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-head333" xml:space="preserve">PROPOSITIO VI. & VII.</head>
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            <s xml:id="echoid-s10297" xml:space="preserve">SI in hyperbole, aut ellipſi addantur axi tranſuerſo, vel au-
              <lb/>
              <note position="right" xlink:label="note-0316-01" xlink:href="note-0316-01a" xml:space="preserve">a</note>
            ferantur ab inclinato duæ interceptæ A G, C H ab eius
              <lb/>
            terminis A, C, atque à vertice ſectionis A educatur recta linea
              <lb/>
            A B ad terminum alicuius potentialis B E, & </s>
            <s xml:id="echoid-s10298" xml:space="preserve">per centrum D
              <lb/>
              <figure xlink:label="fig-0316-01" xlink:href="fig-0316-01a" number="365">
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            ducãtur diametri coniugatæ I L, N O, ita vt rectus N O æqui-
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            diſtet ipſi lineæ A B: </s>
            <s xml:id="echoid-s10299" xml:space="preserve">vtiquè proportio figuræ inclinatæ, vel
              <lb/>
            tranſuerſæ coniugatarum, quæ eſt eadem proportioni quadrati
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            I L ad quadratum N O, erit quoquè eadem, quàm habent li-
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            neæ inter incidentiam illius ordinatim applicatæ ad axim, & </s>
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            minos diuidentes duarum interceptarũ, ſcilicet vt H E ad E G.</s>
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            <s xml:id="echoid-s10302" xml:space="preserve">Educamus I M tangentem, & </s>
            <s xml:id="echoid-s10303" xml:space="preserve">I S perpendicularem. </s>
            <s xml:id="echoid-s10304" xml:space="preserve">Et quia A D eſt
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            æqualis D C, & </s>
            <s xml:id="echoid-s10305" xml:space="preserve">A K æqualis K B (eo quod I L cum ſit coniugata N O
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            bifariam diuidit A B) erit C B parallela ipſi I D, & </s>
            <s xml:id="echoid-s10306" xml:space="preserve">propterea M S ad
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            S D, nempè A E ad E C (propter ſimilitudinem triangulorum) eſt vt
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            quadratum I M ad quadratum N D (4. </s>
            <s xml:id="echoid-s10307" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10308" xml:space="preserve">& </s>
            <s xml:id="echoid-s10309" xml:space="preserve">quadratum I D ad qua-
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            dratum I M eſt vt quadratum C B ad quadratum B A (propter ſimilitu-
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            dinem triangulorum); </s>
            <s xml:id="echoid-s10310" xml:space="preserve">ergo proportio quadrati I D ad quadratum N D
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            eſt compoſita ex ratione A E ad E C, & </s>
            <s xml:id="echoid-s10311" xml:space="preserve">ex ratione quadrati C B ad qua-
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            dratum B A; </s>
            <s xml:id="echoid-s10312" xml:space="preserve">ſed proportio quadrati C B ad quadratum B A eſt compo-
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            ſita ex ratione quadrati C B ad C E in E H, & </s>
            <s xml:id="echoid-s10313" xml:space="preserve">ex ratione C E in E H
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            ad A E in E G, & </s>
            <s xml:id="echoid-s10314" xml:space="preserve">ex ratione A E in E G ad quadratum A B; </s>
            <s xml:id="echoid-s10315" xml:space="preserve">eſt vero
              <lb/>
            quadratum C B ad C E in E H, vt C A ad A H (3. </s>
            <s xml:id="echoid-s10316" xml:space="preserve">ex 7.) </s>
            <s xml:id="echoid-s10317" xml:space="preserve">atquè A E
              <lb/>
            in E G ad quadratum A B eſt vt G C ad C A (2. </s>
            <s xml:id="echoid-s10318" xml:space="preserve">ex 7.)</s>
            <s xml:id="echoid-s10319" xml:space="preserve">, & </s>
            <s xml:id="echoid-s10320" xml:space="preserve">proportio
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            C E in E H ad A E in E G, componitur ex ratione C E ad A E, & </s>
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