a" xml:space="preserve">Ibidem.</note>
            quàm differentia A C ad differentiam D H. </s>
            <s xml:id="echoid-s1197" xml:space="preserve">Quoniam ex conſtructione A B ad
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            D E eſt vt F B ad H E, erit F B ad H E, vt A F ad D H; </s>
            <s xml:id="echoid-s1198" xml:space="preserve">ſed C B minor
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            eſt quàm F B, atque A C maior quàm A F, & </s>
            <s xml:id="echoid-s1199" xml:space="preserve">A F ad eandem D H minorem
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            proportionem habet quàm A C; </s>
            <s xml:id="echoid-s1200" xml:space="preserve">igitur C B ad H E eo magis habebit minorem
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            proportionem quàm A C ad D H quæ erant oſtendenda.</s>
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          <head xml:id="echoid-head71" xml:space="preserve">SECTIO TERTIA</head>
          <head xml:id="echoid-head72" xml:space="preserve">Continens VIII. IX. X. Propoſ. Apollonij.</head>
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            <s xml:id="echoid-s1202" xml:space="preserve">SI menſura fuerit maior comparata, dummodo in ellipſi minor
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            ſit medietate axis tranſuerſi, tunc minimus ramorum in ſe-
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            ctionibus eſt, cuius potentialis abſcindit à menſura verſus origi-
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            nem in parabola (8) lineam æqualem comparatæ, in hyperbo-
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            la verò (9) & </s>
            <s xml:id="echoid-s1203" xml:space="preserve">in ellipſi (10.) </s>
            <s xml:id="echoid-s1204" xml:space="preserve">lineam, cuius inuerſæ proportio
              <lb/>
            ad illam eſt, vt proportio figuræ & </s>
            <s xml:id="echoid-s1205" xml:space="preserve">reliqui rami, quo accedunt
              <lb/>
            ad minimum ſunt minores remotioribus; </s>
            <s xml:id="echoid-s1206" xml:space="preserve">& </s>
            <s xml:id="echoid-s1207" xml:space="preserve">quadratum minimæ
              <lb/>
            minus eſt quadrato cuiuslibet rami aſſignati in parabola quidem
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            (8) quadrato exceſſus ſuarum abſciſſarum, & </s>
            <s xml:id="echoid-s1208" xml:space="preserve">in hyperbola (9)
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            & </s>
            <s xml:id="echoid-s1209" xml:space="preserve">ellipſi (10.) </s>
            <s xml:id="echoid-s1210" xml:space="preserve">exemplari applicato ad exceſſum ſuarum inuer-
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            ſarum.</s>
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            <s xml:id="echoid-s1212" xml:space="preserve">SIt itaque ſectio A B C, & </s>
            <s xml:id="echoid-s1213" xml:space="preserve">menſura I C, inclinatus, ſiue tranſuerſa E C,
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              <note position="right" xlink:label="note-0054-03" xlink:href="note-0054-03a" xml:space="preserve">b</note>
            dimidium erecti C G, centrum F, origo I, & </s>
            <s xml:id="echoid-s1214" xml:space="preserve">I H in parabola ſit equa-
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            lis C G, & </s>
            <s xml:id="echoid-s1215" xml:space="preserve">in hyperbola, & </s>
            <s xml:id="echoid-s1216" xml:space="preserve">ellipſi F H ad H I ſit, vt F C dimidium incli-
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            nati, ſeu tranſuerſæ ad C G, dimidium erecti, & </s>
            <s xml:id="echoid-s1217" xml:space="preserve">educta ex H perpendi-
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            culari H N, & </s>
            <s xml:id="echoid-s1218" xml:space="preserve">coniuncta recta N I; </s>
            <s xml:id="echoid-s1219" xml:space="preserve">Dico N I minimum eſſe </s>
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